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Active Forums => QB64 Discussion => Topic started by: NOVARSEG on May 03, 2021, 11:36:08 pm

Title: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 03, 2021, 11:36:08 pm

Looking at vector addition videos example https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vec-add-mag-dir/v/mag-dir-vec-sums

Say 2 objects, with no dimensions, collide at origin 0,0  (heading towards 0, 0)    This is the simple case for 2D collisions.  It is simple because the objects have no dimension and the collision is at 0, 0 .  The vector sum of these 2 objects, gives a resultant vector  (call it the mvector ) that is heading away from 0, 0.   mvector  exists momentarily  since energy is stored if the collision is elastic. For a moment, both objects head in the direction of mVector only for a small distance.

As the objects rebound from the stored energy, mVector determines the resultant direction and velocity of both objects.

The hard part is to calculate the mvector with objects like balls because the angle of collision wont always be parallel to the x axis of the screen

That requires some kind of vector rotation. I'm still working on that.

Any ideas how to do that?

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 04, 2021, 11:54:52 pm

I tried my hand at an abortive attempt at a billiards program without resorting to trig. It had some "issues", and the code is a hot mess, but I imagine a good non-trig way is to obtain a normalized; aka unit, vector of the ball being processed, then use dot product between the balls direction and the strike angle to determine how much of a balls magnitude / speed/ force to apply to another ball. Of course, such a system is not dimensionless, colliding at 0,0

https://www.qb64.org/forum/index.php?topic=2382.msg116030#msg116030

  [ This attachment cannot be displayed inline in 'Print Page' view ]  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 05, 2021, 12:36:14 am

That looks useful.

I've got a program that shows two balls colliding where the strike angle is in the same direction as the cyan colored ball.  I might remove the idea of "dimensionless"  for now because it is an abstract idea.  There is a idea  of "moments" involved because the mvector exits only for a moment.


The resultant direction of the cyan ball should maintain the same direction. This should give a clue on where the mvector is and how to calculate it as a function of strike angle and direction /velocity  of both balls.

run the program and in the top left corner you will see 56 56 that is the  x, y of the strike angle in pixels.  The magnitude is 80 pixels since the ball radius is 40 pixels

If anyone has a pool table at home what happens to the cyan ball does it stop maybe?

Code: QB64: [Select]

1. SCREEN _NEWIMAGE(1024, 768, 32)
2.  
3. DIM originX AS INTEGER
4. originX = _WIDTH / 2
5.  
6. DIM originY AS INTEGER
7. originY = _HEIGHT / 2
8. DIM S AS INTEGER
9. DIM X(1) AS INTEGER 'can't have a fraction of a pixel
10. DIM Y(1) AS INTEGER 'can't have a fraction of a pixel
11. DIM DirY(1) AS INTEGER
12. DIM DirX(1) AS INTEGER
13.  
14. DIM obj AS INTEGER
15.  
16. Y(0) = 672
17. X(0) = originX - (700 - originY)
18.  
19. X(1) = _WIDTH - 40 'originX + (366 - originY)
20. Y(1) = _HEIGHT - 40 '350
21.  
22. DirX(0) = 1
23. DirY(0) = -1
24.  
25. DirX(1) = -1
26. DirY(1) = -1
27.  
28.  
29. DO
30.     _DELAY .003
31.     obj = 0
32.  
33.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 <= 80 AND tog = 0 THEN
34.         tog = 1
35.  
36.         PRINT X(0) - X(1); " "; Y(1) - Y(0)
37.         ' PRINT ABS(3200 - (30 ^ 2)) ^ .5
38.         'PRINT DirX(0) * ABS(3200 + 3200) ^ .5
39.         'PRINT DirY(0) * ABS(3200 - 3200) ^ .5
40.  
41.         PRINT DirX(0) * ABS(3136 + (X(1) - X(0)) ^ 2) ^ .5
42.         PRINT DirY(0) * ABS(3136 - (Y(1) - Y(0)) ^ 2) ^ .5
43.  
44.  
45.  
46.  
47.  
48.         DO
49.             IF INKEY$ <> "" THEN EXIT DO
50.         LOOP
51.  
52.         '_DELAY .6
53.     END IF
54.  
55.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 > 80 AND tog = 1 THEN tog = 0
56.  
57.     r = 0: g = 0: B = 0
58.     FOR S = 1 TO 40
59.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
60.     NEXT
61.  
62.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
63.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
64.     X(obj) = X(obj) + DirX(obj)
65.  
66.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
67.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
68.     Y(obj) = Y(obj) + DirY(obj)
69.  
70.  
71.     r = 255: g = 0: B = 0
72.     FOR S = 1 TO 40
73.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
74.     NEXT
75.  
76.     obj = 1
77.  
78.     r = 0: g = 0: B = 0
79.     FOR S = 1 TO 40
80.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
81.     NEXT
82.  
83.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
84.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
85.     X(obj) = X(obj) + DirX(obj)
86.  
87.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
88.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
89.     Y(obj) = Y(obj) + DirY(obj)
90.  
91.     r = 0: g = 255: B = 255
92.     FOR S = 1 TO 40
93.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
94.     NEXT
95.  
96.     ' _DISPLAY
97.  
98.  
99.  
100.  
101. LOOP
102. END
103.  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 05, 2021, 02:58:08 am

Different ball collision  angles. How is mvector related to collision angle?

Code: QB64: [Select]

1. SCREEN _NEWIMAGE(1024, 768, 32)
2.  
3. DIM originX AS INTEGER
4. originX = _WIDTH / 2
5.  
6. DIM originY AS INTEGER
7. originY = _HEIGHT / 2
8. DIM S AS INTEGER
9. DIM X(1) AS INTEGER 'can't have a fraction of a pixel
10. DIM Y(1) AS INTEGER 'can't have a fraction of a pixel
11. DIM DirY(1) AS INTEGER
12. DIM DirX(1) AS INTEGER
13.  
14. DIM obj AS INTEGER
15. LL1:
16.  
17. IF f1 = 2 THEN f1 = 0
18.  
19. IF f1 = 1 THEN
20.     f1 = 2
21.     Y(0) = 672
22.     X(0) = originX - (700 - originY)
23. END IF
24.  
25. IF f1 = 0 THEN
26.     f1 = 1
27.     Y(0) = 648
28.     X(0) = originX - (700 - originY)
29. END IF
30.  
31. X(1) = _WIDTH - 40
32. Y(1) = _HEIGHT - 40
33.  
34. DirX(0) = 1
35. DirY(0) = -1
36.  
37. DirX(1) = -1
38. DirY(1) = -1
39.  
40. DO
41.     _DELAY .003
42.     obj = 0
43.  
44.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 <= 80 AND tog = 0 THEN
45.         tog = 1
46.  
47.         LOCATE 2, 1: PRINT X(0) - X(1); " X"
48.  
49.         LOCATE 3, 1: PRINT Y(1) - Y(0); " Y"
50.         ' PRINT ABS(3200 - (30 ^ 2)) ^ .5
51.         'PRINT DirX(0) * ABS(3200 + 3200) ^ .5
52.         'PRINT DirY(0) * ABS(3200 - 3200) ^ .5
53.  
54.         '' LOCATE 4, 1: PRINT DirX(0) * ABS(3136 + (X(1) - X(0)) ^ 2) ^ .5
55.         ' LOCATE 5, 1: PRINT DirY(0) * ABS(3136 - (Y(1) - Y(0)) ^ 2) ^ .5
56.  
57.         _DELAY 2
58.         obj = 0
59.         r = 0: g = 0: B = 0
60.         FOR S = 1 TO 40
61.             CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
62.         NEXT
63.  
64.         obj = 1
65.         r = 0: g = 0: B = 0
66.         FOR S = 1 TO 40
67.             CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
68.         NEXT
69.  
70.         GOTO LL1
71.  
72.     END IF
73.  
74.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 > 80 AND tog = 1 THEN tog = 0
75.  
76.     r = 0: g = 0: B = 0
77.     FOR S = 1 TO 40
78.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
79.     NEXT
80.  
81.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
82.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
83.     X(obj) = X(obj) + DirX(obj)
84.  
85.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
86.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
87.     Y(obj) = Y(obj) + DirY(obj)
88.  
89.  
90.     r = 255: g = 0: B = 0
91.     FOR S = 1 TO 40
92.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
93.     NEXT
94.  
95.     obj = 1
96.  
97.     r = 0: g = 0: B = 0
98.     FOR S = 1 TO 40
99.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
100.     NEXT
101.  
102.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
103.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
104.     X(obj) = X(obj) + DirX(obj)
105.  
106.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
107.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
108.     Y(obj) = Y(obj) + DirY(obj)
109.  
110.     r = 0: g = 255: B = 255
111.     FOR S = 1 TO 40
112.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
113.     NEXT
114.  
115. LOOP
116. END
117.  

Another angle added

Code: QB64: [Select]

1. SCREEN _NEWIMAGE(1024, 768, 32)
2.  
3. DIM originX AS INTEGER
4. originX = _WIDTH / 2
5.  
6. DIM originY AS INTEGER
7. originY = _HEIGHT / 2
8. DIM S AS INTEGER
9. DIM X(1) AS INTEGER 'can't have a fraction of a pixel
10. DIM Y(1) AS INTEGER 'can't have a fraction of a pixel
11. DIM DirY(1) AS INTEGER
12. DIM DirX(1) AS INTEGER
13.  
14. DIM obj AS INTEGER
15. LL1:
16.  
17. IF f1 = 3 THEN f1 = 0
18.  
19. IF f1 = 2 THEN
20.     f1 = 3
21.     Y(0) = 728
22.     X(0) = originX - (700 - originY)
23. END IF
24.  
25. 'GOTO LL2
26.  
27.  
28. IF f1 = 1 THEN
29.     f1 = 2
30.     Y(0) = 672
31.     X(0) = originX - (700 - originY)
32. END IF
33.  
34. IF f1 = 0 THEN
35.     f1 = 1
36.     Y(0) = 648
37.     X(0) = originX - (700 - originY)
38. END IF
39. LL2:
40.  
41. X(1) = _WIDTH - 40
42. Y(1) = _HEIGHT - 40
43.  
44. DirX(0) = 1
45. DirY(0) = -1
46.  
47. DirX(1) = -1
48. DirY(1) = -1
49.  
50. DO
51.     _DELAY .003
52.     obj = 0
53.  
54.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 <= 80 AND tog = 0 THEN
55.         tog = 1
56.  
57.         LOCATE 2, 1: PRINT X(0) - X(1); " X"
58.  
59.         LOCATE 3, 1: PRINT Y(1) - Y(0); " Y"
60.         ' PRINT ABS(3200 - (30 ^ 2)) ^ .5
61.         'PRINT DirX(0) * ABS(3200 + 3200) ^ .5
62.         'PRINT DirY(0) * ABS(3200 - 3200) ^ .5
63.  
64.         '' LOCATE 4, 1: PRINT DirX(0) * ABS(3136 + (X(1) - X(0)) ^ 2) ^ .5
65.         ' LOCATE 5, 1: PRINT DirY(0) * ABS(3136 - (Y(1) - Y(0)) ^ 2) ^ .5
66.  
67.         _DELAY 2
68.         obj = 0
69.         r = 0: g = 0: B = 0
70.         FOR S = 1 TO 40
71.             CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
72.         NEXT
73.  
74.         obj = 1
75.         r = 0: g = 0: B = 0
76.         FOR S = 1 TO 40
77.             CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
78.         NEXT
79.  
80.         GOTO LL1
81.  
82.     END IF
83.  
84.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 > 80 AND tog = 1 THEN tog = 0
85.  
86.     r = 0: g = 0: B = 0
87.     FOR S = 1 TO 40
88.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
89.     NEXT
90.  
91.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
92.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
93.     X(obj) = X(obj) + DirX(obj)
94.  
95.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
96.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
97.     Y(obj) = Y(obj) + DirY(obj)
98.  
99.  
100.     r = 255: g = 0: B = 0
101.     FOR S = 1 TO 40
102.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
103.     NEXT
104.  
105.     obj = 1
106.  
107.     r = 0: g = 0: B = 0
108.     FOR S = 1 TO 40
109.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
110.     NEXT
111.  
112.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
113.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
114.     X(obj) = X(obj) + DirX(obj)
115.  
116.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
117.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
118.     Y(obj) = Y(obj) + DirY(obj)
119.  
120.     r = 0: g = 255: B = 255
121.     FOR S = 1 TO 40
122.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
123.     NEXT
124.  
125. LOOP
126. END
127.  

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 05, 2021, 06:59:02 am

referring to the picture I attached, it is showing an exit angle for the striking ball that is orthogonal to the "strike axis" (i.e. the line between the centers of the two balls. The stationary ball moves straight away along that strike axis, mainly because it is not in motion initially. It gets a lot more complex when both balls are moving. At that point I presume that it becomes a function of adding the new (orthogonal) movement vector to the old pre-strike movement vector and modifying the magnitudes of the results according to the dot product result between strike axis and incoming vector. Thereby each ball imparts some of its energy to the other. I was not entirely successful in implementation in my example, as the balls would rather bizarrely swap places with each other or get stuck together on the same spot.

I opted for a Dot Product of unit vector function as it is a relatively straightforward computation and handled all angles reasonably, including head on strikes that would stop a cue ball in its tracks and send the struck ball on its way. Otherwise, I assume that the real world physics are quite beyond my pay grade.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 08, 2021, 03:21:43 am

Vector addition seems to work for simple cases.  I'm running tests on 2 balls with equal mass and velocity using vector addition  and vector rotation.

There are problems with unequal velocities such as when one ball is stationary and the other moving.  Does the stationary ball have a vector?.   So it looks like vector addition is only part of the solution.

'First case: starting vectors
red ball is traveling sqrt(8)x, 0y    towards 0, 0
cyan ball is traveling 2x , -2y        towards 0, 0

let strike angle = 0 (as respects x axis)

At what strike angle do these balls mathematically collide? The vector addition of the ball vectors implies that the bisection angle between the ball vectors is the position of the resultant vector. (mvector)

vector addition gives    sqrt(8) - 2 X  , 2 Y  (mvector)


0 X  , 2.164784 Y   (mvector)

OK  final directions and velocities of both balls.

red ball
sqrt(8)x, 0y   +   0 X  , 2.164784 Y  =  sqrt(8) x ,  2.164784 Y

cyan ball 2x , -2y   +  0 X  , 2.164784 Y =  2x ,  .167484y

Check the math.

According to the literature, the total momentum is preserved. Since the masses are the same then total velocities will do.   The total velocities are red + cyan ball velocity = (8^.5 ) *2

PRINT (4 + .16748 ^ 2) ^ .5 + (8 + 2.16474 ^ 2) ^ .5

= (8^.5 ) *2

Ok the math works out but more tests needed.
**************************
 the above math had some problems

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 09, 2021, 01:29:34 am

2 ball collision.    Both balls equal mass and velocity.

The red ball moves along X axis and the cyan ball moves at a 45 degrees angle.

press any key to run program again.  There are lines that show final direction and velocity.  Not sure if the code is correct.  Does this look OK?

Code: QB64: [Select]

1. SCREEN _NEWIMAGE(1024, 768, 32)
2.  
3. DIM S AS INTEGER
4. DIM X(1) AS INTEGER
5. DIM Y(1) AS INTEGER
6. DIM DirY(1) AS INTEGER
7. DIM DirX(1) AS INTEGER
8.  
9. DIM obj AS INTEGER
10. LL1: CLS
11. Y(0) = _HEIGHT / 2
12. X(0) = 60
13.  
14. X(1) = _WIDTH - 196
15. Y(1) = _HEIGHT - 40
16.  
17. DirX(0) = 1
18. DirY(0) = -1
19.  
20. DirX(1) = -1
21. DirY(1) = -1
22.  
23. DO
24.     _DELAY .003
25.     obj = 0
26.  
27.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 <= 80 AND tog = 0 THEN
28.         tog = 1
29.  
30.         LOCATE 2, 1: PRINT X(0) - X(1); " X"
31.  
32.         LOCATE 3, 1: PRINT Y(1) - Y(0); " Y"
33.         LOCATE 4, 1: PRINT X(0); Y(0)
34.  
35.         rx = -80
36.         ry = 0
37.  
38.         ' rx = 0
39.         ' ry = -80
40.  
41.         ' rx = -(3200 ^ .5) ' * 2
42.         ' ry = (3200 ^ .5) ' / 2
43.  
44.         cx = 3200 ^ .5 '* 2
45.         cy = -(3200 ^ .5) ' / 2
46.  
47.         mvectorx = (0 - rx) - cx
48.         mvectory = (0 - ry) + (0 - cy)
49.         PRINT "mvectorx"; mvectorx
50.         PRINT "mvectory"; mvectory
51.  
52.         'rotates mvector so it is at right angles to X axis
53.         'mvectory = (mvectorx ^ 2 + mvectory ^ 2) ^ .5
54.         ' mvectorx = 0
55.  
56.         rxf = rx + mvectorx
57.         ryf = ry + mvectory
58.         cxf = cx + mvectorx
59.         cyf = cy + mvectory
60.  
61.         PRINT "rxf"; rxf
62.         PRINT "ryf"; ryf
63.         PRINT "cxf"; cxf
64.         PRINT "cyf"; cyf
65.  
66.         rxf = rxf * 3
67.         ryf = ryf * 3
68.         cxf = cxf * 3
69.         cyf = cyf * 3
70.  
71.         LINE (X(0), Y(0))-(X(0) + rxf, Y(0) - ryf)
72.         LINE (X(1), Y(1))-(X(1) + cxf, Y(1) - cyf)
73.  
74.         DO
75.             IF INKEY$ <> "" THEN EXIT DO
76.         LOOP
77.  
78.         obj = 0
79.         r = 0: g = 0: B = 0
80.         FOR S = 1 TO 40
81.             CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
82.         NEXT
83.  
84.         obj = 1
85.         r = 0: g = 0: B = 0
86.         FOR S = 1 TO 40
87.             CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
88.         NEXT
89.  
90.         GOTO LL1
91.  
92.     END IF
93.  
94.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 > 80 AND tog = 1 THEN tog = 0
95.  
96.     r = 0: g = 0: B = 0
97.     FOR S = 1 TO 40
98.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
99.     NEXT
100.  
101.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
102.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
103.     X(obj) = X(obj) + DirX(obj)
104.  
105.     ' IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
106.     ' IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
107.     ' Y(obj) = Y(obj) + DirY(obj)
108.  
109.  
110.     r = 255: g = 0: B = 0
111.     FOR S = 1 TO 40
112.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
113.     NEXT
114.  
115.     obj = 1
116.  
117.     r = 0: g = 0: B = 0
118.     FOR S = 1 TO 40
119.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
120.     NEXT
121.  
122.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
123.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
124.     X(obj) = X(obj) + DirX(obj)
125.  
126.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
127.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
128.     Y(obj) = Y(obj) + DirY(obj)
129.  
130.     r = 0: g = 255: B = 255
131.     FOR S = 1 TO 40
132.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
133.     NEXT
134.  
135. LOOP
136. END
137.  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 09, 2021, 11:48:41 pm

Ball collision code -very simple.  Vector addition only.

Vector rotation not needed in this case.  Have not verified if the collisions are correct but it looks fairly reasonable.

WAIT BUG DETECTED !!!!!!!!!!!!!!!!!!!!!!!!!

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 10, 2021, 03:41:10 am

Nasty bug.  Ball collisions using vector addition only.  Equal velocity and mass.

It looks like the final velocities are unchanged if the original velocities of both balls are the same.

I find it interesting that 99.99 % of internet info about ball collisions is about a moving ball colliding with a stationary ball or wall.  Almost no mention about balls colliding with equal velocity.

I still do not know if the vector addition can describe ball collisions.  Can anyone back this up?

Code: QB64: [Select]

1. SCREEN _NEWIMAGE(1024, 768, 32)
2.  
3. DIM S AS INTEGER
4. DIM X(1) AS INTEGER
5. DIM Y(1) AS INTEGER
6. DIM DirY(1) AS INTEGER
7. DIM DirX(1) AS INTEGER
8.  
9. DIM L AS INTEGER
10. L = 2
11.  
12. DIM obj AS INTEGER
13.  
14. Y(0) = _HEIGHT / 2
15. X(0) = 60
16.  
17. X(1) = _WIDTH - 196
18. Y(1) = _HEIGHT - 40
19.  
20. DirX(0) = 1
21. DirY(0) = 0 '-1
22.  
23. DirX(1) = -1
24. DirY(1) = -1
25. rx = -80
26. ry = 0
27. cx = 3200 ^ .5
28. cy = -(3200 ^ .5)
29.  
30. DO
31.     _DELAY .0015
32.  
33.  
34.     IF (((X(1) - X(0)) ^ 2) + (Y(0) - Y(1)) ^ 2) ^ .5 <= 80 THEN
35.  
36.  
37.         LOCATE 10 + L, 1: PRINT X(0) - X(1); " X"
38.  
39.         LOCATE 11 + L, 1: PRINT Y(1) - Y(0); " Y"
40.  
41.         mvectorx = (0 - rx) + (0 - cx)
42.         mvectory = (0 - ry) + (0 - cy)
43.         LOCATE 12 + L, 1: PRINT "mvectorx"; mvectorx
44.         LOCATE 13 + L, 1: PRINT "mvectory"; mvectory
45.  
46.         rxf = rx + mvectorx
47.         ryf = ry + mvectory
48.         cxf = cx + mvectorx
49.         cyf = cy + mvectory
50.         rx = rxf
51.         ry = -ryf
52.         cx = cxf
53.         cy = -cyf
54.  
55.         LOCATE 14 + L, 1: PRINT "rxf"; rxf; "         "
56.         LOCATE 15 + L, 1: PRINT "ryf"; ryf; "         "
57.         LOCATE 16 + L, 1: PRINT "cxf"; cxf; "         "
58.         LOCATE 17 + L, 1: PRINT "cyf"; cyf; "         "
59.  
60.  
61.         DirX(0) = rxf / 80
62.         DirY(0) = ryf / -80
63.         DirX(1) = cxf / 80
64.         DirY(1) = cyf / -80
65.  
66.         LINE (X(0), Y(0))-(X(0) + rxf * 3, Y(0) - ryf * 3)
67.         LINE (X(1), Y(1))-(X(1) + cxf * 3, Y(1) - cyf * 3)
68.  
69.         _DELAY .5
70.  
71.         obj = 0
72.         r = 0: g = 0: B = 0
73.         FOR S = 1 TO 40
74.             CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
75.         NEXT
76.  
77.         obj = 1
78.         r = 0: g = 0: B = 0
79.         FOR S = 1 TO 40
80.             CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
81.         NEXT
82.  
83.     END IF
84.  
85.     obj = 0
86.  
87.     r = 0: g = 0: B = 0
88.     FOR S = 1 TO 40
89.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
90.     NEXT
91.  
92.     IF X(obj) + 40 = _WIDTH THEN DirX(obj) = -1
93.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
94.  
95.     X(obj) = X(obj) + DirX(obj)
96.  
97.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
98.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
99.  
100.     Y(obj) = Y(obj) + DirY(obj)
101.  
102.  
103.     r = 255: g = 0: B = 0
104.     FOR S = 1 TO 40
105.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
106.     NEXT
107.  
108.     obj = 1
109.  
110.     r = 0: g = 0: B = 0
111.     FOR S = 1 TO 40
112.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
113.     NEXT
114.  
115.     IF X(obj) + 40 >= _WIDTH THEN DirX(obj) = -1
116.     IF X(obj) - 40 = 0 THEN DirX(obj) = 1
117.     X(obj) = X(obj) + DirX(obj)
118.  
119.     IF Y(obj) + 40 = _HEIGHT THEN DirY(obj) = -1
120.     IF Y(obj) - 40 = 0 THEN DirY(obj) = 1
121.     Y(obj) = Y(obj) + DirY(obj)
122.  
123.     r = 0: g = 255: B = 255
124.     FOR S = 1 TO 40
125.         CIRCLE (X(obj), Y(obj)), S, _RGB(r, g, B)
126.     NEXT
127.  
128. LOOP
129. END
130.  

Ok I've been searching the net and there is no examples of 2 ball collisions at the same velocity.  I have no way to verify my results.  Plenty (thousands) of examples of cue balls hitting stationary balls though -sigh

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 10, 2021, 08:41:16 pm

https://www.vobarian.com/collisions/2dcollisions2.pdf

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 11, 2021, 05:11:33 pm

Oh 2 balls same mass and velocity collide dead onto each other is supposed to knock all energy out of each other come to dead stop, right? (Been considering sum of Forces acting on object.)

I think I've been just trading momentums in such circumstance, having them bounce off each other like a off a wall.

Title: Re: 2D ball collisions without trigonometry.
Post by: johnno56 on May 11, 2021, 08:48:50 pm

Trying to get my head around this one.... Same mass. Same Velocity. Assuming they are colliding from directly opposite vectors (head on). The collision would be like hitting a fixed wall. Assuming that both objects can survive the re-percussive force of the collision then both objects should rebound in the opposite direction to their initial vectors. Some energy should be lost and as such reduce the velocities of each object. Of course there are other external influences which have been disregarded... There are a few ways that both objects could come to a dead stop-ish... If both object were not totally solid like steel. Say... plaster. Both objects should shatter. All energy either dissipated or transferred to the fragments. If one object was made of solid copper and the other a mono-pole magnet then both objects would not collide. The magnetic field would be induced into the copper object creating another magnetic field which would repel the magnet. More so as both objects near collision. Both fields opposing the velocities of both objects to the point of reducing momentum to a point of equilibrium.

Or something like that....

Therefore, excluding other external forces, the two spheres should just bounce of each other....

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 11, 2021, 09:22:06 pm

For simplicity sake no other forces, no gravity, no magnetism, no friction, no desire for coffee...

From the paper of OldMoses link https://www.vobarian.com/collisions/2dcollisions2.pdf
v1' = (v1(m1-m2) + 2m2v2)/(m1 + m2)
v2' = (v2(m2-m1) + 2m1v1)/(m1 + m2)

assume for simplicity m1 = m2 = 1 then

v1' = (v1(1-1) + 2v2)/2 = v2 
v2' = (v2(0) + 2v1)/(2) = v1

Ha! they do trade momentums therefore no dead stop which sum of vector forces suggests.

Title: Re: 2D ball collisions without trigonometry.
Post by: johnno56 on May 11, 2021, 09:28:17 pm

WHAT!?!?  No coffee?  Heresy!!!

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 11, 2021, 09:41:45 pm

Quote from: johnno56 on May 11, 2021, 09:28:17 pm

WHAT!?!?  No coffee?  Heresy!!!

I am pretty sure I said no desire for coffee, coffee still exists at least until it gets cyber attacked.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 11, 2021, 09:58:19 pm

For a head on, elastic collision between two moving balls of equal mass and material, I think that trading vector magnitudes in rebound would be appropriate. In lieu of a more complete knowledge of the subject, on my part.

That said, it would be rather rare for two independent balls to be moving on direct, inverted vectors. They're typically going to be striking at different vectors, or be on inverted vectors that are slightly (or grossly) offset. The angle between their travel vector and the line between the ball centers at the point of collision (I'll call it the strike vector) would govern how each shears away from the other.

Most treatises I've seen on the subject give a shear angle that is perpendicular (orthogonal) to the strike vector, although most of those are assuming a stationary target ball, as per the graphic I posted earlier. There are two orthogonals to the strike vector, and one has to control which is used in order for a ball to not deflect to the "inside", which looks rather weird. I reasoned that one would chose the shear orthogonal that would be closest to a projected point of the striking balls original incoming vector. There may be a simpler method that I'm missing.

After that it gets interesting. I normalized the strike vector and the striking balls incoming vector and apply dot product to those to figure out how much force is transferred to the struck ball, while 1 - dot product result would be retained by the striking ball on its new course. That seemed to yield a satisfying look to my eye, but my application had issues with balls blowing through each other and trading places or getting stuck on one another when in tight groups or high relative speeds. I assume they were moving beyond the collision test before it even had a chance to implement. Oh well, back to the drawing board...

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 11, 2021, 10:17:29 pm

Speaking of Dot Product, I call foul! the paper said no Trig but look at how Dot Product is calc'd with COS!
https://www.mathsisfun.com/algebra/vectors-dot-product.html

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 11, 2021, 10:42:28 pm

The easy method of dot product calculation is:

a · b = ax × bx + ay × by

I typically assign a function to it.

Code: QB64: [Select]

1. FUNCTION VecDot (var AS V2, var2 AS V2)
2.     VecDot = var.x * var2.x + var.y * var2.y
3. END FUNCTION 'VecDot
4.  

I have to assume it's much faster than COS in the CPU

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 11, 2021, 10:48:25 pm

Trying to understand the 7 steps and Dot Product is hanging me up.

From Stx notes on vector math here is Dot Product without need of COS(angle between vectors)

Code: QB64: [Select]

1. Function v2DotProduct (A As xyType, B As xyType) 'shadow or projection  if A Dot B = 0 then A , B are perpendicular
2.     v2DotProduct = A.x * B.x + A.y * B.y
3. End Function
4.  

ha I was just going to post this.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 12, 2021, 01:47:45 am

 Working with vector addition using the parallelogram method (what I call the mvector) There are times when this works OK and other times when it don't.  Sometimes the mvector is 0, 0  which is valid for 180 degree collisions with a strike angle of zero but any attempt to rotate 0,  0 to a required vector results in loss of final direction of one of the balls.

Mvector is strange. Sometimes it has no direction or magnitude (0, 0 ) at other times it acts like a real vector.  At other times it points in both directions (or should).

From a code example :  say mvector is  0X,   113.137 Y.  That works fine for the red ball but the cyan ball expects
 0X,   -113.137 Y..     It is possible that mvector can point in opposite directions. I'm not sure if that fits the definitions of a vector.

Title: Re: 2D ball collisions without trigonometry.
Post by: johnno56 on May 12, 2021, 02:39:25 am

Quote from: bplus on May 11, 2021, 09:41:45 pm

I am pretty sure I said no desire for coffee, coffee still exists at least until it gets cyber attacked.

Almost as bad... No 'desire' for coffee... You should have your mouth washed out with soap... Blasphemy! LOL

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 12, 2021, 08:06:04 am

Quote from: NOVARSEG on May 12, 2021, 01:47:45 am

Working with vector addition using the parallelogram method (what I call the mvector) There are times when this works OK and other times when it don't.  Sometimes the mvector is 0, 0  which is valid for 180 degree collisions with a strike angle of zero but any attempt to rotate 0,  0 to a required vector results in loss of final direction of one of the balls.

Mvector is strange. Sometimes it has no direction or magnitude (0, 0 ) at other times it acts like a real vector.  At other times it points in both directions (or should).

From a code example :  say mvector is  0X,   113.137 Y.  That works fine for the red ball but the cyan ball expects
 0X,   -113.137 Y..     It is possible that mvector can point in opposite directions. I'm not sure if that fits the definitions of a vector.

It sounds like your "Mvector" is just like the strike orthogonals that I mention above, which indeed would go in two different directions. One ball would take one "Mvector" and the other ball would take the other. The important part is controlling which takes which. After determining the magnitude of each Mvector, you would then do the vector addition of the balls respective incoming vector and their separate Mvectors. That would conserve some of their original momentum. If the balls were striking head on, then the Dot product calculation would reflect that fact by resulting in an Mvector magnitude of 0, and should result in a swapping of velocities for the balls as Bplus proved earlier. The result would work whether one ball, or both were moving. Isn't math fun....

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 12, 2021, 12:54:45 pm

Quote

Isn't math fun....

It is a total b... until you learn the jargon. I am pretty comfortable with Trig but find physics vectors difficult because I haven't practiced with 100's of exercises in it's terminology. The challenge with Trig and Physics is that Basic uses an upside down Quadrant 1 only graphics system which is not how you learned it in math at school. That, I learned is an artifact of printing with print lines always positive and increasing as you go down the screen a rows and cols system for chars. QB64's Locate row, col is a good example.

I have to say it is fun when it starts producing results for you in computer applications, it's like magic. They say knowledge is power and when math works it is a power alright!

Coffee helps with the practicing ;-)) Maybe something stronger when you've had enough abstract jargon for the day.

2 Ball Collision is really good challenge for any style math.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 12, 2021, 01:06:16 pm

Yeah, the quadrant issue is such a bear that I generally resort to WINDOW to redefine my coordinate system. Then when I do use trig, I have to remain cognizant of the reversals of various SIN/COS/TAN functions with respect to my redefined system.

The only reason that I've been able to fool with vector math is Stx's tutorials, and many hours watching Professor Leonard's calculus videos on Youtube.

I'm toying with doing a little program to demo a Cross product function in action.

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 13, 2021, 09:18:40 am

Quote from: OldMoses on May 10, 2021, 08:41:16 pm

https://www.vobarian.com/collisions/2dcollisions2.pdf

Quote

but my application had issues with balls blowing through each other and trading places or getting stuck on one another when in tight groups or high relative speeds.

Last night I coded the whole paper step by step. The code passes the head on test but I am getting balls sticking together also. I will recheck code today and show. Meanwhile I did get a JB by tsh73 port using vectors working fine and much simpler than paper. I will show that one later too. I want to set up 2 more special cases other than Head on ones where 2 balls travel nearly parallel but converging paths and see their bump and reflection then with 2 balls at 90 degree collision and se that reflection.

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 13, 2021, 04:29:04 pm

OK here is first vector code I got working for 2 or more ball collisions by barrowing from tsh73 at JB forum. He was working study for an app for pin ball and one ball was always moving and the other was stationary circle, so I adapted to 2 moving balls and may have oversimplified. Anyway it can handle 20 balls no sticking:

All the special case experiments work fine with expected results.

Code: QB64: [Select]

1. Option _Explicit
2. _Title "tsh73 from JB: 2 Ball Collision with Vectors,  r will restart a test" 'B+ 2021-05-13
3. ' This is tsh73 code for collision though he was doing stationary and moving, I made mod for both moving.
4. ' The vector functions are modifications of tsh73 JB code converted to QB64 by me.
5. ' earlier code 2 Ball Collision with Vectors by Arrow Addition ' B+ 2021-05-10
6. ' 2021-05-10  fixed arrow so points from base x,y To angle
7. ' from Collision Study #4   press spacebar to toggle tracer" ' b+ 2021-05-09 by bplus
8.  
9. ' !!!!!!!!!!!!!!!! Adjust Ball according to experiment (just after restart: line label) 2 is always good!
10.  
11. 'Const Balls = 2 '<<<<<<<<< change this to 2 to test special case setups: head on, parallel and perpendicular
12. Const Balls = 6 '<<<<<<<<<  no more than 20! because have to start all balls not overlapping any other
13.  
14.  
15. Const Xmax = 600 ' screen width
16. Const Ymax = 600 ' screen height
17. Const R = 50 '     balls radii
18. Const R22 = R * R * 4 ' save some time with (2 * R) * (2 * R)
19.  
20. Const MV_Speed = 45 ' magnitude of Force Arrow say it's constant for simplicity sake
21. Type Ball
22.     As Long x, y
23.     As Double dx, dy, a ' dx, dy = change x, y axis
24.     As _Unsigned Long colr
25. End Type
26.  
27. Randomize Timer
28. Screen _NewImage(Xmax, Ymax, 32)
29. _Delay .25
30. _ScreenMove _Middle
31. ' these can be static as no balls added or subtracted in closed system
32. Dim As Ball b(1 To Balls), nf(1 To Balls) ' b() is current frame balls data , nf( ) is for next frame balls data
33. Dim As Long clrMode, i, j, rdm
34. b(1).colr = &HFFFF0000 'red ball 1 is red
35. b(2).colr = &HFF0000FF 'blue ball 2 is blue
36. clrMode = 1
37. Dim v1$, v2$, dv1$, dv2$, dv1u$, dv2u$, norm$ 'vectors
38.  
39. restart:
40. 'horizontal collisions  Head On
41. 'b(1).dx = 5
42. 'b(1).dy = 0 ' b1 is just moving on x axis to the right at 5 pixels per frame
43. 'b(2).dx = -5
44. 'b(2).dy = 0 ' b2 is just moving on x axis to the left at 5 pixels per frame
45. 'b(1).x = 300 - 5 * b(1).dx - R ' in 5 frames b1 will meet b2  kiss at center of screen
46. 'b(1).y = 300
47. 'b(2).x = 300 - 5 * b(2).dx + R ' in 5 frames b1 will meet b2  kiss at center of screen
48. 'b(2).y = 300
49.  
50. 'vertical collisions  Head On
51. 'b(1).dy = 5
52. 'b(1).dx = 0 ' b1 is just moving on x axis to the right at 5 pixels per frame
53. 'b(2).dy = -5
54. 'b(2).dx = 0 ' b2 is just moving on x axis to the left at 5 pixels per frame
55. 'b(1).y = 300 - 5 * b(1).dy - R ' in 5 frames b1 will meet b2  kiss at center of screen
56. 'b(1).x = 300
57. 'b(2).y = 300 - 5 * b(2).dy + R ' in 5 frames b1 will meet b2  kiss at center of screen
58. 'b(2).x = 300
59.  
60. ' 45 & 135 collsions   Head On
61. 'b(1).dy = 5
62. 'b(1).dx = 5 ' b1 is just moving on x axis to the right at 5 pixels per frame
63. 'b(2).dy = -5
64. 'b(2).dx = -5 ' b2 is just moving on x axis to the left at 5 pixels per frame
65. 'b(1).y = 300 - 5 * b(1).dy - R ' in 5 frames b1 will meet b2  kiss at center of screen
66. 'b(1).x = 300 - 5 * b(1).dx - R
67. 'b(2).y = 300 - 5 * b(2).dy + R ' in 5 frames b1 will meet b2  kiss at center of screen
68. 'b(2).x = 300 - 5 * b(2).dx + R
69.  
70. ' Parallel and converging paths
71. 'b(1).dy = -6
72. 'b(1).dx = 1 ' b1 is just moving on x axis to the right at 5 pixels per frame
73. 'b(2).dy = -6
74. 'b(2).dx = -1 ' b2 is just moving on x axis to the left at 5 pixels per frame
75. 'b(1).y = Ymax - R ' in 5 frames b1 will meet b2  kiss at center of screen
76. 'b(1).x = 300 - 20 * b(1).dx - R
77. 'b(2).y = Ymax - R ' in 5 frames b1 will meet b2  kiss at center of screen
78. 'b(2).x = 300 - 20 * b(2).dx + R
79.  
80. ' Perpendicular and 90 degree collision   should be just before mid screen
81. 'b(1).dy = 0
82. 'b(1).dx = 5
83. 'b(2).dy = -5
84. 'b(2).dx = 0
85. 'b(1).y = 300
86. 'b(1).x = R
87. 'b(2).y = Ymax - R
88. 'b(2).x = 300
89.  
90. ' Random assignments    (comment this block for special case 2 ball experiments  and set balls to 2 !)  ==============
91. For i = 1 To Balls
92.     tryAgain:
93.     Print i
94.     b(i).x = rand&(R, Xmax - R)
95.     b(i).y = rand&(R, Ymax - R)
96.     For j = 1 To i - 1
97.         If _Hypot(b(i).x - b(j).x, b(i).y - b(j).y) < R + R Then GoTo tryAgain
98.     Next
99.     b(i).dx = (Rnd * 4 + 1) * rdir
100.     b(i).dy = (Rnd * 4 + 1) * rdir
101.     rdm = rand&(1, 7)
102.     If rdm < 1 Or rdm > 7 Then Beep
103.     Select Case rdm
104.         Case 1: b(i).colr = _RGB32(Rnd * 200 + 55, 0, 0)
105.         Case 2: b(i).colr = _RGB32(0, Rnd * 100 + 55, 0)
106.         Case 3: b(i).colr = _RGB32(0, 0, Rnd * 200 + 55)
107.         Case 4: b(i).colr = &HFFFF6600
108.         Case 5: b(i).colr = &HFFFF0088
109.         Case 6: b(i).colr = &HFF00FF88
110.         Case 7: b(i).colr = _RGB32(Rnd * 200 + 55, Rnd * 200 + 55, Rnd * 200 + 55)
111.     End Select
112. Next
113. '====================================================================================================================
114.  
115. While _KeyDown(27) = 0
116.     Dim k$
117.     k$ = InKey$
118.     If Len(k$) Then
119.         If Asc(k$) = 32 Then clrMode = -1 * clrMode
120.         If Asc(k$) = 27 And Len(k$) = 1 Then End
121.         If k$ = "r" Then GoTo restart
122.     End If
123.     If clrMode > 0 Then Cls
124.     Circle (300, 300), 2
125.     For i = 1 To Balls ' draw balls then  update for next frame
126.  
127.         ' this just draw the balls with arrows pointing to their headings
128.         Circle (b(i).x, b(i).y), R, b(i).colr
129.         b(i).a = _Atan2(b(i).dy, b(i).dx)
130.         ArrowTo b(i).x, b(i).y, b(i).a, MV_Speed, &HFFFFFF00
131.         ' debug
132.         '_PrintString (b(i).x - 8, b(i).y - 8), _Trim$(Right$("00" + Str$(i), 2)) 'all the balls weren't getting colored
133.  
134.         ' check for collision
135.         Dim cd, saveJ
136.         cd = 100000: saveJ = 0
137.         For j = 1 To Balls 'find deepest collision in case more than one we want earliest = deepest penetration
138.             If i <> j Then
139.                 Dim dx, dy
140.                 dx = b(i).x - b(j).x: dy = b(i).y - b(j).y
141.                 If dx * dx + dy * dy <= R22 Then ' collision but is it first or deepest collision
142.                     If R22 - dx * dx + dy * dy < cd Then cd = R22 - dx * dx + dy * dy: saveJ = j
143.                 End If
144.             End If
145.         Next
146.         If cd <> 100000 Then ' found collision change ball i dx, dy   calc new course for ball i
147.  
148.             ''reflection  from circle  using Vectors  from JB, thanks tsh73
149.             v1$ = vect$(b(i).x, b(i).y) ' circle i
150.             v2$ = vect$(b(saveJ).x, b(saveJ).y) ' the other circle j
151.             dv1$ = vect$(b(i).dx, b(i).dy) ' change in velocity vector
152.             dv2$ = vect$(b(saveJ).dx, b(saveJ).dy)
153.             dv1u$ = vectUnit$(dv1$) '1 pixel
154.             dv2u$ = vectUnit$(dv2$)
155.             'Print dv$, cv$, dv0$   ' check on things
156.             '_Display
157.             'Sleep
158.             Do ' this should back up the balls to kiss point thanks tsh73
159.                 v1$ = vectSub$(v1$, dv1u$)
160.                 v2$ = vectSub(v2$, dv2u$)
161.             Loop While vectLen(vectSub$(v1$, v2$)) < R + R 'back up our circle i to point on kiss
162.             ''now, get reflection
163.             ''radius to radius, norm is
164.             norm$ = vectSub$(v1$, v2$)
165.             dv1$ = vectSub$(vectNorm$(dv1$, norm$), vectTangent$(dv1$, norm$)) 'to this
166.  
167.             ' store in next frame array
168.             nf(i).dx = vectX(dv1$)
169.             nf(i).dy = vectY(dv1$)
170.  
171.         Else ' no collision
172.             nf(i).dx = b(i).dx
173.             nf(i).dy = b(i).dy
174.         End If
175.         'update location of ball next frame
176.         nf(i).x = b(i).x + nf(i).dx
177.         nf(i).y = b(i).y + nf(i).dy
178.  
179.         ' check in bounds next frame
180.         If nf(i).x < R Then nf(i).dx = -nf(i).dx: nf(i).x = R
181.         If nf(i).x > Xmax - R Then nf(i).dx = -nf(i).dx: nf(i).x = Xmax - R
182.         If nf(i).y < R Then nf(i).dy = -nf(i).dy: nf(i).y = R
183.         If nf(i).y > Ymax - R Then nf(i).dy = -nf(i).dy: nf(i).y = Ymax - R
184.     Next
185.  
186.     ''now that we've gone through all old locations update b() with nf() data
187.     For i = 1 To Balls
188.         b(i).x = nf(i).x: b(i).y = nf(i).y
189.         b(i).dx = nf(i).dx: b(i).dy = nf(i).dy
190.     Next
191.     ' next frame ready to draw
192.     _Display
193.     _Limit 30
194. Wend
195. 'Cls   ' debug why aren't all the balls getting colored
196. 'For i = 1 To Balls
197. '    Print i, b(i).colr
198. 'Next
199.  
200. Function rand& (lo As Long, hi As Long) ' fixed?
201.     rand& = Int(Rnd * (hi - lo) + 1) + lo
202. End Function
203.  
204. Function rdir ()
205.     If Rnd < .5 Then rdir = -1 Else rdir = 1
206. End Function
207.  
208. Sub ArrowTo (BaseX As Long, BaseY As Long, rAngle As Double, lngth As Long, colr As _Unsigned Long)
209.     Dim As Long x1, y1, x2, y2, x3, y3
210.     x1 = BaseX + lngth * Cos(rAngle)
211.     y1 = BaseY + lngth * Sin(rAngle)
212.     x2 = BaseX + .8 * lngth * Cos(rAngle - _Pi(.05))
213.     y2 = BaseY + .8 * lngth * Sin(rAngle - _Pi(.05))
214.     x3 = BaseX + .8 * lngth * Cos(rAngle + _Pi(.05))
215.     y3 = BaseY + .8 * lngth * Sin(rAngle + _Pi(.05))
216.     Line (BaseX, BaseY)-(x1, y1), colr
217.     Line (x1, y1)-(x2, y2), colr
218.     Line (x1, y1)-(x3, y3), colr
219. End Sub
220.  
221. ' convert some vector functions from JB, turns out much easier to use string functions to pass vectors
222. ' than using SUBs to do vector calcs
223.  
224. Function vect$ (x, y) ' convert x, y to string for passing vectors with Functions
225.     vect$ = _Trim$(Str$(x)) + "," + _Trim$(Str$(y))
226. End Function
227.  
228. Function vectX (v$)
229.     vectX = Val(LeftOf$(v$, ","))
230. End Function
231.  
232. Function vectY (v$)
233.     vectY = Val(RightOf$(v$, ","))
234. End Function
235.  
236. Function vectLen (v$)
237.     Dim x, y
238.     x = Val(LeftOf$(v$, ","))
239.     y = Val(RightOf$(v$, ","))
240.     vectLen = Sqr(x * x + y * y)
241. End Function
242.  
243. Function vectUnit$ (v$)
244.     Dim x, y, vl
245.     x = Val(LeftOf$(v$, ","))
246.     y = Val(RightOf$(v$, ","))
247.     vl = Sqr(x * x + y * y)
248.     vectUnit$ = vect$(x / vl, y / vl)
249. End Function
250.  
251. Function vectAdd$ (v1$, v2$)
252.     Dim x1, y1, x2, y2
253.     x1 = Val(LeftOf$(v1$, ","))
254.     y1 = Val(RightOf$(v1$, ","))
255.     x2 = Val(LeftOf$(v2$, ","))
256.     y2 = Val(RightOf$(v2$, ","))
257.     vectAdd$ = vect$(x1 + x2, y1 + y2)
258. End Function
259.  
260. Function vectSub$ (v1$, v2$)
261.     Dim x1, y1, x2, y2
262.     x1 = Val(LeftOf$(v1$, ","))
263.     y1 = Val(RightOf$(v1$, ","))
264.     x2 = Val(LeftOf$(v2$, ","))
265.     y2 = Val(RightOf$(v2$, ","))
266.     vectSub$ = vect$(x1 - x2, y1 - y2)
267. End Function
268.  
269. Function vectDotProduct (v1$, v2$)
270.     Dim x1, y1, x2, y2
271.     x1 = Val(LeftOf$(v1$, ","))
272.     y1 = Val(RightOf$(v1$, ","))
273.     x2 = Val(LeftOf$(v2$, ","))
274.     y2 = Val(RightOf$(v2$, ","))
275.     vectDotProduct = x1 * x2 + y1 * y2
276. End Function
277.  
278. Function vectScale$ (a, v$) 'a * vector v$
279.     Dim x, y
280.     x = Val(LeftOf$(v$, ","))
281.     y = Val(RightOf$(v$, ","))
282.     vectScale$ = vect$(a * x, a * y)
283. End Function
284.  
285. Function vectTangent$ (v$, base$)
286.     Dim n$
287.     n$ = vectUnit$(base$)
288.     vectTangent$ = vectScale$(vectDotProduct(n$, v$), n$)
289. End Function
290.  
291. Function vectNorm$ (v$, base$)
292.     vectNorm$ = vectSub$(v$, vectTangent$(v$, base$))
293. End Function
294.  
295. ' update these 2 in case of$ is not found! 2021-02-13
296. Function LeftOf$ (source$, of$)
297.     If InStr(source$, of$) > 0 Then LeftOf$ = Mid$(source$, 1, InStr(source$, of$) - 1) Else LeftOf$ = source$
298. End Function
299.  
300. ' update these 2 in case of$ is not found! 2021-02-13
301. Function RightOf$ (source$, of$)
302.     If InStr(source$, of$) > 0 Then RightOf$ = Mid$(source$, InStr(source$, of$) + Len(of$)) Else RightOf$ = ""
303. End Function
304.  
305.  
306.  

Title: Re: 2D ball collisions without trigonometry.
Post by: justsomeguy on May 13, 2021, 04:42:37 pm

Nice. Seems to work pretty good. Occasionally two balls would get stuck on each other, but awesome progress. Physics is hard! 

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 13, 2021, 04:59:29 pm

Oh man you are getting sticky balls with that code! Well this next is much more fragile keep number of balls low and not too bad, it does really interesting things with ball speeds!

This is my attempt to follow the paper OldMoses gave link to, see ref in code:

Code: QB64: [Select]

1. Option _Explicit
2. _Title "From Paper 2 Ball Collision with Vectors,  press r to restart" 'B+ 2021-05-13
3. ' Collision tests based on Paper       https://www.vobarian.com/collisions/2dcollisions2.pdf
4. ' The vector functions are modifications of tsh73 JB code converted to QB64 by me.
5. ' earlier code 2 Ball Collision with Vectors by Arrow Addition ' B+ 2021-05-10
6. ' 2021-05-10  fixed arrow so points from base x,y To angle
7. ' from Collision Study #4   press spacebar to toggle tracer" ' b+ 2021-05-09
8.  
9. ' !!!!!!!!!!!!!!!! Adjust Ball according to experiment 2 is always good
10.  
11. 'Const Balls = 2 '<<<<<<<<< change this to 2 to test special case setups: head on, parallel and perpendicular
12. Const Balls = 5 '<<<<<<<<< the more the balls the more problems pop up for Random Numbers experiments
13. '                            no more than 20! because have to start all balls not overlapping any other
14.  
15.  
16. Const Xmax = 600 ' screen width
17. Const Ymax = 600 ' screen height
18. Const R = 50 '     balls radii
19. Const R22 = R * R * 4 ' save some time with (2 * R) * (2 * R)
20.  
21. Const MV_Speed = 45 ' magnitude of Force Arrow say it's constant for simplicity sake
22. Type Ball
23.     As Long x, y
24.     As Double dx, dy, a ' dx, dy = change x, y axis
25.     As _Unsigned Long colr
26. End Type
27.  
28. Randomize Timer
29. Screen _NewImage(Xmax, Ymax, 32)
30. _Delay .25
31. _ScreenMove _Middle
32. ' these can be static as no balls added or subtracted in closed system
33. Dim As Ball b(1 To Balls), nf(1 To Balls) ' b() is current frame balls data , nf( ) is for next frame balls data
34. Dim As Long clrMode, i, j, rdm
35. b(1).colr = &HFFFF0000 'red ball 1 is red
36. b(2).colr = &HFF0000FF 'blue ball 2 is blue
37. clrMode = 1
38. Dim v1$, v2$, dv1$, dv2$, dv1u$, dv2u$, norm$, unitNorm$, unitTan$ 'vectors
39. Dim vp1n$, vp1t$, vp2n$, vp2t$ ' post collision vectors
40. Dim As Double v1n, v1t, v2n, v2t ' dot products
41. Dim As Double vp1n, vp1t, vp2n, vp2t ' post collision dot products
42. restart:
43. 'horizontal collisions  Head On
44. 'b(1).dx = 5
45. 'b(1).dy = 0 ' b1 is just moving on x axis to the right at 5 pixels per frame
46. 'b(2).dx = -5
47. 'b(2).dy = 0 ' b2 is just moving on x axis to the left at 5 pixels per frame
48. 'b(1).x = 300 - 5 * b(1).dx - R ' in 5 frames b1 will meet b2  kiss at center of screen
49. 'b(1).y = 300
50. 'b(2).x = 300 - 5 * b(2).dx + R ' in 5 frames b1 will meet b2  kiss at center of screen
51. 'b(2).y = 300
52.  
53. 'vertical collisions  Head On
54. 'b(1).dy = 5
55. 'b(1).dx = 0 ' b1 is just moving on x axis to the right at 5 pixels per frame
56. 'b(2).dy = -5
57. 'b(2).dx = 0 ' b2 is just moving on x axis to the left at 5 pixels per frame
58. 'b(1).y = 300 - 5 * b(1).dy - R ' in 5 frames b1 will meet b2  kiss at center of screen
59. 'b(1).x = 300
60. 'b(2).y = 300 - 5 * b(2).dy + R ' in 5 frames b1 will meet b2  kiss at center of screen
61. 'b(2).x = 300
62.  
63. ' 45 & 135 collsions   Head On
64. 'b(1).dy = 5
65. 'b(1).dx = 5 ' b1 is just moving on x axis to the right at 5 pixels per frame
66. 'b(2).dy = -5
67. 'b(2).dx = -5 ' b2 is just moving on x axis to the left at 5 pixels per frame
68. 'b(1).y = 300 - 5 * b(1).dy - R ' in 5 frames b1 will meet b2  kiss at center of screen
69. 'b(1).x = 300 - 5 * b(1).dx - R
70. 'b(2).y = 300 - 5 * b(2).dy + R ' in 5 frames b1 will meet b2  kiss at center of screen
71. 'b(2).x = 300 - 5 * b(2).dx + R
72.  
73. ' Parallel and converging paths
74. 'b(1).dy = -6
75. 'b(1).dx = 1 ' b1 is just moving on x axis to the right at 5 pixels per frame
76. 'b(2).dy = -6
77. 'b(2).dx = -1 ' b2 is just moving on x axis to the left at 5 pixels per frame
78. 'b(1).y = Ymax - R ' in 5 frames b1 will meet b2  kiss at center of screen
79. 'b(1).x = 300 - 20 * b(1).dx - R
80. 'b(2).y = Ymax - R ' in 5 frames b1 will meet b2  kiss at center of screen
81. 'b(2).x = 300 - 20 * b(2).dx + R
82.  
83. ' Perpendicular and 90 degree collision   should be just before mid screen
84. 'b(1).dy = 0
85. 'b(1).dx = 5
86. 'b(2).dy = -5
87. 'b(2).dx = 0
88. 'b(1).y = 300
89. 'b(1).x = R
90. 'b(2).y = Ymax - R
91. 'b(2).x = 300
92.  
93. ' random assignments
94. For i = 1 To Balls
95.     tryAgain:
96.     Print i
97.     b(i).x = rand&(R, Xmax - R)
98.     b(i).y = rand&(R, Ymax - R)
99.     For j = 1 To i - 1
100.         If _Hypot(b(i).x - b(j).x, b(i).y - b(j).y) < R + R Then GoTo tryAgain
101.     Next
102.     b(i).dx = (Rnd * 4 + 1) * rdir
103.     b(i).dy = (Rnd * 4 + 1) * rdir
104.     rdm = rand&(1, 7)
105.     If rdm < 1 Or rdm > 7 Then Beep
106.     Select Case rdm
107.         Case 1: b(i).colr = _RGB32(Rnd * 200 + 55, 0, 0)
108.         Case 2: b(i).colr = _RGB32(0, Rnd * 100 + 55, 0)
109.         Case 3: b(i).colr = _RGB32(0, 0, Rnd * 200 + 55)
110.         Case 4: b(i).colr = &HFFFF6600
111.         Case 5: b(i).colr = &HFFFF0088
112.         Case 6: b(i).colr = &HFF00FF88
113.         Case 7: b(i).colr = _RGB32(Rnd * 200 + 55, Rnd * 200 + 55, Rnd * 200 + 55)
114.     End Select
115. Next
116.  
117. While _KeyDown(27) = 0
118.     Dim k$
119.     k$ = InKey$
120.     If Len(k$) Then
121.         If Asc(k$) = 32 Then clrMode = -1 * clrMode
122.         If Asc(k$) = 27 And Len(k$) = 1 Then End
123.         If k$ = "r" Then GoTo restart
124.     End If
125.     If clrMode > 0 Then Cls
126.     Circle (300, 300), 2
127.     For i = 1 To Balls ' draw balls then  update for next frame
128.  
129.         ' this just draw the balls with arrows pointing to their headings
130.         Circle (b(i).x, b(i).y), R, b(i).colr
131.         b(i).a = _Atan2(b(i).dy, b(i).dx)
132.         ArrowTo b(i).x, b(i).y, b(i).a, MV_Speed, &HFFFFFF00
133.         ' debug
134.         '_PrintString (b(i).x - 8, b(i).y - 8), _Trim$(Right$("00" + Str$(i), 2)) 'all the balls weren't getting colored
135.  
136.         ' check for collision
137.         Dim cd, saveJ
138.         cd = 100000: saveJ = 0
139.         For j = 1 To Balls 'find deepest collision in case more than one we want earliest = deepest penetration
140.             If i <> j Then
141.                 Dim dx, dy
142.                 dx = b(i).x - b(j).x: dy = b(i).y - b(j).y
143.                 If dx * dx + dy * dy <= R22 Then ' collision but is it first or deepest collision
144.                     If R22 - dx * dx + dy * dy < cd Then cd = R22 - dx * dx + dy * dy: saveJ = j
145.                 End If
146.             End If
147.         Next
148.         If cd <> 100000 Then ' found collision change ball i dx, dy   calc new course for ball i
149.  
150.             ''reflection  from circle  using Vectors  from JB, thanks tsh73
151.             v1$ = vect$(b(i).x, b(i).y) ' circle i
152.             v2$ = vect$(b(saveJ).x, b(saveJ).y) ' the other circle j
153.             dv1$ = vect$(b(i).dx, b(i).dy) ' change in velocity vector
154.             dv2$ = vect$(b(saveJ).dx, b(saveJ).dy)
155.             dv1u$ = vectUnit$(dv1$) '1 pixel
156.             dv2u$ = vectUnit$(dv2$)
157.             'Print dv$, cv$, dv0$   ' check on things
158.             '_Display
159.             'Sleep
160.             Do ' this should back up the balls to kiss point thanks tsh73
161.                 v1$ = vectSub$(v1$, dv1u$)
162.                 v2$ = vectSub(v2$, dv2u$)
163.             Loop While vectLen(vectSub$(v1$, v2$)) < R + R 'back up our circle i to point on kiss
164.             ''now, get reflection speed
165.             ''radius to radius, norm is
166.             norm$ = vectSub$(v1$, v2$) ' this to this worked without all between from that collision paper
167.  
168.             '  step 1 unit norm and tangent
169.             unitNorm$ = vectUnit$(norm$)
170.             unitTan$ = vect$(-vectY(unitNorm$), vectX(unitNorm$))
171.             ' step 2 v$ and cv$ are 2 ball vectors (locations)  done already
172.             ' step 3 dot products before collision projecting onto normal and tangent vectors
173.             v1n = vectDotProduct(dv1$, unitNorm$)
174.             v1t = vectDotProduct(dv1$, unitTan$)
175.             v2n = vectDotProduct(dv2$, unitNorm$)
176.             v2t = vectDotProduct(dv2$, unitTan$)
177.             ' step 4 simplest  post collision dot products
178.             vp1t = v1t
179.             vp2t = v2t
180.             ' step 5  simplified by m = 1 for both balls just swap the numbers
181.             vp1n = v2n
182.             vp2n = v1n
183.             ' step 6  vp vectors mult the n, t numbers by unit vectors
184.             vp1n$ = vectScale$(vp1n, unitNorm$)
185.             vp1t$ = vectScale$(vp1t, unitTan$)
186.             vp2n$ = vectScale$(vp2n, unitNorm$)
187.             vp2t$ = vectScale$(vp2t, unitTan$)
188.             'step  7  add the 2 vectors n and t
189.             dv1$ = vectAdd$(vp1n$, vp1t$)
190.  
191.             ' to this  now just switch tangent and norm
192.             'dv1$ = vectSub$(vectNorm$(dv1$, norm$), vectTangent$(dv1$, norm$)) 'to this
193.  
194.             ' store in next frame array
195.             nf(i).dx = vectX(dv1$)
196.             nf(i).dy = vectY(dv1$)
197.  
198.         Else ' no collision
199.             nf(i).dx = b(i).dx
200.             nf(i).dy = b(i).dy
201.         End If
202.         'update location of ball next frame
203.         nf(i).x = b(i).x + nf(i).dx
204.         nf(i).y = b(i).y + nf(i).dy
205.  
206.         ' check in bounds next frame
207.         If nf(i).x < R Then nf(i).dx = -nf(i).dx: nf(i).x = R
208.         If nf(i).x > Xmax - R Then nf(i).dx = -nf(i).dx: nf(i).x = Xmax - R
209.         If nf(i).y < R Then nf(i).dy = -nf(i).dy: nf(i).y = R
210.         If nf(i).y > Ymax - R Then nf(i).dy = -nf(i).dy: nf(i).y = Ymax - R
211.     Next
212.  
213.     ''now that we've gone through all old locations update b() with nf() data
214.     For i = 1 To Balls
215.         b(i).x = nf(i).x: b(i).y = nf(i).y
216.         b(i).dx = nf(i).dx: b(i).dy = nf(i).dy
217.     Next
218.     ' next frame ready to draw
219.     _Display
220.     _Limit 30
221. Wend
222. 'Cls   ' debug why aren't all the balls getting colored
223. 'For i = 1 To Balls
224. '    Print i, b(i).colr
225. 'Next
226.  
227.  
228. Function rand& (lo As Long, hi As Long) ' fixed?
229.     rand& = Int(Rnd * (hi - lo) + 1) + lo
230. End Function
231.  
232. Function rdir ()
233.     If Rnd < .5 Then rdir = -1 Else rdir = 1
234. End Function
235.  
236.  
237.  
238. Sub ArrowTo (BaseX As Long, BaseY As Long, rAngle As Double, lngth As Long, colr As _Unsigned Long)
239.     Dim As Long x1, y1, x2, y2, x3, y3
240.     x1 = BaseX + lngth * Cos(rAngle)
241.     y1 = BaseY + lngth * Sin(rAngle)
242.     x2 = BaseX + .8 * lngth * Cos(rAngle - _Pi(.05))
243.     y2 = BaseY + .8 * lngth * Sin(rAngle - _Pi(.05))
244.     x3 = BaseX + .8 * lngth * Cos(rAngle + _Pi(.05))
245.     y3 = BaseY + .8 * lngth * Sin(rAngle + _Pi(.05))
246.     Line (BaseX, BaseY)-(x1, y1), colr
247.     Line (x1, y1)-(x2, y2), colr
248.     Line (x1, y1)-(x3, y3), colr
249. End Sub
250.  
251. ' convert some vector functions from JB, turns out much easier to use string functions to pass vectors
252. ' than using SUBs to do vector calcs
253.  
254. Function vect$ (x, y) ' convert x, y to string for passing vectors with Functions
255.     vect$ = _Trim$(Str$(x)) + "," + _Trim$(Str$(y))
256. End Function
257.  
258. Function vectX (v$)
259.     vectX = Val(LeftOf$(v$, ","))
260. End Function
261.  
262. Function vectY (v$)
263.     vectY = Val(RightOf$(v$, ","))
264. End Function
265.  
266. Function vectLen (v$)
267.     Dim x, y
268.     x = Val(LeftOf$(v$, ","))
269.     y = Val(RightOf$(v$, ","))
270.     vectLen = Sqr(x * x + y * y)
271. End Function
272.  
273. Function vectUnit$ (v$)
274.     Dim x, y, vl
275.     x = Val(LeftOf$(v$, ","))
276.     y = Val(RightOf$(v$, ","))
277.     vl = Sqr(x * x + y * y)
278.     vectUnit$ = vect$(x / vl, y / vl)
279. End Function
280.  
281. Function vectAdd$ (v1$, v2$)
282.     Dim x1, y1, x2, y2
283.     x1 = Val(LeftOf$(v1$, ","))
284.     y1 = Val(RightOf$(v1$, ","))
285.     x2 = Val(LeftOf$(v2$, ","))
286.     y2 = Val(RightOf$(v2$, ","))
287.     vectAdd$ = vect$(x1 + x2, y1 + y2)
288. End Function
289.  
290. Function vectSub$ (v1$, v2$)
291.     Dim x1, y1, x2, y2
292.     x1 = Val(LeftOf$(v1$, ","))
293.     y1 = Val(RightOf$(v1$, ","))
294.     x2 = Val(LeftOf$(v2$, ","))
295.     y2 = Val(RightOf$(v2$, ","))
296.     vectSub$ = vect$(x1 - x2, y1 - y2)
297. End Function
298.  
299. Function vectDotProduct (v1$, v2$)
300.     Dim x1, y1, x2, y2
301.     x1 = Val(LeftOf$(v1$, ","))
302.     y1 = Val(RightOf$(v1$, ","))
303.     x2 = Val(LeftOf$(v2$, ","))
304.     y2 = Val(RightOf$(v2$, ","))
305.     vectDotProduct = x1 * x2 + y1 * y2
306. End Function
307.  
308. Function vectScale$ (a, v$) 'a * vector v$
309.     Dim x, y
310.     x = Val(LeftOf$(v$, ","))
311.     y = Val(RightOf$(v$, ","))
312.     vectScale$ = vect$(a * x, a * y)
313. End Function
314.  
315. Function vectTangent$ (v$, base$)
316.     Dim n$
317.     n$ = vectUnit$(base$)
318.     vectTangent$ = vectScale$(vectDotProduct(n$, v$), n$)
319. End Function
320.  
321. Function vectNorm$ (v$, base$)
322.     vectNorm$ = vectSub$(v$, vectTangent$(v$, base$))
323. End Function
324.  
325. ' update these 2 in case of$ is not found! 2021-02-13
326. Function LeftOf$ (source$, of$)
327.     If InStr(source$, of$) > 0 Then LeftOf$ = Mid$(source$, 1, InStr(source$, of$) - 1) Else LeftOf$ = source$
328. End Function
329.  
330. ' update these 2 in case of$ is not found! 2021-02-13
331. Function RightOf$ (source$, of$)
332.     If InStr(source$, of$) > 0 Then RightOf$ = Mid$(source$, InStr(source$, of$) + Len(of$)) Else RightOf$ = ""
333. End Function
334.  
335.  
336.  

PS It also passed all the special case collision tests: head on (3 angles), parallel converging and perpendicular.
The more balls the more sticky ball syndrome and sometime code will hang because not calculating fast enough for _limit to keep it smooth? But as I said really interesting, realistic?, changes in speed from collisions.

PPS make sure you have Const Balls set to 2 for all the Special Case Tests and comment last experiment and uncomment your next experiment.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 13, 2021, 07:13:04 pm

That looks pretty good. I like how it handles balls getting into tight bunches, which was the downfall of my billiards program.

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 14, 2021, 04:07:08 pm

Quote from: OldMoses on May 13, 2021, 07:13:04 pm

That looks pretty good. I like how it handles balls getting into tight bunches, which was the downfall of my billiards program.

Yes, I was very pleasantly surprised the ball action could stun balls into stillness or nearly so and then be made active again with just another little bump. The tsh73 version (which may never have been intended for 2 moving balls) and my own ball collision with trig only always have balls moving. My trig version you could start with overlapping balls and they will sort themselves and be clear of each other in a few frames, never a sticky ball but I never got balls stunned to stillness. It's a nice effect hinting I should do some more work trying to speed up the system.

How could I loose the $ Functions and use numbers and still have functions for vectors?
Yeah go ahead and say FB LOL!

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 17, 2021, 09:16:35 pm

Some vector addition exercises.

vector addition  for 2 ball collisions with equal mass and velocity
********************************************

say, Red ball heading -1x, 0y towards 0, 0  (origin)

say, Cyan ball heading  1x, -1y towards 0, 0  (origin)

add the ball vectors

first reverse signs

red ball =  1x, 0y
cyan ball = -1x, 1y

add the reversed ball vectors
1x+-1x,  0y+ 1y = 0x, 1y (mvector)

mvector is wrong (in this case)  because cyan ball velocity is greater than red ball velocity

 The directions of the red ball -1x, 0y and cyan ball 1x, 1y are correct but their magnitudes are not equal.
the solution is to match the red ball velocity with the cyan ball velocity

 Red ball is now  -2^.5x, 0y

cyan ball the same as before  1x, -1y

try again - first reverse signs

red ball = 2^.5x, 0y
cyan ball = -1x, 1y

add the reversed ball vectors
2^.5x-1x,  0y+ 1y = 0.4142135x, 1y (mvector)

 what angle is that?

 arc tan 0.4142135 = 22.5 degrees

The new ball directions are:

 Red ball vector after collision
 -2^.5x, + 0.4142135x,  0y +  1y    =  -1x,   1 y    (balls have the same final velocity)

 Cyan ball vector after collision
 1x, + 0.4142135x,  -1y +  1y    =  1.4142135x,   0y  (balls have the same final velocity)

 which should be correct if the strike angle is 22.5 degrees. In other words,
 if a line through both ball centers at collision is at a right angle to mvector

*****
With 2 balls of unequal velocity and everything else the same, the direction of mvector will change.  It looks like the difference in velocity is somehow related to a rotation of mvector.  The case where the strike angle agrees with mvector (a line through both ball centers at collision is at a right angle to mvector) was for normalized ball velocities.   

If the ball directions are maintained but the velocities are different then there is a rotation of mvector as respects strike angle agreement.

It is not known if this rotation of mvector represents the correct final ball vectors due to a difference in velocity only.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 17, 2021, 11:10:56 pm

I think the missing element is the balls center positions at contact. You reference "origin", but they can't both occupy (0, 0). There would be no vector from which to obtain a perpendicular movement vector. Not to mention that they would occupy the same point in space...

This is a condensed version of the algorithm I've been working on, using the terms you posted. It seems to work with my billiard ball impacts and yields a unit vector for each ball to exit the collision. Changing the impact positions (redpos & cyanpos) will give the appropriate direction for each ball. That direction can then be scaled up by whatever speeds are determined by further processing. Using the dot product calculation, there is no need to match velocities. Dot product can also handle the force transference.

Code: QB64: [Select]

1. TYPE V2
2.     x AS SINGLE
3.     y AS SINGLE
4. END TYPE
5.  
6. DIM AS V2 redmov, cyanmov, mvec, redpos, cyanpos, strike
7.  
8. 'These are the approach vectors you give
9. redmov.x = -1: redmov.y = 0
10. cyanmov.x = 1: cyanmov.y = -1
11.  
12. 'The important part is, where are the balls when they make contact. This determines the strike vector between them
13. 'choosing arbitrary points of contact... change these around to see the effect to verify its accuracy
14. redpos.x = 2: redpos.y = 2
15. cyanpos.x = 1: cyanpos.y = 1
16.  
17. strike.x = cyanpos.x - redpos.x
18. strike.y = cyanpos.y - redpos.y
19. ShearOrthoUnit mvec, redmov, strike
20. PRINT "red exits at <"; mvec.x; ", "; mvec.y; ">"
21.  
22. strike.x = redpos.x - cyanpos.x
23. strike.y = redpos.y - cyanpos.y
24. ShearOrthoUnit mvec, cyanmov, strike
25. PRINT "cyan exits at <"; mvec.x; ", "; mvec.y; ">"
26. END
27.  
28. SUB ShearOrthoUnit (nv AS V2, in AS V2, stk AS V2)
29.  
30.     DIM AS V2 or1, or2
31.     VecNorm stk '                                               normalize the strike vector
32.     or1.x = stk.y: or1.y = -stk.x '                             obtain two potential orthogonal vectors {or1 & or2} of strike
33.     or2.x = -stk.y: or2.y = stk.x
34.     dot = VecDot(in, or1) '                                     dot product one of them with the incoming vector
35.     nv.x = -or2.x * (dot < 0) - stk.x * (dot = 0) - or1.x * (dot > 0) 'exit vector x component
36.     nv.y = -or2.y * (dot < 0) - stk.y * (dot = 0) - or1.y * (dot > 0) 'exit vector y component
37.  
38. END SUB 'ShearOrthoUnit
39.  
40.  
41. SUB VecNorm (var AS V2)
42.  
43.     m = SQR(var.x * var.x + var.y * var.y)
44.     IF m = 0 THEN
45.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
46.     ELSE
47.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
48.     END IF
49.  
50. END SUB 'VecNorm
51.  
52.  
53. FUNCTION VecDot (var AS V2, var2 AS V2)
54.  
55.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
56.  
57. END FUNCTION 'VecDot
58.  
59.  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 18, 2021, 12:01:54 am

Quote

You reference "origin", but they can't both occupy (0, 0). There would be no vector from which to obtain a perpendicular movement vector. Not to mention that they would occupy the same point in space...

that is correct. I tried  to get around that with "point masses" but that was too abstract.  The ball direction are on a line that crosses 0, 0. The size of the balls (i like 40 pixel radius) determines the magnitude in this case the normal velocity is 80 pixels (per hour?)

The strike vector,  can be referenced to another vector (like mvector) because the strike vector passes through 0x, 0y.  It is somewhat an abstract idea but I don't have any other way of relating mvector to strike angle / vector. I should mention that mvector passes through 0x , 0y as well.


I ran your code  using

red ball   -2^.5x, 0y heading   towards  0, 0

cyan ball  -1x,  1y   heading towards 0, 0

and got different results

Forgot to set the strike vectors
To make this easier Im  gonna use pixels

red ball   -80 , 0y heading   towards  0, 0

cyan ball  (3200^.5) x, -(3200^.5) y   heading towards 0, 0

strike.x = 73.9103 pixels
strike.y = 30.6146 pixels

arc tan 30.6146 / 73.9103 = 22.5 degrees

in this case the strike vector is at a right angle to mvector.  I don't think there is any vector rotation to correct for in this case.

Red ball vector after collision
   =  -(3200^.5) x,  3200^.5 y   ?

 Cyan ball vector after collision
  =  80x,   0y   ?

your code gives different results
 

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 18, 2021, 08:14:38 am

Ugg, it would appear that the code I posted either has a bug, or my math is screwy. I plugged these numbers in: red (-80, 0)   cyan (3200 ^ .5, -(3200 ^ .5))

Quote from: NOVARSEG on May 18, 2021, 12:01:54 am

red ball   -80 , 0y heading   towards  0, 0

cyan ball  (3200^.5) x, -(3200^.5) y   heading towards 0, 0

and got identical exit vectors <-.3826834, -.9238796> for both balls, which should not have happened. The result should have been swapped components and signs from one ball to the other. Embarrassing to do that, I'd much rather be helpful than a distraction. Oh well, back to the drawing board...



On a point of terminology, forgive me if I'm a bit confused by your usage in the above.
I'm used to conceiving vectors as either position references (x, y) relative to origin (0, 0), or to other positions, or as magnitude/speed/force types <x, y> which may exist and be manipulated without reference to positional data.

A red ball at position (-80, 0) moving toward (0, 0) would have a magnitude/speed/force vector <0 - (-80)x, 0 - 0y> or <80, 0>. This would 'seem' to be how you're using the terms by saying "moving towards".

If, on the other hand the red ball is moving along <-80, 0> a reference to origin shouldn't be necessary for the vector math, except as updating a position after all force vectors are calculated, scaled and added to a previous position.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 18, 2021, 06:05:33 pm

Quote

A red ball at position (-80, 0) moving toward (0, 0) would have a magnitude/speed/force vector <0 - (-80)x, 0 - 0y> or <80, 0>. This would 'seem' to be how you're using the terms by saying "moving towards".

I'm using balls with 40 pixel radius. That gives a normal velocity of 80

red ball heading  -80x, 0y towards 0x , 0y

the magnitude or velocity of the red ball is

(80^2 + 0^2)^.5 = 80

It works out nicely with your strike.x and strike.y

(strike.x ^2 + strike.y ^2).5 = 80 if both balls head towards 0, 0.  The magnitude of strike vector is 80 because there are 80 pixels from ball center to ball center at collision.
The strike vector crosses 0, 0 and so does mvector.

The reference at 0, 0 seems to be necessary because mvector is actually vector addition using the  parallelogram method

where all vectors can start at 0, 0 if you want.

Title: Re: 2D ball collisions without trigonometry.
Post by: _vince on May 18, 2021, 06:49:40 pm

I haven't been following the thread but am just wondering, what is the benefit of no/without trigorometry?  Seems you can always convert between the trig and vector/sqrt/etc equivalent, perhaps not always easily.  FYI, Bill is the original QB-no-Trig:  https://www.tapatalk.com/groups/qbasic/rotation-t29617.html#p172877 (https://www.tapatalk.com/groups/qbasic/rotation-t29617.html#p172877)

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 18, 2021, 07:22:34 pm

probably no benefit, maybe a bit faster ? 

I have resorted to trig just to get this all sorted out.  I still have no proof the mvector method works or not. How can it be proven?

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 19, 2021, 12:02:06 pm

Thanks to @OldMoses  link to paper I finally have decent ball action for Pool Game! As collision demo'd here in this thread:
https://www.qb64.org/forum/index.php?topic=3866.msg132377#msg132377

Can check out Pool code at Steve's forum here (no images all hand drawn)
https://qb64.freeforums.net/thread/150/pool

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 19, 2021, 10:32:27 pm

bplus

say red ball heads -80x, 0y towards 0x, 0y and blue ball heads  0x, -80y  towards 0x, 0y. In this case there is 90 degrees between ball headings and both balls have equal velocity

For the simplest case, vector addition using the parallelogram method simply bisects the angle between red ball and blue ball.  mvector is located on this bisection line.   However for this bisection to occur requires the strike vector to be at right angle to the bisection line

calculate mvector

first reverse signs of balls
red ball  80x, 0y
blue ball   0x, 80y

vector addition

80x +0x,, 0y + 80y = 80x,  80y

so the mvector, in this case, is at a 45 degree angle in the upper right quadrant which is the angle of the bisection line.
now calculate final ball vectors (after collision)
(add original ball vectors to mvector)

red ball
-80x + 80x ,  0y + 80y =   0x, 80y

blue ball
0x + 80x ,  -80y + 80y =   80x, 0y

Are the final vectors correct?


 

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 20, 2021, 12:22:59 am

A red ball heading east towards point 0,0 and blue heading north to 0,0 both equal distance away and equal speed will meet and kiss at tangent angle 45 /225 degree before 0,0 due to their radii and red will deflect North and blue deflect east. I demo'd this or something similar in special case collisions, this thread.

Here is demo for this from tiny mod of previous code in this thread:

Code: QB64: [Select]

1. Option _Explicit
2. _Title "From Paper 2 Ball Collision with Vectors,  press r to restart" 'B+ 2021-05-13
3. ' Collision tests based on Paper       https://www.vobarian.com/collisions/2dcollisions2.pdf
4. ' The vector functions are modifications of tsh73 JB code converted to QB64 by me.
5. ' earlier code 2 Ball Collision with Vectors by Arrow Addition ' B+ 2021-05-10
6. ' 2021-05-10  fixed arrow so points from base x,y To angle
7. ' from Collision Study #4   press spacebar to toggle tracer" ' b+ 2021-05-09
8.  
9. ' !!!!!!!!!!!!!!!! Adjust Ball according to experiment 2 is always good
10.  
11. Const Balls = 2 '<<<<<<<<< change this to 2 to test special case setups: head on, parallel and perpendicular
12. 'Const Balls = 5 '<<<<<<<<< the more the balls the more problems pop up for Random Numbers experiments
13. '                            no more than 20! because have to start all balls not overlapping any other
14.  
15.  
16. Const Xmax = 600 ' screen width
17. Const Ymax = 600 ' screen height
18. Const R = 50 '     balls radii
19. Const R22 = R * R * 4 ' save some time with (2 * R) * (2 * R)
20.  
21. Const MV_Speed = 45 ' magnitude of Force Arrow say it's constant for simplicity sake
22. Type Ball
23.     As Long x, y
24.     As Double dx, dy, a ' dx, dy = change x, y axis
25.     As _Unsigned Long colr
26. End Type
27.  
28. Randomize Timer
29. Screen _NewImage(Xmax, Ymax, 32)
30. _Delay .25
31. _ScreenMove _Middle
32. ' these can be static as no balls added or subtracted in closed system
33. Dim As Ball b(1 To Balls), nf(1 To Balls) ' b() is current frame balls data , nf( ) is for next frame balls data
34. Dim As Long clrMode, i, j, rdm
35. b(1).colr = &HFFFF0000 'red ball 1 is red
36. b(2).colr = &HFF0000FF 'blue ball 2 is blue
37. clrMode = 1
38. Dim v1$, v2$, dv1$, dv2$, dv1u$, dv2u$, norm$, unitNorm$, unitTan$ 'vectors
39. Dim vp1n$, vp1t$, vp2n$, vp2t$ ' post collision vectors
40. Dim As Double v1n, v1t, v2n, v2t ' dot products
41. Dim As Double vp1n, vp1t, vp2n, vp2t ' post collision dot products
42. restart:
43. 'horizontal collisions  Head On
44. 'b(1).dx = 5
45. 'b(1).dy = 0 ' b1 is just moving on x axis to the right at 5 pixels per frame
46. 'b(2).dx = -5
47. 'b(2).dy = 0 ' b2 is just moving on x axis to the left at 5 pixels per frame
48. 'b(1).x = 300 - 5 * b(1).dx - R ' in 5 frames b1 will meet b2  kiss at center of screen
49. 'b(1).y = 300
50. 'b(2).x = 300 - 5 * b(2).dx + R ' in 5 frames b1 will meet b2  kiss at center of screen
51. 'b(2).y = 300
52.  
53. 'vertical collisions  Head On
54. 'b(1).dy = 5
55. 'b(1).dx = 0 ' b1 is just moving on x axis to the right at 5 pixels per frame
56. 'b(2).dy = -5
57. 'b(2).dx = 0 ' b2 is just moving on x axis to the left at 5 pixels per frame
58. 'b(1).y = 300 - 5 * b(1).dy - R ' in 5 frames b1 will meet b2  kiss at center of screen
59. 'b(1).x = 300
60. 'b(2).y = 300 - 5 * b(2).dy + R ' in 5 frames b1 will meet b2  kiss at center of screen
61. 'b(2).x = 300
62.  
63. ' 45 & 135 collsions   Head On
64. 'b(1).dy = 5
65. 'b(1).dx = 5 ' b1 is just moving on x axis to the right at 5 pixels per frame
66. 'b(2).dy = -5
67. 'b(2).dx = -5 ' b2 is just moving on x axis to the left at 5 pixels per frame
68. 'b(1).y = 300 - 5 * b(1).dy - R ' in 5 frames b1 will meet b2  kiss at center of screen
69. 'b(1).x = 300 - 5 * b(1).dx - R
70. 'b(2).y = 300 - 5 * b(2).dy + R ' in 5 frames b1 will meet b2  kiss at center of screen
71. 'b(2).x = 300 - 5 * b(2).dx + R
72.  
73. ' Parallel and converging paths
74. 'b(1).dy = -6
75. 'b(1).dx = 1 ' b1 is just moving on x axis to the right at 5 pixels per frame
76. 'b(2).dy = -6
77. 'b(2).dx = -1 ' b2 is just moving on x axis to the left at 5 pixels per frame
78. 'b(1).y = Ymax - R ' in 5 frames b1 will meet b2  kiss at center of screen
79. 'b(1).x = 300 - 20 * b(1).dx - R
80. 'b(2).y = Ymax - R ' in 5 frames b1 will meet b2  kiss at center of screen
81. 'b(2).x = 300 - 20 * b(2).dx + R
82.  
83. ' Perpendicular and 90 degree collision   should be just before mid screen
84. b(1).dy = 0
85. b(1).dx = -5
86. b(2).dy = -5
87. b(2).dx = 0
88. b(1).y = 300
89. b(1).x = Xmax - R
90. b(2).y = Ymax - R ' north
91. b(2).x = 300
92.  
93. ' random assignments
94. 'For i = 1 To Balls
95. '    tryAgain:
96. '    Print i
97. '    b(i).x = rand&(R, Xmax - R)
98. '    b(i).y = rand&(R, Ymax - R)
99. '    For j = 1 To i - 1
100. '        If _Hypot(b(i).x - b(j).x, b(i).y - b(j).y) < R + R Then GoTo tryAgain
101. '    Next
102. '    b(i).dx = (Rnd * 4 + 1) * rdir
103. '    b(i).dy = (Rnd * 4 + 1) * rdir
104. '    rdm = rand&(1, 7)
105. '    If rdm < 1 Or rdm > 7 Then Beep
106. '    Select Case rdm
107. '        Case 1: b(i).colr = _RGB32(Rnd * 200 + 55, 0, 0)
108. '        Case 2: b(i).colr = _RGB32(0, Rnd * 100 + 55, 0)
109. '        Case 3: b(i).colr = _RGB32(0, 0, Rnd * 200 + 55)
110. '        Case 4: b(i).colr = &HFFFF6600
111. '        Case 5: b(i).colr = &HFFFF0088
112. '        Case 6: b(i).colr = &HFF00FF88
113. '        Case 7: b(i).colr = _RGB32(Rnd * 200 + 55, Rnd * 200 + 55, Rnd * 200 + 55)
114. '    End Select
115. 'Next
116.  
117. While _KeyDown(27) = 0
118.     Dim k$
119.     k$ = InKey$
120.     If Len(k$) Then
121.         If Asc(k$) = 32 Then clrMode = -1 * clrMode
122.         If Asc(k$) = 27 And Len(k$) = 1 Then End
123.         If k$ = "r" Then GoTo restart
124.     End If
125.     If clrMode > 0 Then Cls
126.     Circle (300, 300), 2
127.     For i = 1 To Balls ' draw balls then  update for next frame
128.  
129.         ' this just draw the balls with arrows pointing to their headings
130.         Circle (b(i).x, b(i).y), R, b(i).colr
131.         b(i).a = _Atan2(b(i).dy, b(i).dx)
132.         ArrowTo b(i).x, b(i).y, b(i).a, MV_Speed, &HFFFFFF00
133.         ' debug
134.         '_PrintString (b(i).x - 8, b(i).y - 8), _Trim$(Right$("00" + Str$(i), 2)) 'all the balls weren't getting colored
135.  
136.         ' check for collision
137.         Dim cd, saveJ
138.         cd = 100000: saveJ = 0
139.         For j = 1 To Balls 'find deepest collision in case more than one we want earliest = deepest penetration
140.             If i <> j Then
141.                 Dim dx, dy
142.                 dx = b(i).x - b(j).x: dy = b(i).y - b(j).y
143.                 If dx * dx + dy * dy <= R22 Then ' collision but is it first or deepest collision
144.                     If R22 - dx * dx + dy * dy < cd Then cd = R22 - dx * dx + dy * dy: saveJ = j
145.                 End If
146.             End If
147.         Next
148.         If cd <> 100000 Then ' found collision change ball i dx, dy   calc new course for ball i
149.  
150.             ''reflection  from circle  using Vectors  from JB, thanks tsh73
151.             v1$ = vect$(b(i).x, b(i).y) ' circle i
152.             v2$ = vect$(b(saveJ).x, b(saveJ).y) ' the other circle j
153.             dv1$ = vect$(b(i).dx, b(i).dy) ' change in velocity vector
154.             dv2$ = vect$(b(saveJ).dx, b(saveJ).dy)
155.             dv1u$ = vectUnit$(dv1$) '1 pixel
156.             dv2u$ = vectUnit$(dv2$)
157.             'Print dv$, cv$, dv0$   ' check on things
158.             '_Display
159.             'Sleep
160.             Do ' this should back up the balls to kiss point thanks tsh73
161.                 v1$ = vectSub$(v1$, dv1u$)
162.                 v2$ = vectSub(v2$, dv2u$)
163.             Loop While vectLen(vectSub$(v1$, v2$)) < R + R 'back up our circle i to point on kiss
164.             ''now, get reflection speed
165.             ''radius to radius, norm is
166.             norm$ = vectSub$(v1$, v2$) ' this to this worked without all between from that collision paper
167.  
168.             '  step 1 unit norm and tangent
169.             unitNorm$ = vectUnit$(norm$)
170.             unitTan$ = vect$(-vectY(unitNorm$), vectX(unitNorm$))
171.             ' step 2 v$ and cv$ are 2 ball vectors (locations)  done already
172.             ' step 3 dot products before collision projecting onto normal and tangent vectors
173.             v1n = vectDotProduct(dv1$, unitNorm$)
174.             v1t = vectDotProduct(dv1$, unitTan$)
175.             v2n = vectDotProduct(dv2$, unitNorm$)
176.             v2t = vectDotProduct(dv2$, unitTan$)
177.             ' step 4 simplest  post collision dot products
178.             vp1t = v1t
179.             vp2t = v2t
180.             ' step 5  simplified by m = 1 for both balls just swap the numbers
181.             vp1n = v2n
182.             vp2n = v1n
183.             ' step 6  vp vectors mult the n, t numbers by unit vectors
184.             vp1n$ = vectScale$(vp1n, unitNorm$)
185.             vp1t$ = vectScale$(vp1t, unitTan$)
186.             vp2n$ = vectScale$(vp2n, unitNorm$)
187.             vp2t$ = vectScale$(vp2t, unitTan$)
188.             'step  7  add the 2 vectors n and t
189.             dv1$ = vectAdd$(vp1n$, vp1t$)
190.  
191.             ' to this  now just switch tangent and norm
192.             'dv1$ = vectSub$(vectNorm$(dv1$, norm$), vectTangent$(dv1$, norm$)) 'to this
193.  
194.             ' store in next frame array
195.             nf(i).dx = vectX(dv1$)
196.             nf(i).dy = vectY(dv1$)
197.  
198.         Else ' no collision
199.             nf(i).dx = b(i).dx
200.             nf(i).dy = b(i).dy
201.         End If
202.         'update location of ball next frame
203.         nf(i).x = b(i).x + nf(i).dx
204.         nf(i).y = b(i).y + nf(i).dy
205.  
206.         ' check in bounds next frame
207.         If nf(i).x < R Then nf(i).dx = -nf(i).dx: nf(i).x = R
208.         If nf(i).x > Xmax - R Then nf(i).dx = -nf(i).dx: nf(i).x = Xmax - R
209.         If nf(i).y < R Then nf(i).dy = -nf(i).dy: nf(i).y = R
210.         If nf(i).y > Ymax - R Then nf(i).dy = -nf(i).dy: nf(i).y = Ymax - R
211.     Next
212.  
213.     ''now that we've gone through all old locations update b() with nf() data
214.     For i = 1 To Balls
215.         b(i).x = nf(i).x: b(i).y = nf(i).y
216.         b(i).dx = nf(i).dx: b(i).dy = nf(i).dy
217.     Next
218.     ' next frame ready to draw
219.     _Display
220.     _Limit 30
221. Wend
222. 'Cls   ' debug why aren't all the balls getting colored
223. 'For i = 1 To Balls
224. '    Print i, b(i).colr
225. 'Next
226.  
227.  
228. Function rand& (lo As Long, hi As Long) ' fixed?
229.     rand& = Int(Rnd * (hi - lo) + 1) + lo
230. End Function
231.  
232. Function rdir ()
233.     If Rnd < .5 Then rdir = -1 Else rdir = 1
234. End Function
235.  
236.  
237.  
238. Sub ArrowTo (BaseX As Long, BaseY As Long, rAngle As Double, lngth As Long, colr As _Unsigned Long)
239.     Dim As Long x1, y1, x2, y2, x3, y3
240.     x1 = BaseX + lngth * Cos(rAngle)
241.     y1 = BaseY + lngth * Sin(rAngle)
242.     x2 = BaseX + .8 * lngth * Cos(rAngle - _Pi(.05))
243.     y2 = BaseY + .8 * lngth * Sin(rAngle - _Pi(.05))
244.     x3 = BaseX + .8 * lngth * Cos(rAngle + _Pi(.05))
245.     y3 = BaseY + .8 * lngth * Sin(rAngle + _Pi(.05))
246.     Line (BaseX, BaseY)-(x1, y1), colr
247.     Line (x1, y1)-(x2, y2), colr
248.     Line (x1, y1)-(x3, y3), colr
249. End Sub
250.  
251. ' convert some vector functions from JB, turns out much easier to use string functions to pass vectors
252. ' than using SUBs to do vector calcs
253.  
254. Function vect$ (x, y) ' convert x, y to string for passing vectors with Functions
255.     vect$ = _Trim$(Str$(x)) + "," + _Trim$(Str$(y))
256. End Function
257.  
258. Function vectX (v$)
259.     vectX = Val(LeftOf$(v$, ","))
260. End Function
261.  
262. Function vectY (v$)
263.     vectY = Val(RightOf$(v$, ","))
264. End Function
265.  
266. Function vectLen (v$)
267.     Dim x, y
268.     x = Val(LeftOf$(v$, ","))
269.     y = Val(RightOf$(v$, ","))
270.     vectLen = Sqr(x * x + y * y)
271. End Function
272.  
273. Function vectUnit$ (v$)
274.     Dim x, y, vl
275.     x = Val(LeftOf$(v$, ","))
276.     y = Val(RightOf$(v$, ","))
277.     vl = Sqr(x * x + y * y)
278.     vectUnit$ = vect$(x / vl, y / vl)
279. End Function
280.  
281. Function vectAdd$ (v1$, v2$)
282.     Dim x1, y1, x2, y2
283.     x1 = Val(LeftOf$(v1$, ","))
284.     y1 = Val(RightOf$(v1$, ","))
285.     x2 = Val(LeftOf$(v2$, ","))
286.     y2 = Val(RightOf$(v2$, ","))
287.     vectAdd$ = vect$(x1 + x2, y1 + y2)
288. End Function
289.  
290. Function vectSub$ (v1$, v2$)
291.     Dim x1, y1, x2, y2
292.     x1 = Val(LeftOf$(v1$, ","))
293.     y1 = Val(RightOf$(v1$, ","))
294.     x2 = Val(LeftOf$(v2$, ","))
295.     y2 = Val(RightOf$(v2$, ","))
296.     vectSub$ = vect$(x1 - x2, y1 - y2)
297. End Function
298.  
299. Function vectDotProduct (v1$, v2$)
300.     Dim x1, y1, x2, y2
301.     x1 = Val(LeftOf$(v1$, ","))
302.     y1 = Val(RightOf$(v1$, ","))
303.     x2 = Val(LeftOf$(v2$, ","))
304.     y2 = Val(RightOf$(v2$, ","))
305.     vectDotProduct = x1 * x2 + y1 * y2
306. End Function
307.  
308. Function vectScale$ (a, v$) 'a * vector v$
309.     Dim x, y
310.     x = Val(LeftOf$(v$, ","))
311.     y = Val(RightOf$(v$, ","))
312.     vectScale$ = vect$(a * x, a * y)
313. End Function
314.  
315. Function vectTangent$ (v$, base$)
316.     Dim n$
317.     n$ = vectUnit$(base$)
318.     vectTangent$ = vectScale$(vectDotProduct(n$, v$), n$)
319. End Function
320.  
321. Function vectNorm$ (v$, base$)
322.     vectNorm$ = vectSub$(v$, vectTangent$(v$, base$))
323. End Function
324.  
325. ' update these 2 in case of$ is not found! 2021-02-13
326. Function LeftOf$ (source$, of$)
327.     If InStr(source$, of$) > 0 Then LeftOf$ = Mid$(source$, 1, InStr(source$, of$) - 1) Else LeftOf$ = source$
328. End Function
329.  
330. ' update these 2 in case of$ is not found! 2021-02-13
331. Function RightOf$ (source$, of$)
332.     If InStr(source$, of$) > 0 Then RightOf$ = Mid$(source$, InStr(source$, of$) + Len(of$)) Else RightOf$ = ""
333. End Function
334.  
335.  

You need to know not only their new headings but the points they are at when they kiss and change direction.

Quote

red ball
-80x + 80x ,  0y + 80y =   0x, 80y

blue ball
0x + 80x ,  -80y + 80y =   80x, 0y

Are the final vectors correct?

I would say no, though your vector system unrecognizable to me but blue is definitely traveling in -x direction and red in  -y direction as shown in demo after they collide.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 20, 2021, 12:35:07 am

Quote

red will deflect North and blue deflect east.

good we got the same answer!

Quote

You need to know not only their new headings but the points they are at when they kiss and change direction.

yep OldMoses calls it the strike vector.  And yes, red will deflect North and blue deflect east only if strike vector is at right angle to bisection line.

With the same headings, if the strike vector changes, then the mvector is no longer on the bisection line.
I'm working on some math to prove where mvector ends up when that happens.

I'm hoping that if mvector can be located /calculated properly then all the math of 2d ball collisions can be derived from mvector only

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 20, 2021, 12:51:06 am

Quote

I would say no, though your vector system unrecognizable to me but blue is definitely traveling in -x direction and red in  -y direction as shown in demo after they collide.

if the red heads in a -y direction (after collision) that is south ?  how can that be if the blue was heading north before collision?

north = top of screen
west  = left of screen
east = right of screen
south = bottom of screen

my vector system is vector addition.  No dot  products - not yet anyway

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 20, 2021, 02:45:40 am

Strike vector can be calculated from mvector (on bisection line). The magnitude of strike vector is 80 pixels because the ball radius is 40 pixels.  When the balls collide there is a distance of 80 pixels between ball centers which is the hypotenuse of the x, y  strike components

Code: QB64: [Select]

1. DIM strikeX AS SINGLE
2. DIM strikeY AS SINGLE
3. DIM mvecX AS SINGLE
4. DIM mvecY AS SINGLE
5. DIM ballDIA AS INTEGER
6. ballDIA = 80 'pixels
7.  
8. mvecX = 80 'x component of mvector (mvector on bisection line)
9. mvecY = 80 'y component of mvector (mvector on bisection line)
10.  
11. strikeX = (ballDIA ^ 2 / (mvecX / mvecY + 1)) ^ .5
12. PRINT "strikeX"; strikeX
13.  
14. strikeY = (ballDIA ^ 2 / (mvecY / mvecX + 1)) ^ .5
15.  
16. PRINT "strikeY"; strikeY
17.  

 Working on math to calculate mvector from strike vector if mvector magnitude on bisection line is known.

Expecting the final ball velocities to vary with a change in strike vector

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 20, 2021, 04:18:25 am

More code.  Ok not verified yet.  Have to run a simulation to see if there are any bugs. Introduced bvector which is mvector on bisection line.  bvecX and bvecY are set to 80.

Code: QB64: [Select]

1. DIM strikeX AS SINGLE
2. DIM strikeY AS SINGLE
3. DIM bvecX AS SINGLE 'bvector is mvector on bisection line
4. DIM bvecY AS SINGLE 'bvector is mvector on bisection line
5. DIM mvecX AS SINGLE
6. DIM mvecY AS SINGLE
7. DIM bvecMAG AS SINGLE
8. DIM strikeMAG AS INTEGER
9. DIM ballRAD AS INTEGER 'ball radius in pixels
10. ballRAD = 40 'pixels
11. strikeMAG = 2 * ballRAD
12.  
13.  
14. bvecX = 80 'mvector on bisection line
15. bvecY = 80 'mvector on bisection line
16. bvecMAG = (bvecX ^ 2 + bvecY ^ 2) ^ .5
17.  
18. strikeX = (strikeMAG ^ 2 / (bvecX ^ 2 / bvecY ^ 2 + 1)) ^ .5
19. PRINT "strikeX"; strikeX
20.  
21. strikeY = (strikeMAG ^ 2 / (bvecY ^ 2 / bvecX ^ 2 + 1)) ^ .5
22.  
23. PRINT "strikeY"; strikeY
24.  
25. '*************  calculate mvector from strike vector and bvector
26.  
27. mvecX = (bvecMAG ^ 2 / (strikeX ^ 2 / strikeY ^ 2 + 1)) ^ .5
28. mvecY = (bvecMAG ^ 2 / (strikeY ^ 2 / strikeX ^ 2 + 1)) ^ .5
29.  
30. PRINT "mvecX"; mvecX
31. PRINT "mvecY"; mvecY

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 20, 2021, 01:08:31 pm

Quote from: NOVARSEG on May 20, 2021, 12:51:06 am

if the red heads in a -y direction (after collision) that is south ?  how can that be if the blue was heading north before collision?

north = top of screen
west  = left of screen
east = right of screen
south = bottom of screen

my vector system is vector addition.  No dot  products - not yet anyway

Oh man! I still don't know my left and right or I should say my West from my East! Left Is heading West and moving to the right IS East.

I meant to say the Blue ball moving North will be deflected West, to the left.
and the Red ball moving West will be deflected North, up.

The demo is correct even if my description is wrong, sorry for making a difficult subject more confusing.

Vector addition should work, it was drilled into my head in Physics 101 College Course (for non Physics Majors that didn't do Calculus side by side with Physics like they do for Physics Majors which is so much better in my opinion).
But not drilled into my head was vectors that went at any angle even in degrees let alone radians!

To find which way a body will move you add up all the vector forces applied to the center of the body mass which for a ball is easiest to describe and find, its the origin of the circle.

And we drew arrows and placed the tail of one arrow at the head of the other for the "resultant" force an arrow from body center to head of the first arrow. That was as far as it got we did not have computers then just graduating from slide rules to hand calculators.

So these arrows have x, y components, add x components and y components yeah NOVARSEG you seem to be on right track so far.

But at moment of collision how do you calculate the force of the other ball acting on the first ball?

Don't you have to look at the angle the balls are at to each other, because the tangent line they will reflect from (just like light off a surface) is perpendicular to the angle the balls are at when they kiss. Angle in = Angle out off that tangent line at kiss point. Easy to describe a real b... to get mathematically!

Reflecting off a box boundary is piece of cake just reverse the dx or dy direction with a negative sign.
Bouncing off an angled surface not so fun because both dx, dy components are effected and most of the time unequally.

And in Basic Graphics  decreasing y is moving North and  increasing y is moving South another bug-a-boo obstacle to easy understanding and communication between math and science students and computer apps in Basic.

North is up in direction and y decreases to get there.
South is down direction and y increases to get there, it is Basic Fact of computer life face it or get out your Window command and fix your graphics to work as you learn it math or science class.

When you use Window command you have to know which graphics command can follow: line, circle (though you better check out arcs) pset these work with Window coordinate system. Mouse x, y doesn't work but does have a PMAP fix that comes with Basic read your Wiki carefully about WINDOW command.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 20, 2021, 06:45:50 pm

Quote

Don't you have to look at the angle the balls are at to each other, because the tangent line they will reflect from (just like light off a surface) is perpendicular to the angle the balls are at when they kiss. Angle in = Angle out off that tangent line at kiss point. Easy to describe a real b... to get mathematically!

For a ball striking a wall, ya, it's angle in, angle out.

Trying to code an interactive tool that will show two circles at the point of contact.   The strike vector will be rotatable by visual means of two circles rotating about 0x,0y.  (80 pixels from center to center)The bisection line is shown. As strike vector is rotated the mvector will move. Also shown are the final ball vectors.   I thought this tool would be a better way to show ball collisions without any moving balls.

As strike vector is rotated, mvector will line up with the bisection line which is also bvector
 Well I have not even started coding this yet.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 20, 2021, 07:35:09 pm

Speaking of interactive tools. I've been trying to wrap my poor tender head around this algorithm for quite some time and thought that something like that would be helpful to watch the effects of various changes to the equations. Maybe someone can make use of some or all of the following code, and/or substitute their own math functions, as mine are as useful as a turd in a public pool at the moment... ;)  But of course that's why I need this. It's cobbled together from the bones of what I posted earlier.

Anyway, the idea is that you can left click on the ends of the solid line vectors (i.e. incoming vector) and move them around and see what applied algorithms effects are on the exit paths. It acts a bit squirrely and you might have to do a pre-click on a vertex to sort of wake it up that its not a previous move continued. I'm not terribly familiar with Steve's MBS function for drag and drop ops, but figured that there's no better time than the present to play with it.

Moving the ball centers changes their radii, maintaining equivalent size, as I never conceived this as anything beyond identical billiard ball type stuff. It also redefines the coordinate system with WINDOW as Bplus mentioned earlier.

EDIT: Ah! I've discovered the secret to using my own code. Get near the desired vertex, click and hold until the line jumps to the mouse cursor. I guess I wasn't giving time for the delay parameter in Steve's MBS function.

Code: QB64: [Select]

1. $COLOR:32
2. TYPE V2
3.     x AS SINGLE
4.     y AS SINGLE
5. END TYPE
6.  
7. TYPE ball
8.     cn AS STRING * 4 '                                          ball name by color
9.     c AS _UNSIGNED LONG '                                       color
10.     p AS V2 '                                                   position
11.     m AS V2 '                                                   movement (pre-contact) incoming
12.     u AS V2 '                                                   unit vector of ball.m
13.     x AS V2 '                                                   vector of post contact movement
14.     s AS INTEGER '                                              magnitude of movement
15.     sd AS SINGLE '                                              strike dot
16. END TYPE
17.  
18. DIM AS V2 mvec, strike
19. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
20. DIM mouse AS V2
21. DIM b(1) AS ball
22. DIM SHARED AS V2 origin
23. origin.x = 0: origin.y = 0
24. b(0).c = Red: b(0).cn = "red"
25. b(1).c = Cyan: b(1).cn = "cyan"
26.  
27. SCREEN _NEWIMAGE(600, 600, 32)
28. DO: LOOP UNTIL _SCREENEXISTS
29. _SCREENMOVE 10, 10
30. WINDOW (-300, 300)-(300, -300)
31. 'These are the approach vectors you give
32. b(0).m.x = 0: b(0).m.y = -100 '                                 reds approach vector
33. b(0).s = PyT(origin, b(0).m) '                                  reds magnitude (speed or force)
34. b(1).m.x = 100: b(1).m.y = -100 '                               cyans approach vector
35. b(1).s = PyT(origin, b(1).m) '                                  cyans magnitude (speed or force)
36.  
37. 'The important part is, where are the balls when they make contact. This determines the strike vector between them
38. 'choosing arbitrary points of contact... change these around to see the effect to verify its accuracy
39. b(0).p.x = 30: b(0).p.y = 10
40. b(1).p.x = -17: b(1).p.y = 0
41.  
42. DO
43.     ms = MBS '                                                  process mouse actions dragging endpoints
44.     IF ms AND 64 THEN
45.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
46.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
47.         FOR x = 0 TO 1
48.             FOR y = 0 TO 1
49.                 ds! = PyT(vertex(x, y), mouse)
50.                 IF ds! < ballradius * .5 THEN i = x: j = y
51.             NEXT y
52.         NEXT x
53.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
54.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
55.                 b(i).p = mouse
56.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
57.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
58.         END SELECT
59.     ELSE
60.     END IF
61.  
62.  
63.     'START OF COLLISION MATHEMATICS SECTION
64.     ballradius = PyT(b(0).p, b(1).p) / 2
65.     CLS
66.  
67.     FOR bn = 0 TO 1
68.         other = ABS(NOT -bn) '                                  if we're on 0 the other is 1 and vice versa
69.         b(bn).u = b(bn).m: VecNorm b(bn).u '                    normalize the movement vector
70.         strike.x = b(other).p.x - b(bn).p.x '                   obtain a strike vector
71.         strike.y = b(other).p.y - b(bn).p.y
72.         ShearOrthoUnit mvec, b(bn).m, strike '                  strike is converted to a unit vector and mvec is orthogonal unit of strike
73.         b(bn).x = mvec '                                        keep the result of mvec in the exit vector, we'll grow it in the next loop
74.  
75.         'now this is what we're really shooting for
76.         b(bn).sd = VecDot(b(bn).u, strike)
77.  
78.         'establish the mouse handles for scenario manipulations
79.         vertex(bn, 0) = b(bn).p
80.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1
81.     NEXT bn
82.     'we finish the above FOR/NEXT loop so that we have all respective mvec's stored in b(#).x
83.     'then we rerun the loop, converting b(#).x to a full exit vector
84.     FOR bn = 0 TO 1
85.         other = ABS(NOT -bn)
86.         b(bn).x.x = b(bn).x.x * (b(bn).s * b(other).sd)
87.         b(bn).x.y = b(bn).x.y * (b(bn).s * b(other).sd)
88.         'PRINT b(bn).cn; " exits at <"; b(bn).x.x; ", "; b(bn).x.y; ">"
89.     NEXT bn
90.     'END OF COLLISION MATHEMATICS SECTION
91.  
92.     'graphic representation
93.     FOR grid = -300 TO 300 STEP 20
94.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
95.         LINE (grid, 300)-(grid, -300), c& 'Gray
96.         LINE (-300, grid)-(300, grid), c& ' Gray
97.     NEXT grid
98.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
99.     FOR dr = 0 TO 1
100.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c
101.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x - b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
102.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
103.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
104.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
105.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">"
106.         _PRINTSTRING (0, 567 + (16 * dr)), b$
107.     NEXT dr
108.  
109.     _LIMIT 50
110.     _DISPLAY
111. LOOP UNTIL _KEYDOWN(27)
112. END
113.  
114.  
115. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
116.     STATIC StartTimer AS _FLOAT
117.     STATIC ButtonDown AS INTEGER
118.     STATIC ClickCount AS INTEGER
119.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
120.     '                          Down longer counts as a HOLD event.
121.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
122.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
123.         SELECT CASE SGN(_MOUSEWHEEL)
124.             CASE 1: MBS = MBS OR 512
125.             CASE -1: MBS = MBS OR 1024
126.         END SELECT
127.     WEND
128.  
129.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
130.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
131.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
132.  
133.     IF StartTimer = 0 THEN
134.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
135.             ButtonDown = 1: StartTimer = TIMER(0.01)
136.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
137.         ELSEIF _MOUSEBUTTON(2) THEN
138.             ButtonDown = 2: StartTimer = TIMER(0.01)
139.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
140.         ELSEIF _MOUSEBUTTON(3) THEN
141.             ButtonDown = 3: StartTimer = TIMER(0.01)
142.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
143.         END IF
144.     ELSE
145.         BD = ButtonDown MOD 3
146.         IF BD = 0 THEN BD = 3
147.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
148.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
149.         ELSE
150.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
151.                 MBS = 0: ButtonDown = 0: StartTimer = 0
152.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
153.             ELSE 'We've now started the hold event
154.                 MBS = MBS OR 32 * 2 ^ ButtonDown
155.             END IF
156.         END IF
157.     END IF
158. END FUNCTION 'MBS%
159.  
160.  
161. FUNCTION PyT (var1 AS V2, var2 AS V2)
162.  
163.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
164.  
165. END FUNCTION 'PyT
166.  
167.  
168. SUB ShearOrthoUnit (nv AS V2, in AS V2, stk AS V2)
169.  
170.     DIM AS V2 or1, or2
171.     VecNorm stk '                                               normalize the strike vector
172.     or1.x = stk.y: or1.y = -stk.x '                             obtain two potential orthogonal vectors {or1 & or2} of strike
173.     or2.x = -stk.y: or2.y = stk.x
174.     dot = VecDot(in, or1) '                                     dot product one of them with the incoming vector
175.     nv.x = -or2.x * (dot < 0) - stk.x * (dot = 0) - or1.x * (dot > 0) 'exit vector x component
176.     nv.y = -or2.y * (dot < 0) - stk.y * (dot = 0) - or1.y * (dot > 0) 'exit vector y component
177.  
178. END SUB 'ShearOrthoUnit
179.  
180.  
181. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
182.  
183.     var.x = var.x + (var2.x * var3)
184.     var.y = var.y + (var2.y * var3)
185.  
186. END SUB 'Add_Vector
187.  
188.  
189. SUB VecNorm (var AS V2)
190.  
191.     m = PyT(origin, var)
192.     IF m = 0 THEN
193.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
194.     ELSE
195.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
196.     END IF
197.  
198. END SUB 'VecNorm
199.  
200.  
201. FUNCTION VecDot (var AS V2, var2 AS V2)
202.  
203.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
204.  
205. END FUNCTION 'VecDot
206.  
207.  
208. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
209.  
210.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
211.  
212. END FUNCTION 'map!
213.  
214.  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 20, 2021, 09:11:16 pm

OldMoses hey  that  is what I was thinking of.  Great code example.


Are the dashed lines the final ball vectors or are they ball vectors before collision.

Bplus we are both wrong, according to OldMoses simulator the red and blue balls head off in a PARALLEL direction. Both balls have a final heading of north  east. Adjust the strike vector so it is at right angles to a line bisecting the angle between red and blue before collision.

(LATER (never mined what I just said, I misinterpreted what the dashed lines meant)

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 20, 2021, 09:24:16 pm

Quote from: NOVARSEG on May 20, 2021, 09:11:16 pm

OldMoses hey  that  is what I was thinking of.  Great code example.


Are the dashed lines the final ball vectors or are they ball vectors before collision.

Bplus we are both wrong, according to OldMoses simulator the red and blue balls head off in a PARALLEL direction. Both balls have a final heading of north  east. Adjust the strike vector so it is at right angles to a line bisecting the angle between red and blue before collision.

Thanks, yes the dashed lines are are "supposed" to be the mvectors, but I have my doubts about the math as one can set up some wierd scenarios. I think my math needs a good deal more work on force transference between the balls, but I'm fairly confident that the graphics part is working properly.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 20, 2021, 09:47:04 pm

Ok scrap whaat I said before.  I kinda see what you've done. Each ball has it's own mvector.  My view of mvector is that it originates at the contact point between balls.  SO maybe 2 mvectors are needed but I was hoping that a single mvector would be enough.

There is an very interesting collision.

say red ball heads -80x, 0y towards 0, 0  and blue ball heads  0x, -80y towards 0, 0 with strike vector along y axis

according to the simulator the red ball does not change direction but the blue ball  reverses?? direction
****
Im not sure if the blue ball reverses direction or comes to a stop. Also does the red ball speed up?
****

If the red ball had been stationary it would head off  in the direction of the blue ball  and the blue ball would come to a stop

****

Another thing it looks like the strike vector is ALWAYS at a right angle to the mvectors which looks to be correct

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 21, 2021, 12:31:59 am

Quote from: NOVARSEG on May 20, 2021, 09:47:04 pm

There is an very interesting collision.

say red ball heads -80x, 0y towards 0, 0  and blue ball heads  0x, -80y towards 0, 0 with strike vector along y axis

according to the simulator the red ball does not change direction but the blue ball  reverses direction.

If the red ball had been stationary it would head off  in the direction of the blue ball  and the blue ball would come to a stop

That's where my algorithm isn't working as I would expect, another thing that jumped out at me was head on collisions, which should rebound like that, but the program shows them rebounding at right angles.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 21, 2021, 01:07:19 am

Here is one where it is almost correct.

red @ (-100, 0)    along (100, 0)    exit along (50, 50)   should be (70, 70)   ?         

cyan @ (0, -100)  along (0, 100)    exit along ((70, 70) correct


70 approx 5000^.5

I looked at the head on collisions and that is basically correct. If you fix the above one then that'll look good too.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 21, 2021, 08:13:20 am

I've gone back to the Berchek paper instead of my own crazy experiments and came up with this variation. While I think the math is getting better as the magnitudes seem to be right, there seems to be an inversion in the code somewhere. The exits consistantly converge instead of rebounding.

Interesting results though...

EDIT:
Even better, adding IF...THEN starting at line 78 seems to have corrected the inversion. Berchek was correct, you only need one strike vector. The second one just confused the issue.

Code: QB64: [Select]

1. $COLOR:32
2. TYPE V2
3.     x AS SINGLE
4.     y AS SINGLE
5. END TYPE
6.  
7. TYPE ball
8.     cn AS STRING * 4 '                                          ball name by color
9.     c AS _UNSIGNED LONG '                                       color
10.     p AS V2 '                                                   position
11.     m AS V2 '                                                   movement (pre-contact) incoming
12.     um AS V2 '                                                  unit vector of ball.m
13.     x AS V2 '                                                   vector of post contact movement
14.     un AS V2 '                                                  unit normal; obtained from strike
15.     ut AS V2 '                                                  unit tangent; reciprocated from un
16.     nci AS SINGLE '                                             normal component of input velocity
17.     tci AS SINGLE '                                             tangential component of input velocity
18.     ncx AS SINGLE '                                             normal component of exit velocity
19.     tcx AS SINGLE '                                             tangential component of exit velocity
20.     s AS INTEGER '                                              magnitude of movement
21.     sd AS SINGLE '                                              strike dot
22. END TYPE
23.  
24. DIM AS V2 strike, norcom, tancom
25. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
26. DIM mouse AS V2
27. DIM b(1) AS ball
28. DIM SHARED AS V2 origin
29. origin.x = 0: origin.y = 0
30. b(0).c = Red: b(0).cn = "red"
31. b(1).c = Cyan: b(1).cn = "cyan"
32.  
33. SCREEN _NEWIMAGE(600, 600, 32)
34. DO: LOOP UNTIL _SCREENEXISTS
35. _SCREENMOVE 10, 10
36. WINDOW (-300, 300)-(300, -300)
37. 'These are the approach vectors you give
38. b(0).m.x = 0: b(0).m.y = -100 '                                 reds approach vector
39. b(0).s = PyT(origin, b(0).m) '                                  reds magnitude (speed or force)
40. b(1).m.x = 100: b(1).m.y = -100 '                               cyans approach vector
41. b(1).s = PyT(origin, b(1).m) '                                  cyans magnitude (speed or force)
42.  
43. b(0).p.x = 30: b(0).p.y = 10
44. b(1).p.x = -17: b(1).p.y = 0
45.  
46. DO
47.     ms = MBS '                                                  process mouse actions dragging endpoints
48.     IF ms AND 64 THEN
49.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
50.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
51.         FOR x = 0 TO 1
52.             FOR y = 0 TO 1
53.                 ds! = PyT(vertex(x, y), mouse)
54.                 IF ds! < ballradius * .5 THEN i = x: j = y
55.             NEXT y
56.         NEXT x
57.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
58.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
59.                 b(i).p = mouse
60.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
61.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
62.         END SELECT
63.     ELSE
64.     END IF
65.  
66.     'START OF COLLISION MATHEMATICS SECTION
67.     ballradius = PyT(b(0).p, b(1).p) / 2
68.     CLS
69.  
70.     FOR bn = 0 TO 1
71.         other = ABS(NOT -bn) '                                  if we're on 0 the other is 1 and vice versa
72.  
73.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
74.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
75.  
76.         'Now for collision processing
77.         b(bn).um = b(bn).m: VecNorm b(bn).um '                  normalize the movement vector
78.         IF bn = 0 THEN '                                        we only need one strike vector from the first ball
79.             strike = b(other).p: VecAdd strike, b(bn).p, -1 '   obtain a strike vector (Berchek step 1)
80.         END IF
81.         b(bn).un = strike: VecNorm b(bn).un '                   compute unit normal (Berchek step 1)
82.         b(bn).ut.x = -b(bn).un.y: b(bn).ut.y = b(bn).un.x '     compute unit tangent (Berchek step 1)
83.         b(bn).nci = VecDot(b(bn).un, b(bn).m) '                 compute normal component of velocity (Berchek step 3)
84.         b(bn).tci = VecDot(b(bn).ut, b(bn).m) '                 compute tangential component of velocity (Berchek step 3)
85.     NEXT bn
86.     'we finish the above FOR/NEXT loop so that we have all respective data stored in the two ball variables
87.     'then we rerun the loop, converting b(#).x to a full exit vector
88.     FOR bn = 0 TO 1
89.         other = ABS(NOT -bn)
90.         'Now we tackle Berchek's step 4 tangential and normal velocities
91.         'It is assumed that both balls are of unit mass, therefore:
92.         'From Berchek's one dimensional collision formula
93.         ' b(bn).ncx = (b(bn).nci * (1 - 1) + 2 * 1 * b(other).nci) / (1 + 1), therefore:
94.         ' b(bn).ncx = (b(bn).nci * 0 + 2 * b(other).nci) / 2, therefore:
95.         ' b(bn).ncx = 2 * b(other).nci / 2, therefore:
96.         b(bn).ncx = b(other).nci '                              compute normal component of exit velocity (Berchek step 5)
97.         'and this concurs with Bplus' conclusion, that under equal mass the balls transfer velocity
98.         'https://www.qb64.org/forum/index.php?topic=3866.msg132332#msg132332
99.  
100.         b(bn).tcx = b(bn).tci '                                 compute tangent component of exit velocity (Berchek step 4)
101.         'Since these are equivalent, according to Berchek, it is unnecessary to assign a tangent component of exit velocity variable
102.         'it's only done for ordering the thought process
103.  
104.         'and now for step 6, we're almost there...
105.         norcom = b(bn).un: VecMult norcom, b(bn).ncx '          unit normal exit vector x normal component of exit vector
106.         tancom = b(bn).ut: VecMult tancom, b(bn).tcx '          unit tangent exit vector x tangent component of exit vector
107.  
108.         'Finally, at step 7, add norcom and tancom to get b(bn).x
109.         b(bn).x = norcom: VecAdd b(bn).x, tancom, 1 '           add normal and tangent exit vectors
110.         'after that we can update any other ball parameters for subsequent moves
111.     NEXT bn
112.     'END OF COLLISION MATHEMATICS SECTION
113.  
114.     'graphic representation
115.     FOR grid = -300 TO 300 STEP 20
116.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
117.         LINE (grid, 300)-(grid, -300), c& 'Gray
118.         LINE (-300, grid)-(300, grid), c& ' Gray
119.     NEXT grid
120.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
121.     FOR dr = 0 TO 1
122.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c
123.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x - b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
124.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
125.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
126.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
127.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">"
128.         _PRINTSTRING (0, 567 + (16 * dr)), b$
129.     NEXT dr
130.  
131.     _LIMIT 50
132.     _DISPLAY
133. LOOP UNTIL _KEYDOWN(27)
134. END
135.  
136.  
137. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
138.     STATIC StartTimer AS _FLOAT
139.     STATIC ButtonDown AS INTEGER
140.     STATIC ClickCount AS INTEGER
141.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
142.     '                          Down longer counts as a HOLD event.
143.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
144.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
145.         SELECT CASE SGN(_MOUSEWHEEL)
146.             CASE 1: MBS = MBS OR 512
147.             CASE -1: MBS = MBS OR 1024
148.         END SELECT
149.     WEND
150.  
151.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
152.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
153.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
154.  
155.     IF StartTimer = 0 THEN
156.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
157.             ButtonDown = 1: StartTimer = TIMER(0.01)
158.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
159.         ELSEIF _MOUSEBUTTON(2) THEN
160.             ButtonDown = 2: StartTimer = TIMER(0.01)
161.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
162.         ELSEIF _MOUSEBUTTON(3) THEN
163.             ButtonDown = 3: StartTimer = TIMER(0.01)
164.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
165.         END IF
166.     ELSE
167.         BD = ButtonDown MOD 3
168.         IF BD = 0 THEN BD = 3
169.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
170.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
171.         ELSE
172.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
173.                 MBS = 0: ButtonDown = 0: StartTimer = 0
174.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
175.             ELSE 'We've now started the hold event
176.                 MBS = MBS OR 32 * 2 ^ ButtonDown
177.             END IF
178.         END IF
179.     END IF
180. END FUNCTION 'MBS%
181.  
182.  
183. FUNCTION PyT (var1 AS V2, var2 AS V2)
184.  
185.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
186.  
187. END FUNCTION 'PyT
188.  
189.  
190. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
191.  
192.     var.x = var.x + (var2.x * var3)
193.     var.y = var.y + (var2.y * var3)
194.  
195. END SUB 'Add_Vector
196.  
197.  
198. SUB VecMult (vec AS V2, multiplier AS SINGLE)
199.  
200.     'multiply vector by scalar value
201.     vec.x = vec.x * multiplier
202.     vec.y = vec.y * multiplier
203.  
204. END SUB 'Vec_Mult
205.  
206.  
207. SUB VecNorm (var AS V2)
208.  
209.     m = PyT(origin, var)
210.     IF m = 0 THEN
211.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
212.     ELSE
213.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
214.     END IF
215.  
216. END SUB 'VecNorm
217.  
218.  
219. FUNCTION VecDot (var AS V2, var2 AS V2)
220.  
221.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
222.  
223. END FUNCTION 'VecDot
224.  
225.  
226. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
227.  
228.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
229.  
230. END FUNCTION 'map!
231.  

Here's the same thing reduced and optimized to a single SUB call, it seems to still work the same.

Code: QB64: [Select]

1. $COLOR:32
2. TYPE V2
3.     x AS SINGLE
4.     y AS SINGLE
5. END TYPE
6.  
7. TYPE ball
8.     cn AS STRING * 4 '                                          ball name by color
9.     c AS _UNSIGNED LONG '                                       color
10.     p AS V2 '                                                   position
11.     m AS V2 '                                                   movement (pre-contact) incoming
12.     x AS V2 '                                                   vector of post contact movement
13.     s AS INTEGER '                                              magnitude of movement
14. END TYPE
15.  
16. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
17. DIM mouse AS V2
18. DIM b(1) AS ball
19. DIM SHARED AS V2 origin
20. origin.x = 0: origin.y = 0
21. b(0).c = Red: b(0).cn = "red"
22. b(1).c = Cyan: b(1).cn = "cyan"
23.  
24. SCREEN _NEWIMAGE(600, 600, 32)
25. DO: LOOP UNTIL _SCREENEXISTS
26. _SCREENMOVE 10, 10
27. WINDOW (-300, 300)-(300, -300)
28.  
29. 'starting state
30. b(0).m.x = 0: b(0).m.y = -100 '                                 reds approach vector
31. b(0).s = PyT(origin, b(0).m) '                                  reds magnitude (speed or force)
32. b(1).m.x = 100: b(1).m.y = -100 '                               cyans approach vector
33. b(1).s = PyT(origin, b(1).m) '                                  cyans magnitude (speed or force)
34.  
35. b(0).p.x = 30: b(0).p.y = 10
36. b(1).p.x = -17: b(1).p.y = 0
37.  
38. DO
39.     ms = MBS '                                                  process mouse actions dragging endpoints
40.     IF ms AND 64 THEN
41.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
42.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
43.         FOR x = 0 TO 1
44.             FOR y = 0 TO 1
45.                 ds! = PyT(vertex(x, y), mouse)
46.                 IF ds! < ballradius * .5 THEN i = x: j = y
47.             NEXT y
48.         NEXT x
49.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
50.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
51.                 b(i).p = mouse
52.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
53.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
54.         END SELECT
55.     ELSE
56.     END IF
57.  
58.     'START OF COLLISION MATHEMATICS SECTION
59.     ballradius = PyT(b(0).p, b(1).p) / 2
60.     CLS
61.  
62.     FOR bn = 0 TO 1
63.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
64.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
65.     NEXT bn
66.  
67.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
68.     B2BCollision b(0), b(1)
69.     'END OF COLLISION MATHEMATICS SECTION
70.  
71.     'graphic representation
72.     FOR grid = -300 TO 300 STEP 20
73.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
74.         LINE (grid, 300)-(grid, -300), c& 'Gray
75.         LINE (-300, grid)-(300, grid), c& ' Gray
76.     NEXT grid
77.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
78.     FOR dr = 0 TO 1
79.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c
80.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x - b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
81.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
82.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
83.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
84.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">"
85.         _PRINTSTRING (0, 567 + (16 * dr)), b$
86.     NEXT dr
87.  
88.     _LIMIT 50
89.     _DISPLAY
90. LOOP UNTIL _KEYDOWN(27)
91. END
92.  
93.  
94. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
95.  
96.     DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
97.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
98.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
99.     bnci1 = VecDot(un, ball1.m) '
100.     bnci2 = VecDot(un, ball2.m) '
101.     btci1 = VecDot(ut, ball1.m) '
102.     btci2 = VecDot(ut, ball2.m) '
103.  
104.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
105.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
106.  
107.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
108.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
109.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
110.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
111.  
112.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
113.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
114.  
115. END SUB 'B2BCollision
116.  
117.  
118. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
119.  
120.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
121.  
122. END FUNCTION 'map!
123.  
124.  
125. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
126.     STATIC StartTimer AS _FLOAT
127.     STATIC ButtonDown AS INTEGER
128.     STATIC ClickCount AS INTEGER
129.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
130.     '                          Down longer counts as a HOLD event.
131.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
132.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
133.         SELECT CASE SGN(_MOUSEWHEEL)
134.             CASE 1: MBS = MBS OR 512
135.             CASE -1: MBS = MBS OR 1024
136.         END SELECT
137.     WEND
138.  
139.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
140.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
141.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
142.  
143.     IF StartTimer = 0 THEN
144.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
145.             ButtonDown = 1: StartTimer = TIMER(0.01)
146.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
147.         ELSEIF _MOUSEBUTTON(2) THEN
148.             ButtonDown = 2: StartTimer = TIMER(0.01)
149.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
150.         ELSEIF _MOUSEBUTTON(3) THEN
151.             ButtonDown = 3: StartTimer = TIMER(0.01)
152.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
153.         END IF
154.     ELSE
155.         BD = ButtonDown MOD 3
156.         IF BD = 0 THEN BD = 3
157.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
158.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
159.         ELSE
160.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
161.                 MBS = 0: ButtonDown = 0: StartTimer = 0
162.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
163.             ELSE 'We've now started the hold event
164.                 MBS = MBS OR 32 * 2 ^ ButtonDown
165.             END IF
166.         END IF
167.     END IF
168. END FUNCTION 'MBS%
169.  
170.  
171. FUNCTION PyT (var1 AS V2, var2 AS V2)
172.  
173.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
174.  
175. END FUNCTION 'PyT
176.  
177.  
178. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
179.  
180.     var.x = var.x + (var2.x * var3) '                           add vector (or a scalar multiple of) var2 to var
181.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
182.  
183. END SUB 'Add_Vector
184.  
185.  
186. FUNCTION VecDot (var AS V2, var2 AS V2)
187.  
188.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
189.  
190. END FUNCTION 'VecDot
191.  
192.  
193. SUB VecMult (vec AS V2, multiplier AS SINGLE)
194.  
195.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
196.     vec.y = vec.y * multiplier
197.  
198. END SUB 'Vec_Mult
199.  
200.  
201. SUB VecNorm (var AS V2)
202.  
203.     m = PyT(origin, var)
204.     IF m = 0 THEN
205.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
206.     ELSE
207.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
208.     END IF
209.  
210. END SUB 'VecNorm
211.  

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 21, 2021, 12:19:10 pm

@OldMoses was that Berchek paper the same you gave link to that I used?

Oh yeah, I see at end 2009 Chad Berchek. It worked for me except for the problem of hanging when balls overlap. I am still trying to figure out how to get rid of that specially on breaks in Pool.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 21, 2021, 12:41:09 pm

It's the same issue I had with mine, the breaks, tight groups and/or high speeds made weird things happen. At least I seem to have a good handle, provisionally speaking, on how the balls are supposed to move now.


EDIT:
I'm thinking that if one were to obtain the magnitude of the fastest ball and use that as the upper end of a loop counter, you could advance the fast ball one unit vector at a time, while using FUNCTION map! to advance the slower ball by the proper amount, you could determine more precise ball (x, y) positions at impact. Use those points as temporary positions to get the exit vectors and then finish out the movement along those new vectors. I used a similar system for planet/ship collisions in my starship program where both entities were in motion.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 22, 2021, 12:26:43 am

The dashed lines are the exit vectors.   Dotted line is the strike vector. solid lines are the ball headings. 

example
red  @ (0, 0)  along <0, 100>  exits along <100, -1>
cyan @ (-100, 100)  along <100, 0>  exits along <0, 100>

Exit vectors are correct.   The -1 looks to be a rounding error.

Now move cyan ball to

red  @ (0, 0)  along <0, 100>  exits along <100, 100>
cyan @ (-100, 0)  along <100, 0>  exits along <0, 0>

And a very interesting result. The cyan ball comes to a complete stop and the red ball speeds up. Intuitive guess is the red ball should be travelling twice as fast (200) but the red ball exit velocity is

(100^ + 100^2 ).5 = 141.421356

Solving for kinetic energy
                                     red             cyan
141.421356 ^ 2 / 2 =   100^2 /2 + 100^2 /2   =  10000

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 22, 2021, 07:27:39 am

Quote from: NOVARSEG on May 22, 2021, 12:26:43 am

example
red  @ (0, 0)  along <0, 100>  exits along <100, -1>
cyan @ (-100, 100)  along <100, 0>  exits along <0, 100>

Exit vectors are correct.   The -1 looks to be a rounding error.

Yeah, for the actual vector components I'm using SINGLE, but the data bar is using INT on the numbers. I imagine it has oodles of rounding issues.

Quote from: NOVARSEG on May 22, 2021, 12:26:43 am

Now move cyan ball to

red  @ (0, 0)  along <0, 100>  exits along <100, 100>
cyan @ (-100, 0)  along <100, 0>  exits along <0, 0>

And a very interesting result. The cyan ball comes to a complete stop and the red ball speeds up. Intuitive guess is the red ball should be travelling twice as fast (200) but the red ball exit velocity is

Now that seems appropriate, given that the cyan is striking red square while red is getting T-boned. Red retains its unit tangent component (along Y) and receives all the energy from cyan along the unit normal component (along X). Red is imparting zero force along its unit tangent in X to Cyan. Ergo, cyan loses all momentum.

In trying to set up the scenarios you tested, I've had some challenge getting things to set on the exact numbers. Mouse control is a bit coarse. So I added some _KEYDOWNs to allow finer control.

"r" to choose red ball
"c" to choose cyan ball
, or the last ball chosen by the mouse will be active
arrow keys will move the chosen ball in x/y
"aswd" keys will move the input vector tail in x/y

Code: QB64: [Select]

1. $COLOR:32
2. TYPE V2
3.     x AS SINGLE
4.     y AS SINGLE
5. END TYPE
6.  
7. TYPE ball
8.     cn AS STRING * 4 '                                          ball name by color
9.     c AS _UNSIGNED LONG '                                       color
10.     p AS V2 '                                                   position
11.     m AS V2 '                                                   movement (pre-contact) incoming
12.     x AS V2 '                                                   vector of post contact movement
13.     s AS INTEGER '                                              magnitude of movement
14. END TYPE
15.  
16. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
17. DIM mouse AS V2
18. DIM b(1) AS ball
19. DIM SHARED AS V2 origin
20. origin.x = 0: origin.y = 0
21. b(0).c = Red: b(0).cn = "red"
22. b(1).c = Cyan: b(1).cn = "cyan"
23.  
24. SCREEN _NEWIMAGE(600, 600, 32)
25. DO: LOOP UNTIL _SCREENEXISTS
26. _SCREENMOVE 10, 10
27. WINDOW (-300, 300)-(300, -300)
28.  
29. 'starting state
30. b(0).m.x = 0: b(0).m.y = -100 '                                 reds approach vector
31. b(0).s = PyT(origin, b(0).m) '                                  reds magnitude (speed or force)
32. b(1).m.x = 100: b(1).m.y = -100 '                               cyans approach vector
33. b(1).s = PyT(origin, b(1).m) '                                  cyans magnitude (speed or force)
34.  
35. b(0).p.x = 30: b(0).p.y = 10
36. b(1).p.x = -17: b(1).p.y = 0
37.  
38. DO
39.     ms = MBS '                                                  process mouse actions dragging endpoints
40.     IF ms AND 64 THEN
41.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
42.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
43.         FOR x = 0 TO 1
44.             FOR y = 0 TO 1
45.                 ds! = PyT(vertex(x, y), mouse)
46.                 IF ds! < ballradius * .5 THEN i = x: j = y
47.             NEXT y
48.         NEXT x
49.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
50.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
51.                 b(i).p = mouse
52.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
53.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
54.         END SELECT
55.     ELSE
56.         IF _KEYDOWN(114) THEN i = 0
57.         IF _KEYDOWN(99) THEN i = 1
58.         IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
59.         IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
60.         IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
61.         IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
62.         IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
63.         IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
64.         IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
65.         IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
66.         _DELAY .1
67.     END IF
68.  
69.     'START OF COLLISION MATHEMATICS SECTION
70.     ballradius = PyT(b(0).p, b(1).p) / 2
71.     CLS
72.  
73.     FOR bn = 0 TO 1
74.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
75.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
76.     NEXT bn
77.  
78.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
79.     B2BCollision b(0), b(1)
80.     'END OF COLLISION MATHEMATICS SECTION
81.  
82.     'graphic representation
83.     FOR grid = -300 TO 300 STEP 20
84.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
85.         LINE (grid, 300)-(grid, -300), c& 'Gray
86.         LINE (-300, grid)-(300, grid), c& ' Gray
87.     NEXT grid
88.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
89.     FOR dr = 0 TO 1
90.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c
91.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x - b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
92.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
93.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
94.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
95.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">"
96.         _PRINTSTRING (0, 567 + (16 * dr)), b$
97.     NEXT dr
98.  
99.     _LIMIT 50
100.     _DISPLAY
101. LOOP UNTIL _KEYDOWN(27)
102. END
103.  
104.  
105. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
106.  
107.     DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
108.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
109.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
110.     bnci1 = VecDot(un, ball1.m) '
111.     bnci2 = VecDot(un, ball2.m) '
112.     btci1 = VecDot(ut, ball1.m) '
113.     btci2 = VecDot(ut, ball2.m) '
114.  
115.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
116.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
117.  
118.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
119.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
120.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
121.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
122.  
123.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
124.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
125.  
126. END SUB 'B2BCollision
127.  
128.  
129. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
130.  
131.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
132.  
133. END FUNCTION 'map!
134.  
135.  
136. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
137.     STATIC StartTimer AS _FLOAT
138.     STATIC ButtonDown AS INTEGER
139.     STATIC ClickCount AS INTEGER
140.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
141.     '                          Down longer counts as a HOLD event.
142.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
143.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
144.         SELECT CASE SGN(_MOUSEWHEEL)
145.             CASE 1: MBS = MBS OR 512
146.             CASE -1: MBS = MBS OR 1024
147.         END SELECT
148.     WEND
149.  
150.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
151.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
152.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
153.  
154.     IF StartTimer = 0 THEN
155.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
156.             ButtonDown = 1: StartTimer = TIMER(0.01)
157.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
158.         ELSEIF _MOUSEBUTTON(2) THEN
159.             ButtonDown = 2: StartTimer = TIMER(0.01)
160.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
161.         ELSEIF _MOUSEBUTTON(3) THEN
162.             ButtonDown = 3: StartTimer = TIMER(0.01)
163.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
164.         END IF
165.     ELSE
166.         BD = ButtonDown MOD 3
167.         IF BD = 0 THEN BD = 3
168.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
169.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
170.         ELSE
171.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
172.                 MBS = 0: ButtonDown = 0: StartTimer = 0
173.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
174.             ELSE 'We've now started the hold event
175.                 MBS = MBS OR 32 * 2 ^ ButtonDown
176.             END IF
177.         END IF
178.     END IF
179. END FUNCTION 'MBS%
180.  
181.  
182. FUNCTION PyT (var1 AS V2, var2 AS V2)
183.  
184.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
185.  
186. END FUNCTION 'PyT
187.  
188.  
189. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
190.  
191.     var.x = var.x + (var2.x * var3) '                           add vector (or a scalar multiple of) var2 to var
192.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
193.  
194. END SUB 'Add_Vector
195.  
196.  
197. FUNCTION VecDot (var AS V2, var2 AS V2)
198.  
199.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
200.  
201. END FUNCTION 'VecDot
202.  
203.  
204. SUB VecMult (vec AS V2, multiplier AS SINGLE)
205.  
206.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
207.     vec.y = vec.y * multiplier
208.  
209. END SUB 'Vec_Mult
210.  
211.  
212. SUB VecNorm (var AS V2)
213.  
214.     m = PyT(origin, var)
215.     IF m = 0 THEN
216.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
217.     ELSE
218.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
219.     END IF
220.  
221. END SUB 'VecNorm
222.  

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 22, 2021, 07:20:55 pm

Well some folks might have big balls, but I've had teleporting balls and now I have magnetic balls. :D

Anyway, this is the result of plugging SUB B2BCollision into my billiards project. The basic issue has to be impact point control, but I have to say, I found the bug much more amusing this time.

left click to shoot the cue ball, right click to re-rack em, esc to quit.

Code: QB64: [Select]

1. $COLOR:32
2.  
3. 'ball colors 1 yellow 2 blue 3 red 4 purple 5 orange 6 green 7 maroon 8 black
4. '9 yellow/s 10 blue/s 11 red/s 12 purple/s 13 orange/s 14 green/s 15 maroon/s
5.  
6. TYPE V2
7.     x AS SINGLE
8.     y AS SINGLE
9. END TYPE
10.  
11. TYPE ball
12.     sunk AS _BYTE '                                             has ball been sunk true/false
13.     im AS _BYTE '                                               impact register
14.     c AS _UNSIGNED LONG '                                       ball color
15.     p AS V2 '                                                 position vector
16.     d AS V2 '                                                 direction vector
17.     n AS V2 '                                                 normalized direction vector
18.     s AS SINGLE '                                               speed
19.     r AS _BYTE '                                                rack position
20. END TYPE
21.  
22. DIM SHARED xtable AS INTEGER
23. DIM SHARED ytable AS INTEGER
24. DIM SHARED bsiz AS INTEGER '                                    radius of ball
25. DIM SHARED bsiz2 AS INTEGER '                                   ball diameter or sphere of contact
26. DIM SHARED bl(15) AS ball '                                     ball data
27. DIM SHARED bnum(15) AS LONG
28. DIM SHARED smack(15, 16) AS _BYTE
29. DIM SHARED origin AS V2
30. origin.x = 0: origin.y = 0
31.  
32. 'Set the table size
33. IF _DESKTOPWIDTH > _DESKTOPHEIGHT * 1.6 THEN
34.     xtable = _DESKTOPWIDTH - 100: ytable = xtable / 2
35. ELSE
36.     ytable = _DESKTOPHEIGHT - 80: xtable = ytable * 2
37. END IF
38.  
39. bsiz = INT(((xtable / 118.1102) * 2.375) / 2) '                 size balls to table
40. bsiz2 = bsiz * 2
41.  
42. RANDOMIZE TIMER
43. RESTORE hue
44. FOR x = 0 TO 15
45.     READ bl(x).c
46. NEXT x
47.  
48. MakeBalls
49. RackEmUp
50. bl(0).p.y = INT(ytable * .5) '                                  position the cue
51. bl(0).p.x = INT(xtable * .75)
52.  
53.  
54. a& = _NEWIMAGE(xtable, ytable, 32)
55. shot& = _NEWIMAGE(xtable, ytable, 32)
56. _DEST a&: SCREEN a&
57. DO: LOOP UNTIL _SCREENEXISTS
58. _SCREENMOVE 5, 5
59. COLOR , &HFF3AAF61
60. 'set up the table
61. CLS
62. FOR x = 0 TO 2
63.     LINE (x, x)-(xtable - x, ytable - x), Black, B
64.     FCirc xtable * .75, ytable * .5, 5, Gray, Gray
65.     FCirc xtable * .75, ytable * .5, 2, White, White
66. NEXT x
67. DO
68.     CLS
69.     FOR x = 0 TO 15
70.         VecAdd bl(x).p, bl(x).d, 1
71.         VecMult bl(x).d, .99
72.         ColCheck x
73.         _PUTIMAGE (INT(bl(x).p.x) - CINT(_WIDTH(bnum(x)) / 2), INT(bl(x).p.y) - CINT(_HEIGHT(bnum(x)) / 2)), bnum(x), a&
74.     NEXT x
75.  
76.     ms = MBS%
77.     IF ms AND 1 THEN
78.         bl(0).d.x = (bl(0).p.x - _MOUSEX) * 0.05
79.         bl(0).d.y = (bl(0).p.y - _MOUSEY) * 0.05
80.     END IF
81.     IF ms AND 2 THEN
82.         BallStop
83.         bl(0).p.y = INT(ytable * .5)
84.         bl(0).p.x = INT(xtable * .75)
85.         RackEmUp
86.     END IF
87.     LINE (_MOUSEX, _MOUSEY)-(CINT(bl(0).p.x), CINT(bl(0).p.y))
88.     'slope of target line
89.     pathx = CINT(bl(0).p.x) - _MOUSEX: pathy = CINT(bl(0).p.y) - _MOUSEY
90.     LINE (bl(0).p.x, bl(0).p.y)-(pathx * 1000, pathy * 1000), Blue
91.     _DISPLAY
92.     _LIMIT 100 '100 seems good
93. LOOP UNTIL _KEYDOWN(27)
94.  
95. END
96.  
97. '                                                               DATA SECTION
98. hue:
99. DATA 4294967295,4294967040,4278190335,4294901760,4286578816,4294944000,4278222848,4286578688
100. DATA 4278190080,4294967040,4278190335,4294901760,4286578816,4294944000,4278222848,4286578688
101.  
102. start:
103. DATA 1,2,15,14,8,3,4,6,11,13,12,7,9,10,5,0
104.  
105. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
106.  
107.     DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
108.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
109.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
110.     bnci1 = VecDot(un, ball1.d) '                               ball 1 normal component of input velocity
111.     bnci2 = VecDot(un, ball2.d) '                               ball 2 normal component of input velocity
112.     btci1 = VecDot(ut, ball1.d) '                               ball 1 tangent component of input velocity
113.     btci2 = VecDot(ut, ball2.d) '                               ball 2 tangent component of input velocity
114.  
115.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
116.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
117.  
118.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
119.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
120.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
121.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
122.  
123.     ball1.d = ncomp1: VecAdd ball1.d, tcomp1, 1 '               add normal and tangent exit vectors
124.     ball2.d = ncomp2: VecAdd ball2.d, tcomp2, 1 '               add normal and tangent exit vectors
125.  
126. END SUB 'B2BCollision
127.  
128.  
129. SUB BallStop
130.  
131.     FOR x = 0 TO 15
132.         bl(x).d = origin
133.     NEXT x
134.  
135. END SUB 'BallStop
136.  
137.  
138. SUB ColCheck (var AS INTEGER)
139.  
140.     'check for ball in displacement radius
141.     disp = SQR(bl(var).d.x * bl(var).d.x + bl(var).d.y * bl(var).d.y) 'vector magnitude for this iteration
142.     FOR x = 0 TO 15
143.         IF x <> var THEN '                                      won't collide with self so skip self check
144.             IF NOT bl(var).sunk THEN '                          if ball not already out of play
145.                 dist = PyT(bl(var).p, bl(x).p) '                calculate distance between var and x
146.                 IF dist - bsiz2 < disp THEN '                   if ball x is within reach of magnitude
147.                     'check to see if there is an impact point-  Ray trace routine
148.                     DIM neari AS V2
149.                     'DIM strike AS V2
150.                     'DIM strikeorth AS V2
151.                     'DIM striker AS V2
152.                     'DIM strikee AS V2
153.                     'DIM orthox AS V2
154.                     'DIM orthoy AS V2
155.  
156.                     'Using a variation of the collision routine from CTVector.bas
157.                     'but the damn thing isn't working as envisioned... well it didn't work there either.
158.                     dx = bl(var).p.x - bl(x).p.x
159.                     dy = bl(var).p.y - bl(x).p.y
160.                     A## = (bl(var).d.x * bl(var).d.x) + (bl(var).d.y * bl(var).d.y) 'displacement range
161.                     B## = 2 * bl(var).d.x * dx + 2 * bl(var).d.y * dy
162.                         C## = (bl(x).p.x * bl(x).p.x) + (bl(x).p.y * bl(x).p.y) + (bl(var).p.x * bl(var).p.x)_
163.                              + (bl(var).p.y * bl(var).p.y) + -2 * (bl(x).p.x * bl(var).p.x + bl(x).p.y * bl(var).p.y) - (bsiz2 * bsiz2)
164.                     disabc## = (B## * B##) - 4 * A## * C##
165.                     IF disabc## <= 0 THEN 'let's make this <=, since a tangent brush by would ideally not move the ball
166.                     ELSE
167.                         t## = (-B## - ((B## * B##) - 4 * A## * C##) ^ .5) / (2 * A##) 'near intersect quadratic gives percentage of displacement to contact
168.                         neari.x = bl(var).p.x + t## * bl(var).d.x: neari.y = bl(var).p.y + t## * bl(var).d.y 'contact point
169.                         'now that we have a contact point, we can proceed to deflect the displacements of var and x
170.  
171.                         'Not sure yet how to get impact points but we can replace the following with SUB B2BCollision
172.                         'bl(var).p = neari
173.                         ''// get strike angle unit vector
174.                         'strike.x = bl(x).p.x - neari.x: strike.y = bl(x).p.y - neari.y
175.                         ''// get the two orthogonal vectors to strike
176.                         'orthox.x = -strike.y: orthox.y = strike.x
177.                         'orthoy.x = strike.y: orthoy.y = -strike.x
178.                         ''// add orthogonals to impact point
179.                         'VecAdd orthox, neari, 1: VecAdd orthoy, neari, 1
180.                         ''// add present var displacement to ortho's
181.                         'VecAdd orthox, bl(var).d, 1: VecAdd orthoy, bl(var).d, 1
182.                         ''// check distances and compare, using farthest one for striker's new vector
183.                         'vox = PyT(orthox, bl(x).p): voy = PyT(orthoy, bl(x).p)
184.                         'IF vox > voy THEN
185.                         '    strikeorth.x = -strike.y: strikeorth.y = strike.x
186.                         'ELSEIF vox = voy THEN
187.                         '    strikeorth = strike
188.                         'ELSE
189.                         '    strikeorth.x = strike.y: strikeorth.y = -strike.x
190.                         'END IF
191.                         ''// normalize strike vectors
192.                         'VecNorm strike: VecNorm strikeorth
193.  
194.  
195.                         'striker = bl(var).d: VecNorm striker '                  get striker unit vector
196.                         'strikee = bl(x).d: VecNorm strikee '                    get strikee unit vector
197.                         'dot = striker.x * strike.x + striker.y * strike.y '     apply to struck balls displacement magnitude along strike
198.                         'dotback = 1 - dot '                                     apply to striking balls displacement along orthogonal of strike
199.  
200.                         ''get proportion of energy transfer and add it to existing vector of unit x
201.                         'VecMult strike, 0.99 * dot * PyT(origin, bl(var).d)
202.                         'VecAdd bl(x).d, strike, 1
203.                         ''do the same with var using balance of energy
204.                         'VecMult strikeorth, 0.99 * dotback * PyT(origin, bl(var).d)
205.                         ''VecAdd bl(var).d, strikeorth, 1
206.                         'bl(var).d = strikeorth
207.                         ''bl(var).d.x = -bl(var).d.x: bl(var).d.y = -bl(var).d.y
208.                         B2BCollision bl(var), bl(x)
209.                     END IF 'disabc <= 0
210.                 END IF 'dist < disp
211.             END IF 'NOT bl(var).sunk
212.         END IF 'x <> var
213.     NEXT x
214.  
215.     'wall bounces
216.     IF bl(var).p.x < bsiz OR bl(var).p.x > xtable - bsiz THEN
217.         bl(var).d.x = -bl(var).d.x
218.         IF bl(var).p.x < bsiz THEN '                            if beyond left edge
219.             bl(var).p.y = bl(var).p.y - (bl(var).d.y * ((bl(var).p.x - bsiz) / bl(var).d.x))
220.             bl(var).p.x = bsiz
221.         END IF
222.         IF bl(var).p.x > xtable - bsiz THEN '                   if beyond right edge
223.             bl(var).p.y = bl(var).p.y - (bl(var).d.y * ((bl(var).p.x - xtable + bsiz) / bl(var).d.x))
224.             bl(var).p.x = xtable - bsiz
225.         END IF
226.     END IF
227.     IF bl(var).p.y < bsiz OR bl(var).p.y > ytable - bsiz THEN
228.         bl(var).d.y = -bl(var).d.y
229.         IF bl(var).p.y < bsiz THEN '                            if beyond top edge
230.             bl(var).p.x = bl(var).p.x - (bl(var).d.x * ((bl(var).p.y - bsiz) / bl(var).d.y))
231.             bl(var).p.y = bsiz
232.         END IF
233.         IF bl(var).p.y > ytable - bsiz THEN '                   if beyond bottom edge
234.             bl(var).p.x = bl(var).p.x - (bl(var).d.x * ((bl(var).p.y - ytable + bsiz) / bl(var).d.y))
235.             bl(var).p.y = ytable - bsiz
236.         END IF
237.     END IF
238.  
239. END SUB 'ColCheck
240.  
241.  
242. SUB FCirc (CX AS INTEGER, CY AS INTEGER, RR AS INTEGER, C AS _UNSIGNED LONG, C2 AS _UNSIGNED LONG)
243.     DIM R AS INTEGER, RError AS INTEGER '                       SMcNeill's circle fill
244.     DIM X AS INTEGER, Y AS INTEGER
245.  
246.     R = ABS(RR)
247.     RError = -R
248.     X = R
249.     Y = 0
250.     IF R = 0 THEN PSET (CX, CY), C: EXIT SUB
251.     LINE (CX - X, CY)-(CX + X, CY), C, BF
252.     WHILE X > Y
253.         RError = RError + Y * 2 + 1
254.         IF RError >= 0 THEN
255.             IF X <> Y + 1 THEN
256.                 LINE (CX - Y, CY - X)-(CX + Y, CY - X), C2, BF 'these two need white here for 9-15 balls
257.                 LINE (CX - Y, CY + X)-(CX + Y, CY + X), C2, BF
258.             END IF
259.             X = X - 1
260.             RError = RError - X * 2
261.         END IF
262.         Y = Y + 1
263.         LINE (CX - X, CY - Y)-(CX + X, CY - Y), C, BF
264.         LINE (CX - X, CY + Y)-(CX + X, CY + Y), C, BF
265.     WEND
266. END SUB 'FCirc
267.  
268.  
269. SUB LoadColArray
270.  
271.     FOR a = 0 TO 15
272.         FOR b = 0 TO 16
273.  
274.     NEXT b, a
275.  
276. END SUB 'LoadColArray
277.  
278.  
279. SUB MakeBalls
280.  
281.     FOR x = 0 TO 15
282.         'make ball images here
283.         bnum(x) = _NEWIMAGE(bsiz * 2 + 4, bsiz * 2 + 4, 32)
284.         _DEST bnum(x)
285.         IF x = 0 THEN '                                         Cue ball
286.             FCirc INT(_WIDTH(bnum(x)) / 2), INT(_HEIGHT(bnum(x)) / 2), bsiz, bl(x).c, bl(x).c
287.             CIRCLE (_WIDTH(bnum(x)) / 2, _HEIGHT(bnum(x)) / 2), bsiz + 1, Black
288.         ELSE
289.             'Solids or stripes
290.             IF x <= 8 THEN
291.                 FCirc INT(_WIDTH(bnum(x)) / 2), INT(_HEIGHT(bnum(x)) / 2), bsiz, bl(x).c, bl(x).c ' solid
292.             ELSE
293.                 FCirc INT(_WIDTH(bnum(x)) / 2), INT(_HEIGHT(bnum(x)) / 2), bsiz, bl(x).c, White '   stripe
294.             END IF
295.             FCirc INT(_WIDTH(bnum(x)) / 2), INT(_HEIGHT(bnum(x)) / 2), bsiz - 5, White, White 'number circle
296.             CIRCLE (_WIDTH(bnum(x)) / 2, _HEIGHT(bnum(x)) / 2), bsiz + 1, Black
297.             n$ = _TRIM$(STR$(x))
298.             t& = _NEWIMAGE(16, 16, 32)
299.             _DEST t&
300.             COLOR Black
301.             _PRINTMODE _KEEPBACKGROUND
302.             IF LEN(n$) > 1 THEN a = 0 ELSE a = 4
303.             _PRINTSTRING (a, 0), n$, t&
304.             _DEST bnum(x)
305.             _PUTIMAGE (8, 8)-(_WIDTH(bnum(x)) - 8, _HEIGHT(bnum(x)) - 8), t&, bnum(x)
306.             _FREEIMAGE t&
307.         END IF
308.     NEXT x
309.  
310. END SUB 'MakeBalls
311.  
312.  
313. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
314.     STATIC StartTimer AS _FLOAT
315.     STATIC ButtonDown AS INTEGER
316.     STATIC ClickCount AS INTEGER
317.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
318.     '                          Down longer counts as a HOLD event.
319.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
320.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
321.         SELECT CASE SGN(_MOUSEWHEEL)
322.             CASE 1: MBS = MBS OR 512
323.             CASE -1: MBS = MBS OR 1024
324.         END SELECT
325.     WEND
326.  
327.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
328.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
329.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
330.  
331.     IF StartTimer = 0 THEN
332.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
333.             ButtonDown = 1: StartTimer = TIMER(0.01)
334.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
335.         ELSEIF _MOUSEBUTTON(2) THEN
336.             ButtonDown = 2: StartTimer = TIMER(0.01)
337.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
338.         ELSEIF _MOUSEBUTTON(3) THEN
339.             ButtonDown = 3: StartTimer = TIMER(0.01)
340.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
341.         END IF
342.     ELSE
343.         BD = ButtonDown MOD 3
344.         IF BD = 0 THEN BD = 3
345.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
346.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
347.         ELSE
348.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
349.                 MBS = 0: ButtonDown = 0: StartTimer = 0
350.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
351.             ELSE 'We've now started the hold event
352.                 MBS = MBS OR 32 * 2 ^ ButtonDown
353.             END IF
354.         END IF
355.     END IF
356. END FUNCTION 'MBS%
357.  
358.  
359. FUNCTION PyT (var1 AS V2, var2 AS V2)
360.  
361.     PyT = _HYPOT(ABS(var1.x - var2.x), ABS(var1.y - var2.y)) '  distances and magnitudes
362.  
363. END FUNCTION 'PyT
364.  
365.  
366. SUB RackEmUp
367.  
368.     yoff = bsiz2 + 4
369.     xoff = SQR((yoff / 2) * (yoff / 2) + yoff * yoff)
370.  
371.     RESTORE start
372.     FOR rank = 1 TO 5
373.         FOR b = 1 TO rank
374.             READ k
375.             bl(k).p.x = (.25 * xtable) - (xoff * (rank - 1))
376.             bl(k).p.y = (.5 * ytable) - ((rank - 1) * (.5 * yoff)) + ((b - 1) * yoff)
377.         NEXT b
378.     NEXT rank
379.  
380. END SUB 'RackEmUp
381.  
382.  
383. SUB VecAdd (var AS V2, var2 AS V2, var3 AS INTEGER)
384.  
385.     var.x = var.x + (var2.x * var3) '                           add (or subtract) two vectors defined by unitpoint
386.     var.y = var.y + (var2.y * var3) '                           var= base vector, var2= vector to add
387.  
388. END SUB 'VecAdd
389.  
390.  
391. FUNCTION VecDot (var AS V2, var2 AS V2)
392.  
393.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
394.  
395. END FUNCTION 'VecDot
396.  
397.  
398. SUB VecMult (vec AS V2, multiplier AS SINGLE)
399.  
400.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
401.     vec.y = vec.y * multiplier
402.  
403. END SUB 'VecMult
404.  
405. SUB VecNorm (var AS V2)
406.  
407.     m = SQR(var.x * var.x + var.y * var.y) '                    convert var to unit vector
408.     var.x = var.x / m
409.     var.y = var.y / m
410.  
411. END SUB 'VecNorm
412.  
413.  

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 22, 2021, 09:14:54 pm

@OldMoses

Well if this is wrong I don't want to be right, I like the look of your balls, I'm still trying to figure how you get the stripe but going with images is good. I could do it with lines and Paint I guess.

For sticky, balls I've found if you back the collided balls back to collision kiss point then calculate the vectors they don't stick.

The ball angles look pretty good too!

Update: Oh you changed the Fcirc sub to make stripes.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 22, 2021, 09:54:49 pm

Once upon a time, I wanted to figure out how Steve's circle fill worked, and so I put a couple sleep commands in and watched it progress. When I started the billiards thing, it seemed the natural solution. It might even be good with rotozoom.

I'm trying to come up with a handler that will do a break, but I'm getting a nagging suspicion that I might have to do something recursive to deal with potential multiple strikes in a single displacement loop. Never tried anything like that before...beyond here there be dragons...

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 23, 2021, 03:44:35 am

Ha! I stopped overlapping balls and now cue ball goes through rack like Moses parting the Red Sea ;-)) crazy!

That wasn't my hanging problem because it still does.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 23, 2021, 03:51:30 am

Oldmoses

Quote

b(0).s = PyT(origin, b(0).m)

what does  variable "origin" refer to ?

Quote

TYPE V2
    x AS SINGLE
    y AS SINGLE
END TYPE

DIM SHARED origin AS V2

Quote

origin.x = 0: origin.y = 0

Ok I think Ive answered my own question

Quote

FUNCTION PyT (var1 AS V2, var2 AS V2)
 
    PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
 
END FUNCTION 'PyT

the .x or .y are supplied in the function.   I really don't get the dot stuff   The only advantage is a smaller DIM list.    I find the dot stuff harder to read

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 23, 2021, 07:40:59 am

PyT is my method of using pythagorean theorem for obtaining speeds/magnitudes of vectors AND distances between points. I usually define an "origin" so that I can do the former, and simply plug in the two points if I'm after the later.

In this application, PyT only handles the V2 type, but in another of my projects it does both R2 and R3 vectors by accepting a third parameter telling it which to work on.

Code: QB64: [Select]

1. FUNCTION PyT (var AS _BYTE, var1 AS V3, var2 AS V3)
2.  
3.     SELECT CASE var   'find distance/magnitude between 2D or 3D points
4.         CASE IS = 2
5.             PyT = _HYPOT(var1.pX - var2.pX, var1.pY - var2.pY)
6.         CASE IS = 3
7.             PyT = _HYPOT(_HYPOT(var1.pX - var2.pX, var1.pY - var2.pY), var1.pZ - var2.pZ)
8.     END SELECT
9.  
10. END FUNCTION 'PyT
11.  

In some speed testing I've done, I've found the _HYPOT command to be as fast or faster than more traditional methods. I'm thinking of trying to optimize that some more, by ditching the SELECT CASE part.

On the Dot Product topic, I only became aware of it a few months ago and was shocked to discover that it is an indispensable tool for game design. Getting at this sort of programming problem without it is like changing a water pump without wrenches. You might be able to use other tools, but the job will be exponentially harder.

Dot Product is a way of multiplying two vectors together which results in a non-vector number (scalar). The result gives one the ability to determine how much of one vector is "projected" onto another. In our case it is the ability to obtain the portion of red ball's force that is applied directly at cyan ball and what is directed toward red balls exit motion, and of course the same applied from cyan to red and cyan's exit.

  [ This attachment cannot be displayed inline in 'Print Page' view ]  

You needn't worry about the trig formula in the picture, that's mainly for obtaining a dot product when theta is a known quantity, which we're not concerned with in this topic. It might also be apparent, by the picture, that dot product is also closely related to the pythagorean theorem.

In ball collision we are primarily concerned with how much of the unit normal and unit tangent vectors are applied by a collision, which dot product supplies quite well.

Dot Product simply takes the components of two vectors, multiplies them together and sums the results. Example, two vectors A and B, dotted together are:

 A dot B = A.x * B.x + A.y * B.y    'and that doesn't get much simpler for what can be done with it...

and if you're dealing in 3D:

A dot B = A.x * B.x + A.y * B.y + A.z * B.z

Which is exactly what SUB VecDot does in my code, for our 2D representation. The order doesn't matter, but it is good to convert one of the vectors you're projecting into a unit vector, if vector projection is your main purpose. That's what my SUB VecNorm does to the "strike" (aka unit normal), and it's orthogonal (aka unit tangent). BTW, you were correct, I didn't need different strikes & orthogonals for each ball. One was sufficient.

The number that dot product returns will also tell you how the vectors are oriented to each other. A negative dot product indicates vectors angled away from each other (obtuse), a dot product of 0 indicates vectors that are perpendicular, and a positive dot product are vectors that subtend an acute angle. The closest thing to a mathematical multi-tool that I've seen so far. Once you learn it, you'll be looking for places to use it.

This guy does a pretty good job of presenting Dot Product:

&t=31s

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 23, 2021, 01:57:50 pm

Going back to the interactive analysis tool, I've added fine dashed lines to represent the normal and tangent vectors that influence how each ball's position and incoming vector affect the final exit vector. Each is colored by where its influence derives from.

Code: QB64: [Select]

1. $COLOR:32
2. TYPE V2
3.     x AS SINGLE
4.     y AS SINGLE
5. END TYPE
6.  
7. TYPE ball
8.     cn AS STRING * 4 '                                          ball name by color
9.     c AS _UNSIGNED LONG '                                       color
10.     p AS V2 '                                                   position
11.     m AS V2 '                                                   movement (pre-contact) incoming
12.     x AS V2 '                                                   vector of post contact movement
13.     s AS INTEGER '                                              magnitude of movement
14. END TYPE
15.  
16. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
17. DIM mouse AS V2
18. DIM b(1) AS ball
19. DIM SHARED AS V2 origin
20. origin.x = 0: origin.y = 0
21. b(0).c = Red: b(0).cn = "red"
22. b(1).c = Cyan: b(1).cn = "cyan"
23.  
24. SCREEN _NEWIMAGE(600, 600, 32)
25. DO: LOOP UNTIL _SCREENEXISTS
26. _SCREENMOVE 10, 10
27. WINDOW (-300, 300)-(300, -300)
28.  
29. 'starting state
30. b(0).m.x = 0: b(0).m.y = -100 '                                 reds approach vector
31. b(0).s = PyT(origin, b(0).m) '                                  reds magnitude (speed or force)
32. b(1).m.x = 100: b(1).m.y = -100 '                               cyans approach vector
33. b(1).s = PyT(origin, b(1).m) '                                  cyans magnitude (speed or force)
34.  
35. b(0).p.x = 30: b(0).p.y = 10
36. b(1).p.x = -17: b(1).p.y = 0
37.  
38. DO
39.     ms = MBS '                                                  process mouse actions dragging endpoints
40.     IF ms AND 64 THEN
41.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
42.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
43.         FOR x = 0 TO 1
44.             FOR y = 0 TO 1
45.                 ds! = PyT(vertex(x, y), mouse)
46.                 IF ds! < ballradius * .5 THEN i = x: j = y
47.             NEXT y
48.         NEXT x
49.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
50.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
51.                 b(i).p = mouse
52.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
53.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
54.         END SELECT
55.     ELSE
56.         IF _KEYDOWN(114) THEN i = 0
57.         IF _KEYDOWN(99) THEN i = 1
58.         IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
59.         IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
60.         IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
61.         IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
62.         IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
63.         IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
64.         IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
65.         IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
66.         _DELAY .1
67.     END IF
68.  
69.     'START OF COLLISION MATHEMATICS SECTION
70.     ballradius = PyT(b(0).p, b(1).p) / 2
71.     CLS
72.  
73.     FOR bn = 0 TO 1
74.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
75.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
76.     NEXT bn
77.  
78.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
79.     B2BCollision b(0), b(1)
80.     'END OF COLLISION MATHEMATICS SECTION
81.  
82.     'graphic representation
83.     FOR grid = -300 TO 300 STEP 20
84.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
85.         LINE (grid, 300)-(grid, -300), c& 'Gray
86.         LINE (-300, grid)-(300, grid), c& ' Gray
87.     NEXT grid
88.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
89.     FOR dr = 0 TO 1
90.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c
91.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x - b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
92.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111110011111100 'exit vector
93.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
94.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
95.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">"
96.         _PRINTSTRING (0, 567 + (16 * dr)), b$
97.     NEXT dr
98.  
99.     _LIMIT 50
100.     _DISPLAY
101. LOOP UNTIL _KEYDOWN(27)
102. END
103.  
104.  
105. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
106.  
107.     DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
108.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
109.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
110.     bnci1 = VecDot(un, ball1.m) '                               ball 1 normal component of input velocity
111.     bnci2 = VecDot(un, ball2.m) '                               ball 2 normal component of input velocity
112.     btci1 = VecDot(ut, ball1.m) '                               ball 1 tangent component of input velocity
113.     btci2 = VecDot(ut, ball2.m) '                               ball 2 tangent component of input velocity
114.  
115.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
116.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
117.  
118.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
119.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
120.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
121.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
122.  
123.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
124.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
125.  
126.     'The following is for graphic representation only and can be removed without affecting the SUB's purpose
127.     LINE (ball1.p.x, ball1.p.y)-(ball1.p.x + ncomp1.x, ball1.p.y + ncomp1.y), &H9F00FFFF, , &B0011001100110011
128.     LINE (ball1.p.x, ball1.p.y)-(ball1.p.x + tcomp1.x, ball1.p.y + tcomp1.y), &H9FFF7F7F, , &B0011001100110011
129.     LINE (ball2.p.x, ball2.p.y)-(ball2.p.x + ncomp2.x, ball2.p.y + ncomp2.y), &H9FFF7F7F, , &B0011001100110011
130.     LINE (ball2.p.x, ball2.p.y)-(ball2.p.x + tcomp2.x, ball2.p.y + tcomp2.y), &H9F00FFFF, , &B0011001100110011
131.  
132. END SUB 'B2BCollision
133.  
134.  
135. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
136.  
137.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
138.  
139. END FUNCTION 'map!
140.  
141.  
142. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
143.     STATIC StartTimer AS _FLOAT
144.     STATIC ButtonDown AS INTEGER
145.     STATIC ClickCount AS INTEGER
146.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
147.     '                          Down longer counts as a HOLD event.
148.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
149.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
150.         SELECT CASE SGN(_MOUSEWHEEL)
151.             CASE 1: MBS = MBS OR 512
152.             CASE -1: MBS = MBS OR 1024
153.         END SELECT
154.     WEND
155.  
156.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
157.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
158.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
159.  
160.     IF StartTimer = 0 THEN
161.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
162.             ButtonDown = 1: StartTimer = TIMER(0.01)
163.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
164.         ELSEIF _MOUSEBUTTON(2) THEN
165.             ButtonDown = 2: StartTimer = TIMER(0.01)
166.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
167.         ELSEIF _MOUSEBUTTON(3) THEN
168.             ButtonDown = 3: StartTimer = TIMER(0.01)
169.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
170.         END IF
171.     ELSE
172.         BD = ButtonDown MOD 3
173.         IF BD = 0 THEN BD = 3
174.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
175.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
176.         ELSE
177.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
178.                 MBS = 0: ButtonDown = 0: StartTimer = 0
179.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
180.             ELSE 'We've now started the hold event
181.                 MBS = MBS OR 32 * 2 ^ ButtonDown
182.             END IF
183.         END IF
184.     END IF
185. END FUNCTION 'MBS%
186.  
187.  
188. FUNCTION PyT (var1 AS V2, var2 AS V2)
189.  
190.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
191.  
192. END FUNCTION 'PyT
193.  
194.  
195. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
196.  
197.     var.x = var.x + (var2.x * var3) '                           add vector (or a scalar multiple of) var2 to var
198.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
199.  
200. END SUB 'Add_Vector
201.  
202.  
203. FUNCTION VecDot (var AS V2, var2 AS V2)
204.  
205.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
206.  
207. END FUNCTION 'VecDot
208.  
209.  
210. SUB VecMult (vec AS V2, multiplier AS SINGLE)
211.  
212.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
213.     vec.y = vec.y * multiplier
214.  
215. END SUB 'Vec_Mult
216.  
217.  
218. SUB VecNorm (var AS V2)
219.  
220.     m = PyT(origin, var)
221.     IF m = 0 THEN
222.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
223.     ELSE
224.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
225.     END IF
226.  
227. END SUB 'VecNorm
228.  

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 23, 2021, 06:26:58 pm

Found source of hanging problem, it wasn't overlapping balls, it was infinite loop of subtracting vectors of no length.

This code does cleanup overlapping balls before next shot, Pool 2 at Steve's forum:
https://qb64.freeforums.net/thread/150/pool?page=1&scrollTo=615

So OldMoses link to paper still works.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 23, 2021, 07:12:34 pm

That was outstanding, I ran the whole table with no issues at all.

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 23, 2021, 09:57:57 pm

Quote from: OldMoses on May 23, 2021, 07:12:34 pm

That was outstanding, I ran the whole table with no issues at all.

Holy balls the whole table!? Man I am just now converted to ball images like you and am patting myself on back at how much easier to see shots because I made all outside edges the same color.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 23, 2021, 10:18:44 pm

OldMoses

The position fine tuning works great.

red  @ (0, 0)  along <0, 100>  exits along <0, 100>
cyan @ (-100, 100)  along <-100, 0>  exits along <-100, 0>

"along <-100, 0>" is correct but the actual cyan vector on the screen shows
<100, 0>

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 24, 2021, 03:19:11 am

Quote from: NOVARSEG on May 23, 2021, 10:18:44 pm

"along <-100, 0>" is correct but the actual cyan vector on the screen shows
<100, 0>

I tried setting that up, but kept getting a slight rounding error on the cyan's exit vector. It would add a 1 in the Y axis

Is this similar to what you're getting?

  [ This attachment cannot be displayed inline in 'Print Page' view ]  

If so, I'd say it's working OK.

I've seen the math do some funny things with it, but that mostly happens when it's representing scenarios that are highly unlikely to happen in a real world ball collision. Such as when a slow ball gets around the backside of a fast one. In fact, I'm wondering if that might be the source of my magnetic ball bug.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 25, 2021, 09:50:41 pm

Code added to OldMoses program.
(some trig used)

Keys to rotate vector are z or x
keys to adjust vector magnitude (ball velocity) are c or v
Key to toggle red or cyan ball is b

As in the original code, the arrow keys move the ball positions.

rotate vector has an auto fine / coarse control.   hold down key longer, for coarse rotation and momentary for fine rotation

Don't know how this will interact with the mouse.
There might be a few bugs?

Will run on the older version of QB64 as well

Oh, If you hit the f key the ball parameters are saved in a file called
BALL STUFF.TXT and you can copy and paste from notepad etc.

Code: QB64: [Select]

1. 'Original code by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   position
14.     m AS V2 '                                                   movement (pre-contact) incoming
15.     x AS V2 '                                                   vector of post contact movement
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18. DIM TEXT(1) AS STRING
19. DIM RAD AS SINGLE
20. RAD = 0 ' * _PI
21. DIM c(1) AS STRING
22.  
23. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
24. DIM mouse AS V2
25. DIM b(1) AS ball
26. 'DIM SHARED AS V2 origin
27. DIM SHARED origin AS V2
28. origin.x = 0: origin.y = 0
29. b(0).c = Red: b(0).cn = "red"
30. b(1).c = Cyan: b(1).cn = "cyan"
31.  
32. SCREEN _NEWIMAGE(600, 600, 32)
33. DO: LOOP UNTIL _SCREENEXISTS
34. _SCREENMOVE 10, 10
35. WINDOW (-300, 300)-(300, -300)
36.  
37. 'starting state
38. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
39. b(0).s = PyT(origin, b(0).m)
40. 'b(0).s = _HYPOT(origin.x - b(0).m.x, origin.y - b(0).m.y) ' reds magnitude (speed or force)
41.  
42. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
43. b(1).s = PyT(origin, b(1).m)
44. 'b(1).s = _HYPOT(origin.x - b(1).m.x, origin.y - b(1).m.y) ' cyans magnitude (speed or force)
45.  
46. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
47. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
48. f3 = 0
49. DO
50.     CLS
51.     ms = MBS '                                                  process mouse actions dragging endpoints
52.     IF ms AND 64 THEN
53.         LOCATE 10, 10: PRINT "mousex"; mouse.x
54.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
55.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
56.         ' LOCATE 10, 10: PRINT "mousex"; mouse.x
57.         FOR x = 0 TO 1
58.             FOR y = 0 TO 1
59.                 ds! = PyT(vertex(x, y), mouse)
60.                 IF ds! < ballradius * .5 THEN i = x: j = y
61.             NEXT y
62.         NEXT x
63.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
64.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
65.                 b(i).p = mouse
66.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
67.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
68.         END SELECT
69.     ELSE
70.         'IF _KEYDOWN(114) THEN i = 0
71.         'IF _KEYDOWN(99) THEN i = 1
72.         IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
73.         IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
74.         IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
75.         IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
76.  
77.         'IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
78.         'IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
79.         'IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
80.         'IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
81.  
82.         '**************Code added by Novarseg
83.         'Vector rotation and vector magnitude adjustment using keyboard input
84.  
85.         I$ = INKEY$
86.         IF f3 = 0 THEN I$ = "b": f3 = 1
87.         IF I$ = "b" AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
88.         IF I$ = "b" AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
89.         LL1:
90.  
91.         IF I$ = "c" THEN 'increase vector magnitude
92.             mult = 1.01
93.             VecMult b(i).m, mult
94.         END IF
95.  
96.         IF I$ = "v" THEN 'decrease vector magnitude
97.             mult = 1.01 'should be div to avoid confusion, still works though
98.             VecDIV b(i).m, mult 'added a new sub
99.         END IF
100.  
101.  
102.         IF I$ = "z" THEN 'rotate vector counter clockwise
103.             IF RAD > _PI * 2 THEN RAD = 0
104.             'IF RAD < 0 THEN RAD = _PI * 2
105.             IF INKEY$ <> "z" THEN f1 = 0
106.             IF f1 = 0 THEN t1 = TIMER
107.             f1 = 1
108.             RAD = RAD + .005
109.             IF TIMER - t1 > 1.5 THEN
110.                 RAD = RAD + .05
111.             END IF
112.             signC = COS(RAD) * 1 / ABS(COS(RAD))
113.             signS = SIN(RAD) * 1 / ABS(SIN(RAD))
114.             b(i).s = PyT(origin, b(i).m)
115.             b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
116.             b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
117.  
118.         END IF
119.  
120.         IF I$ = "x" THEN 'rotate vector clockwise
121.  
122.             'IF RAD > _PI * 2 THEN RAD = 0
123.             IF RAD < 0 THEN RAD = _PI * 2
124.  
125.             IF INKEY$ <> "x" THEN f1 = 0
126.             IF f1 = 0 THEN t1 = TIMER
127.             f1 = 1
128.             RAD = RAD - .005
129.             IF TIMER - t1 > 1.5 THEN
130.                 RAD = RAD - .05
131.             END IF
132.             signC = COS(RAD) * 1 / ABS(COS(RAD))
133.             signS = SIN(RAD) * 1 / ABS(SIN(RAD))
134.             b(i).s = PyT(origin, b(i).m)
135.             b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
136.             b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
137.  
138.             '**************END Code added Novarseg
139.         END IF
140.  
141.         _DELAY .1
142.     END IF
143.     mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
144.  
145.  
146.     'START OF COLLISION MATHEMATICS SECTION
147.     ballradius = PyT(b(0).p, b(1).p) / 2
148.  
149.     FOR bn = 0 TO 1
150.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
151.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
152.     NEXT bn
153.  
154.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
155.     B2BCollision b(0), b(1)
156.     'END OF COLLISION MATHEMATICS SECTION
157.  
158.     'graphic representation
159.     FOR grid = -300 TO 300 STEP 20
160.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
161.         LINE (grid, 300)-(grid, -300), c& 'Gray
162.         LINE (-300, grid)-(300, grid), c& ' Gray
163.     NEXT grid
164.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
165.  
166.     FOR dr = 0 TO 1
167.  
168.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c
169.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
170.  
171.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
172.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
173.  
174.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
175.         _PRINTSTRING (0, 567 + (16 * dr)), SPACE$(80)
176.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
177.  
178.         _PRINTSTRING (0, 567 + (16 * dr)), b$
179.  
180.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
181.     NEXT dr
182.  
183.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
184.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
185.         PUT #1, , TEXT(0) 'NOVARSEG added this line
186.         PUT #1, , TEXT(1) 'NOVARSEG added this line
187.         CLOSE 'NOVARSEG added this line
188.     END IF 'NOVARSEG added this line
189.  
190.     _LIMIT 50
191.     _DISPLAY
192. LOOP UNTIL _KEYDOWN(27)
193. END
194.  
195.  
196. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
197.  
198.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
199.     DIM un AS V2
200.     DIM ut AS V2
201.     DIM ncomp1 AS V2
202.     DIM ncomp2 AS V2
203.     DIM tcomp1 AS V2
204.     DIM tcomp2 AS V2
205.  
206.  
207.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
208.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
209.     bnci1 = VecDot(un, ball1.m) '
210.     bnci2 = VecDot(un, ball2.m) '
211.     btci1 = VecDot(ut, ball1.m) '
212.     btci2 = VecDot(ut, ball2.m) '
213.  
214.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
215.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
216.  
217.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
218.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
219.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
220.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
221.  
222.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
223.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
224.  
225. END SUB 'B2BCollision
226.  
227.  
228. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
229.  
230.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
231.  
232. END FUNCTION 'map!
233.  
234.  
235. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
236.     STATIC StartTimer AS _FLOAT
237.     STATIC ButtonDown AS INTEGER
238.     STATIC ClickCount AS INTEGER
239.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
240.     '                          Down longer counts as a HOLD event.
241.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
242.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
243.         SELECT CASE SGN(_MOUSEWHEEL)
244.             CASE 1: MBS = MBS OR 512
245.             CASE -1: MBS = MBS OR 1024
246.         END SELECT
247.     WEND
248.  
249.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
250.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
251.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
252.  
253.     IF StartTimer = 0 THEN
254.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
255.             ButtonDown = 1: StartTimer = TIMER(0.01)
256.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
257.         ELSEIF _MOUSEBUTTON(2) THEN
258.             ButtonDown = 2: StartTimer = TIMER(0.01)
259.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
260.         ELSEIF _MOUSEBUTTON(3) THEN
261.             ButtonDown = 3: StartTimer = TIMER(0.01)
262.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
263.         END IF
264.     ELSE
265.         BD = ButtonDown MOD 3
266.         IF BD = 0 THEN BD = 3
267.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
268.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
269.         ELSE
270.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
271.                 MBS = 0: ButtonDown = 0: StartTimer = 0
272.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
273.             ELSE 'We've now started the hold event
274.                 MBS = MBS OR 32 * 2 ^ ButtonDown
275.             END IF
276.         END IF
277.     END IF
278. END FUNCTION 'MBS%
279.  
280.  
281. FUNCTION PyT (var1 AS V2, var2 AS V2)
282.  
283.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
284.  
285. END FUNCTION 'PyT
286.  
287.  
288. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
289.  
290.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
291.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
292.  
293. END SUB 'Add_Vector
294.  
295.  
296. FUNCTION VecDot (var AS V2, var2 AS V2)
297.  
298.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
299.  
300. END FUNCTION 'VecDot
301.  
302.  
303. SUB VecMult (vec AS V2, multiplier AS SINGLE)
304.  
305.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
306.     vec.y = vec.y * multiplier
307.  
308. END SUB 'Vec_Mult
309.  
310. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
311.  
312.     vec.x = vec.x / divisor
313.     vec.y = vec.y / divisor
314.  
315. END SUB 'VecDIV
316.  
317.  
318. SUB VecNorm (var AS V2)
319.  
320.     m = PyT(origin, var)
321.     IF m = 0 THEN
322.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
323.     ELSE
324.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
325.     END IF
326.  
327. END SUB 'VecNorm

example:
red  @ (0, 0)  along <0, 100>  exits along <200, 100>           
cyan @ (-100, 0)  along <-201, 0>  exits along <0, 0>  SELECTED

the cyan ball will come to a complete stop no matter how fast it's going


Added FULLSCREEN use q or w keys to adjust aspect ratio

Balls don't contact in FULLSCREEN mode, working on code to fix that

Code: QB64: [Select]

1. 'Original code by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   position
14.     m AS V2 '                                                   movement (pre-contact) incoming
15.     x AS V2 '                                                   vector of post contact movement
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18. DIM TEXT(1) AS STRING
19. DIM RAD AS SINGLE
20. RAD = 0 ' * _PI
21. DIM c(1) AS STRING
22.  
23. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
24. DIM mouse AS V2
25. DIM b(1) AS ball
26. 'DIM SHARED AS V2 origin
27. DIM SHARED origin AS V2
28. origin.x = 0: origin.y = 0
29. b(0).c = Red: b(0).cn = "red"
30. b(1).c = Cyan: b(1).cn = "cyan"
31.  
32. SCREEN _NEWIMAGE(600, 600, 32)
33. DO: LOOP UNTIL _SCREENEXISTS
34. _SCREENMOVE 10, 10
35. WINDOW (-300, 300)-(300, -300)
36. _FULLSCREEN
37.  
38. 'starting state
39. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
40. b(0).s = PyT(origin, b(0).m)
41. 'b(0).s = _HYPOT(origin.x - b(0).m.x, origin.y - b(0).m.y) ' reds magnitude (speed or force)
42.  
43. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
44. b(1).s = PyT(origin, b(1).m)
45. 'b(1).s = _HYPOT(origin.x - b(1).m.x, origin.y - b(1).m.y) ' cyans magnitude (speed or force)
46.  
47. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
48. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
49. f3 = 0
50. ar = 1.5
51. DO
52.     CLS
53.     ms = MBS '                                                  process mouse actions dragging endpoints
54.     IF ms AND 64 THEN
55.         LOCATE 10, 10: PRINT "mousex"; mouse.x
56.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
57.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
58.         ' LOCATE 10, 10: PRINT "mousex"; mouse.x
59.         FOR x = 0 TO 1
60.             FOR y = 0 TO 1
61.                 ds! = PyT(vertex(x, y), mouse)
62.                 IF ds! < ballradius * .5 THEN i = x: j = y
63.             NEXT y
64.         NEXT x
65.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
66.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
67.                 b(i).p = mouse
68.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
69.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
70.         END SELECT
71.     ELSE
72.         'IF _KEYDOWN(114) THEN i = 0
73.         'IF _KEYDOWN(99) THEN i = 1
74.         IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
75.         IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
76.         IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
77.         IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
78.  
79.         'IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
80.         'IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
81.         'IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
82.         'IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
83.  
84.         '**************Code added by Novarseg
85.         'Vector rotation and vector magnitude adjustment using keyboard input
86.  
87.         I$ = INKEY$
88.         IF f3 = 0 THEN I$ = "b": f3 = 1
89.         IF I$ = "b" AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
90.         IF I$ = "b" AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
91.         LL1:
92.  
93.         IF I$ = "c" THEN 'increase vector magnitude
94.             mult = 1.01
95.             VecMult b(i).m, mult
96.         END IF
97.  
98.         IF I$ = "v" THEN 'decrease vector magnitude
99.             mult = 1.01 'should be div to avoid confusion, still works though
100.             VecDIV b(i).m, mult 'added a new sub
101.         END IF
102.  
103.  
104.         IF I$ = "z" THEN 'rotate vector counter clockwise
105.             IF RAD > _PI * 2 THEN RAD = 0
106.             'IF RAD < 0 THEN RAD = _PI * 2
107.             IF INKEY$ <> "z" THEN f1 = 0
108.             IF f1 = 0 THEN t1 = TIMER
109.             f1 = 1
110.             RAD = RAD + .005
111.             IF TIMER - t1 > 1.5 THEN
112.                 RAD = RAD + .05
113.             END IF
114.             signC = COS(RAD) * 1 / ABS(COS(RAD))
115.             signS = SIN(RAD) * 1 / ABS(SIN(RAD))
116.             b(i).s = PyT(origin, b(i).m)
117.             b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
118.             b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
119.  
120.         END IF
121.  
122.         IF I$ = "x" THEN 'rotate vector clockwise
123.  
124.             'IF RAD > _PI * 2 THEN RAD = 0
125.             IF RAD < 0 THEN RAD = _PI * 2
126.  
127.             IF INKEY$ <> "x" THEN f1 = 0
128.             IF f1 = 0 THEN t1 = TIMER
129.             f1 = 1
130.             RAD = RAD - .005
131.             IF TIMER - t1 > 1.5 THEN
132.                 RAD = RAD - .05
133.             END IF
134.             signC = COS(RAD) * 1 / ABS(COS(RAD))
135.             signS = SIN(RAD) * 1 / ABS(SIN(RAD))
136.             b(i).s = PyT(origin, b(i).m)
137.             b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
138.             b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
139.  
140.             '**************END Code added Novarseg
141.         END IF
142.  
143.         IF I$ = "q" THEN
144.             ar = ar + .01
145.         END IF
146.  
147.         IF I$ = "w" THEN
148.             ar = ar - .01
149.         END IF
150.  
151.  
152.         _DELAY .1
153.     END IF
154.     mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
155.  
156.  
157.     'START OF COLLISION MATHEMATICS SECTION
158.     ballradius = PyT(b(0).p, b(1).p) / 2
159.  
160.     FOR bn = 0 TO 1
161.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
162.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
163.     NEXT bn
164.  
165.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
166.     B2BCollision b(0), b(1)
167.     'END OF COLLISION MATHEMATICS SECTION
168.  
169.     'graphic representation
170.     FOR grid = -300 TO 300 STEP 20
171.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
172.         LINE (grid, 300)-(grid, -300), c& 'Gray
173.         LINE (-300, grid)-(300, grid), c& ' Gray
174.     NEXT grid
175.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
176.  
177.     FOR dr = 0 TO 1
178.  
179.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , ar
180.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
181.  
182.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
183.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
184.  
185.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
186.         _PRINTSTRING (0, 567 + (16 * dr)), SPACE$(80)
187.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
188.  
189.         _PRINTSTRING (0, 567 + (16 * dr)), b$
190.  
191.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
192.     NEXT dr
193.  
194.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
195.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
196.         PUT #1, , TEXT(0) 'NOVARSEG added this line
197.         PUT #1, , TEXT(1) 'NOVARSEG added this line
198.         CLOSE 'NOVARSEG added this line
199.     END IF 'NOVARSEG added this line
200.  
201.     _LIMIT 50
202.     _DISPLAY
203. LOOP UNTIL _KEYDOWN(27)
204. END
205.  
206.  
207. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
208.  
209.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
210.     DIM un AS V2
211.     DIM ut AS V2
212.     DIM ncomp1 AS V2
213.     DIM ncomp2 AS V2
214.     DIM tcomp1 AS V2
215.     DIM tcomp2 AS V2
216.  
217.  
218.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
219.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
220.     bnci1 = VecDot(un, ball1.m) '
221.     bnci2 = VecDot(un, ball2.m) '
222.     btci1 = VecDot(ut, ball1.m) '
223.     btci2 = VecDot(ut, ball2.m) '
224.  
225.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
226.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
227.  
228.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
229.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
230.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
231.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
232.  
233.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
234.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
235.  
236. END SUB 'B2BCollision
237.  
238.  
239. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
240.  
241.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
242.  
243. END FUNCTION 'map!
244.  
245.  
246. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
247.     STATIC StartTimer AS _FLOAT
248.     STATIC ButtonDown AS INTEGER
249.     STATIC ClickCount AS INTEGER
250.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
251.     '                          Down longer counts as a HOLD event.
252.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
253.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
254.         SELECT CASE SGN(_MOUSEWHEEL)
255.             CASE 1: MBS = MBS OR 512
256.             CASE -1: MBS = MBS OR 1024
257.         END SELECT
258.     WEND
259.  
260.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
261.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
262.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
263.  
264.     IF StartTimer = 0 THEN
265.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
266.             ButtonDown = 1: StartTimer = TIMER(0.01)
267.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
268.         ELSEIF _MOUSEBUTTON(2) THEN
269.             ButtonDown = 2: StartTimer = TIMER(0.01)
270.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
271.         ELSEIF _MOUSEBUTTON(3) THEN
272.             ButtonDown = 3: StartTimer = TIMER(0.01)
273.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
274.         END IF
275.     ELSE
276.         BD = ButtonDown MOD 3
277.         IF BD = 0 THEN BD = 3
278.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
279.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
280.         ELSE
281.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
282.                 MBS = 0: ButtonDown = 0: StartTimer = 0
283.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
284.             ELSE 'We've now started the hold event
285.                 MBS = MBS OR 32 * 2 ^ ButtonDown
286.             END IF
287.         END IF
288.     END IF
289. END FUNCTION 'MBS%
290.  
291.  
292. FUNCTION PyT (var1 AS V2, var2 AS V2)
293.  
294.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
295.  
296. END FUNCTION 'PyT
297.  
298.  
299. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
300.  
301.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
302.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
303.  
304. END SUB 'Add_Vector
305.  
306.  
307. FUNCTION VecDot (var AS V2, var2 AS V2)
308.  
309.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
310.  
311. END FUNCTION 'VecDot
312.  
313.  
314. SUB VecMult (vec AS V2, multiplier AS SINGLE)
315.  
316.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
317.     vec.y = vec.y * multiplier
318.  
319. END SUB 'Vec_Mult
320.  
321. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
322.  
323.     vec.x = vec.x / divisor
324.     vec.y = vec.y / divisor
325.  
326. END SUB 'VecDIV
327.  
328.  
329. SUB VecNorm (var AS V2)
330.  
331.     m = PyT(origin, var)
332.     IF m = 0 THEN
333.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
334.     ELSE
335.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
336.     END IF
337.  
338. END SUB 'VecNorm

FULLSCREEN distorts the x  y axis so the vector magnitude will appear to be changing when rotating. That is from the x y distortion - not the code.

 Trying to correct distortion when in FULLSCREEN mode.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 26, 2021, 06:22:16 am

It did mess with the mouse some, but it's more intuitive to use on the keyboard.

I suspect the issue with full screen distortion is that WINDOW needs to be altered to reflect the full screen aspect ratio. Grid drawing loop will need changing too, I believe.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 26, 2021, 04:21:31 pm

How does FULLSCREEN calculate the aspect ratio?

Quote

WINDOW needs to be altered to reflect the full screen aspect ratio

I will try that

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 26, 2021, 05:22:05 pm

_FULLSCREEN just stretches the QB64 screen over your computer screen.

For Square Window SqrXSqr, use a square QB64 screen, that should eliminate distortions.
ie Screen _NewImage(mySqr, mySqr, 32)

Oh you want _DeskTopWidth and _DeskTopHeight for your screen dimensions. Ah! then use those for _FullScreen without distortion.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 26, 2021, 05:56:00 pm

Interesting
Lets say FULLSCREEN uses _DeskTopWidth and _DeskTopHeight  so taking your square screen idea like newimage(600,600,32).

  x1 = ( 600 / (  (_DeskTopWidth  /_DeskTopHeight ) + 1 )  )
y1 = ( 600 / (  (_DeskTopHeight  /_DeskTopWidth  ) + 1 )  )


WINDOW (-x1,y1)-(x1,-y1)
er maybe it's
WINDOW (-x1,300)-(x1,-300)?

will it work?  The result should be an expanded square screen that will fit into DeskTopHeight dimensions. The negative signs make the center of the screen 0x, 0y

Gotta use _FULLSCREEN as well to make this work

Example, say DeskTopWidth  /_DeskTopHeight   = 1   then 1 + 1 = 2

600 / 2 = 300

WINDOW (-300, 300)-(300, -300)  the original code

but as we know, most if not all computer screens have more pixels wide than high so it looks that is why _FULLSCREEN distorts in certain cases.  Nothing wrong with FULLSCREEN though.

example say DeskTopWidth  /_DeskTopHeight   = 1.5   then 1.5 + 1 = 2.5

600 / 2.5 = 240

WINDOW (-240, 300)-(240, -300)

will that correct FULLSCREEN distortion?.  As OldMoses pointed out, the code that draws the grid has to work with these numbers as well.

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 26, 2021, 06:45:02 pm

Don't "gotta use full screen to make this work"

gotta use full screen to make this complicated as hell ;-))

Whatever your screen ratio height to width has to be matched in QB64 screen and Window screen they all need same proportions for _FULLSCREEN not to be distorted.

Say your Desktopwidth to height is 4 to 3 then make qb64 screen 400 X 300 or 800x600 or 1200x900
and window -200 to 200, 150 to -150 or -400 to 400, 300, -300.

And note your screen is not same as every one else screen. I would skip FULLSCREEN.

If you don't use FULLSCREEN then you can keep things simple with square ranges of x and y.


Wait is -200 to 200 = 400 pixels or 401 pixels probably 401 pixels.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 26, 2021, 07:01:19 pm

@bplus

Ok I will try coding that later. For now I'm just playing with the numbers.  The idea behind using FULLSCREEN is that it has the ability to fill the entire screen.   Doing an 800,600,32 with newimage will be close to the solution. 

The main thing is to have a nice undistorted grid with fullscreen.  I want to use the entire computer display.  Fullscreen also makes graphics  appear larger. (at times)

example
newimage (_DeskTopWidth  ,_DeskTopHeight ,32)

so I think that a FULLSCREEN after this won't have any effect because it can not stretch the image. ?

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 26, 2021, 07:21:09 pm

I tweaked this a little bit earlier today for a large display. I still haven't gotten back mouse function on the input vector grab, IDK what is wrong there. Funny how sometimes a modeling tool will distract one from an original topic.

It's like, "Oh look, a chicken.":D


EDIT:
I almost forgot to fix the grid...that should do it

Code: QB64: [Select]

1. 'Original code & some full display adjustments by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   position
14.     m AS V2 '                                                   movement (pre-contact) incoming
15.     x AS V2 '                                                   vector of post contact movement
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18. DIM TEXT(1) AS STRING
19. DIM RAD AS SINGLE
20. RAD = 0 ' * _PI
21. DIM c(1) AS STRING
22.  
23. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
24. DIM mouse AS V2
25. DIM b(1) AS ball
26. 'DIM SHARED AS V2 origin
27. DIM SHARED origin AS V2
28. origin.x = 0: origin.y = 0
29. b(0).c = Red: b(0).cn = "red"
30. b(1).c = Cyan: b(1).cn = "cyan"
31.  
32. SCREEN _NEWIMAGE(_DESKTOPWIDTH, _DESKTOPHEIGHT, 32)
33. DO: LOOP UNTIL _SCREENEXISTS
34. _SCREENMOVE 0, 0
35. WINDOW (-_DESKTOPWIDTH / 2, _DESKTOPHEIGHT / 2)-(_DESKTOPWIDTH / 2, -_DESKTOPHEIGHT / 2)
36. '_FULLSCREEN
37.  
38. 'starting state
39. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
40. b(0).s = PyT(origin, b(0).m)
41.  
42. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
43. b(1).s = PyT(origin, b(1).m)
44.  
45. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
46. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
47. f3 = 0
48. ar = 1
49. DO
50.     CLS
51.     ms = MBS '                                                  process mouse actions dragging endpoints
52.     IF ms AND 64 THEN
53.         _PRINTSTRING (0, 0), "mouse (" + STR$(mouse.x) + ", " + STR$(mouse.y) + ")"
54.         mouse.x = map!(_MOUSEX, 0, _DESKTOPWIDTH - 1, -_DESKTOPWIDTH / 2, _DESKTOPWIDTH / 2)
55.         mouse.y = map!(_MOUSEY, 0, _DESKTOPHEIGHT - 1, _DESKTOPHEIGHT / 2, -_DESKTOPHEIGHT / 2)
56.         FOR x = 0 TO 1
57.             FOR y = 0 TO 1
58.                 ds! = PyT(vertex(x, y), mouse)
59.                 IF ds! < ballradius * .25 THEN i = x: j = y
60.             NEXT y
61.         NEXT x
62.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
63.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
64.                 b(i).p = mouse
65.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
66.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
67.         END SELECT
68.     ELSE
69.         IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
70.         IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
71.         IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
72.         IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
73.  
74.         '**************Code added by Novarseg
75.         'Vector rotation and vector magnitude adjustment using keyboard input
76.  
77.         I$ = INKEY$
78.         IF f3 = 0 THEN I$ = "b": f3 = 1
79.         IF I$ = "b" AND i = 0 THEN i = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
80.         IF I$ = "b" AND i = 1 THEN i = 0: c(0) = "  SELECTED": c(1) = "           " 'red
81.         LL1:
82.  
83.         IF I$ = "c" THEN 'increase vector magnitude
84.             mult = 1.01
85.             VecMult b(i).m, mult
86.         END IF
87.  
88.         IF I$ = "v" THEN 'decrease vector magnitude
89.             mult = 1.01 'should be div to avoid confusion, still works though
90.             VecDIV b(i).m, mult 'added a new sub
91.         END IF
92.  
93.  
94.         IF I$ = "z" THEN 'rotate vector counter clockwise
95.             IF RAD > _PI * 2 THEN RAD = 0
96.             'IF RAD < 0 THEN RAD = _PI * 2
97.             IF INKEY$ <> "z" THEN f1 = 0
98.             IF f1 = 0 THEN t1 = TIMER
99.             f1 = 1
100.             RAD = RAD + .005
101.             IF TIMER - t1 > 1.5 THEN
102.                 RAD = RAD + .05
103.             END IF
104.             signC = COS(RAD) * 1 / ABS(COS(RAD))
105.             signS = SIN(RAD) * 1 / ABS(SIN(RAD))
106.             b(i).s = PyT(origin, b(i).m)
107.             b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
108.             b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
109.  
110.         END IF
111.  
112.         IF I$ = "x" THEN 'rotate vector clockwise
113.  
114.             'IF RAD > _PI * 2 THEN RAD = 0
115.             IF RAD < 0 THEN RAD = _PI * 2
116.  
117.             IF INKEY$ <> "x" THEN f1 = 0
118.             IF f1 = 0 THEN t1 = TIMER
119.             f1 = 1
120.             RAD = RAD - .005
121.             IF TIMER - t1 > 1.5 THEN
122.                 RAD = RAD - .05
123.             END IF
124.             signC = COS(RAD) * 1 / ABS(COS(RAD))
125.             signS = SIN(RAD) * 1 / ABS(SIN(RAD))
126.             b(i).s = PyT(origin, b(i).m)
127.             b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
128.             b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
129.  
130.             '**************END Code added Novarseg
131.         END IF
132.  
133.         IF I$ = "q" THEN
134.             ar = ar + .01
135.         END IF
136.  
137.         IF I$ = "w" THEN
138.             ar = ar - .01
139.         END IF
140.  
141.  
142.         _DELAY .1
143.     END IF
144.     'mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
145.  
146.  
147.     'START OF COLLISION MATHEMATICS SECTION
148.     ballradius = PyT(b(0).p, b(1).p) / 2
149.  
150.     FOR bn = 0 TO 1
151.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
152.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
153.     NEXT bn
154.  
155.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
156.     B2BCollision b(0), b(1)
157.     'END OF COLLISION MATHEMATICS SECTION
158.  
159.     'graphic representation
160.     FOR grid = -_DESKTOPWIDTH / 2 TO _DESKTOPWIDTH / 2 'STEP 20
161.         IF grid MOD 20 <> 0 THEN _CONTINUE
162.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
163.         LINE (grid, _DESKTOPHEIGHT / 2)-(grid, -_DESKTOPHEIGHT / 2), c& 'Gray
164.         LINE (-_DESKTOPWIDTH / 2, grid)-(_DESKTOPWIDTH / 2, grid), c& ' Gray
165.     NEXT grid
166.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
167.  
168.     FOR dr = 0 TO 1
169.  
170.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , ar
171.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
172.  
173.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
174.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
175.  
176.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
177.         _PRINTSTRING (0, _DESKTOPHEIGHT - 80 + (16 * dr)), SPACE$(80)
178.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
179.  
180.         _PRINTSTRING (0, _DESKTOPHEIGHT - 80 + (16 * dr)), b$
181.  
182.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
183.     NEXT dr
184.  
185.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
186.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
187.         PUT #1, , TEXT(0) 'NOVARSEG added this line
188.         PUT #1, , TEXT(1) 'NOVARSEG added this line
189.         CLOSE 'NOVARSEG added this line
190.     END IF 'NOVARSEG added this line
191.  
192.     _LIMIT 50
193.     _DISPLAY
194. LOOP UNTIL _KEYDOWN(27)
195. END
196.  
197.  
198. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
199.  
200.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
201.     DIM un AS V2
202.     DIM ut AS V2
203.     DIM ncomp1 AS V2
204.     DIM ncomp2 AS V2
205.     DIM tcomp1 AS V2
206.     DIM tcomp2 AS V2
207.  
208.  
209.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
210.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
211.     bnci1 = VecDot(un, ball1.m) '
212.     bnci2 = VecDot(un, ball2.m) '
213.     btci1 = VecDot(ut, ball1.m) '
214.     btci2 = VecDot(ut, ball2.m) '
215.  
216.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
217.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
218.  
219.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
220.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
221.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
222.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
223.  
224.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
225.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
226.  
227. END SUB 'B2BCollision
228.  
229.  
230. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
231.  
232.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
233.  
234. END FUNCTION 'map!
235.  
236.  
237. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
238.     STATIC StartTimer AS _FLOAT
239.     STATIC ButtonDown AS INTEGER
240.     STATIC ClickCount AS INTEGER
241.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
242.     '                          Down longer counts as a HOLD event.
243.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
244.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
245.         SELECT CASE SGN(_MOUSEWHEEL)
246.             CASE 1: MBS = MBS OR 512
247.             CASE -1: MBS = MBS OR 1024
248.         END SELECT
249.     WEND
250.  
251.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
252.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
253.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
254.  
255.     IF StartTimer = 0 THEN
256.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
257.             ButtonDown = 1: StartTimer = TIMER(0.01)
258.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
259.         ELSEIF _MOUSEBUTTON(2) THEN
260.             ButtonDown = 2: StartTimer = TIMER(0.01)
261.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
262.         ELSEIF _MOUSEBUTTON(3) THEN
263.             ButtonDown = 3: StartTimer = TIMER(0.01)
264.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
265.         END IF
266.     ELSE
267.         BD = ButtonDown MOD 3
268.         IF BD = 0 THEN BD = 3
269.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
270.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
271.         ELSE
272.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
273.                 MBS = 0: ButtonDown = 0: StartTimer = 0
274.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
275.             ELSE 'We've now started the hold event
276.                 MBS = MBS OR 32 * 2 ^ ButtonDown
277.             END IF
278.         END IF
279.     END IF
280. END FUNCTION 'MBS%
281.  
282.  
283. FUNCTION PyT (var1 AS V2, var2 AS V2)
284.  
285.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
286.  
287. END FUNCTION 'PyT
288.  
289.  
290. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
291.  
292.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
293.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
294.  
295. END SUB 'Add_Vector
296.  
297.  
298. FUNCTION VecDot (var AS V2, var2 AS V2)
299.  
300.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
301.  
302. END FUNCTION 'VecDot
303.  
304.  
305. SUB VecMult (vec AS V2, multiplier AS SINGLE)
306.  
307.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
308.     vec.y = vec.y * multiplier
309.  
310. END SUB 'Vec_Mult
311.  
312. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
313.  
314.     vec.x = vec.x / divisor
315.     vec.y = vec.y / divisor
316.  
317. END SUB 'VecDIV
318.  
319.  
320. SUB VecNorm (var AS V2)
321.  
322.     m = PyT(origin, var)
323.     IF m = 0 THEN
324.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
325.     ELSE
326.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
327.     END IF
328.  
329. END SUB 'VecNorm
330.  
331.  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 26, 2021, 07:42:16 pm

@OldMoses
Nice display.

 FULLSCREEN enabled

Can't see parameter text at bottom though

Code: QB64: [Select]

1. 'Original code & some full display adjustments by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   position
14.     m AS V2 '                                                   movement (pre-contact) incoming
15.     x AS V2 '                                                   vector of post contact movement
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18. DIM TEXT(1) AS STRING
19. DIM RAD AS SINGLE
20. RAD = 0 ' * _PI
21. DIM c(1) AS STRING
22.  
23. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
24. DIM mouse AS V2
25. DIM b(1) AS ball
26. 'DIM SHARED AS V2 origin
27. DIM SHARED origin AS V2
28. origin.x = 0: origin.y = 0
29. b(0).c = Red: b(0).cn = "red"
30. b(1).c = Cyan: b(1).cn = "cyan"
31.  
32. SCREEN _NEWIMAGE(_DESKTOPWIDTH * .5, _DESKTOPHEIGHT * .5, 32)
33. DO: LOOP UNTIL _SCREENEXISTS
34. _SCREENMOVE 0, 0
35. WINDOW (-_DESKTOPWIDTH / 4, _DESKTOPHEIGHT / 4)-(_DESKTOPWIDTH / 4, -_DESKTOPHEIGHT / 4)
36. _FULLSCREEN
37.  
38. 'starting state
39. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
40. b(0).s = PyT(origin, b(0).m)
41.  
42. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
43. b(1).s = PyT(origin, b(1).m)
44.  
45. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
46. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
47. f3 = 0
48. ar = 1
49. DO
50.     CLS
51.     ms = MBS '                                                  process mouse actions dragging endpoints
52.     IF ms AND 64 THEN
53.         _PRINTSTRING (0, 0), "mouse (" + STR$(mouse.x) + ", " + STR$(mouse.y) + ")"
54.         mouse.x = map!(_MOUSEX, 0, _DESKTOPWIDTH - 1, -_DESKTOPWIDTH / 2, _DESKTOPWIDTH / 2)
55.         mouse.y = map!(_MOUSEY, 0, _DESKTOPHEIGHT - 1, _DESKTOPHEIGHT / 2, -_DESKTOPHEIGHT / 2)
56.         FOR x = 0 TO 1
57.             FOR y = 0 TO 1
58.                 ds! = PyT(vertex(x, y), mouse)
59.                 IF ds! < ballradius * .25 THEN i = x: j = y
60.             NEXT y
61.         NEXT x
62.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
63.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
64.                 b(i).p = mouse
65.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
66.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
67.         END SELECT
68.     ELSE
69.         IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
70.         IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
71.         IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
72.         IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
73.  
74.         '**************Code added by Novarseg
75.         'Vector rotation and vector magnitude adjustment using keyboard input
76.  
77.         I$ = INKEY$
78.         IF f3 = 0 THEN I$ = "b": f3 = 1
79.         IF I$ = "b" AND i = 0 THEN i = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
80.         IF I$ = "b" AND i = 1 THEN i = 0: c(0) = "  SELECTED": c(1) = "           " 'red
81.         LL1:
82.  
83.         IF I$ = "c" THEN 'increase vector magnitude
84.             mult = 1.01
85.             VecMult b(i).m, mult
86.         END IF
87.  
88.         IF I$ = "v" THEN 'decrease vector magnitude
89.             mult = 1.01 'should be div to avoid confusion, still works though
90.             VecDIV b(i).m, mult 'added a new sub
91.         END IF
92.  
93.  
94.         IF I$ = "z" THEN 'rotate vector counter clockwise
95.             IF RAD > _PI * 2 THEN RAD = 0
96.             'IF RAD < 0 THEN RAD = _PI * 2
97.             IF INKEY$ <> "z" THEN f1 = 0
98.             IF f1 = 0 THEN t1 = TIMER
99.             f1 = 1
100.             RAD = RAD + .005
101.             IF TIMER - t1 > 1.5 THEN
102.                 RAD = RAD + .05
103.             END IF
104.             signC = COS(RAD) * 1 / ABS(COS(RAD))
105.             signS = SIN(RAD) * 1 / ABS(SIN(RAD))
106.             b(i).s = PyT(origin, b(i).m)
107.             b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
108.             b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
109.  
110.         END IF
111.  
112.         IF I$ = "x" THEN 'rotate vector clockwise
113.  
114.             'IF RAD > _PI * 2 THEN RAD = 0
115.             IF RAD < 0 THEN RAD = _PI * 2
116.  
117.             IF INKEY$ <> "x" THEN f1 = 0
118.             IF f1 = 0 THEN t1 = TIMER
119.             f1 = 1
120.             RAD = RAD - .005
121.             IF TIMER - t1 > 1.5 THEN
122.                 RAD = RAD - .05
123.             END IF
124.             signC = COS(RAD) * 1 / ABS(COS(RAD))
125.             signS = SIN(RAD) * 1 / ABS(SIN(RAD))
126.             b(i).s = PyT(origin, b(i).m)
127.             b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
128.             b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
129.  
130.             '**************END Code added Novarseg
131.         END IF
132.  
133.         IF I$ = "q" THEN
134.             ar = ar + .01
135.         END IF
136.  
137.         IF I$ = "w" THEN
138.             ar = ar - .01
139.         END IF
140.  
141.  
142.         _DELAY .1
143.     END IF
144.     'mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
145.  
146.  
147.     'START OF COLLISION MATHEMATICS SECTION
148.     ballradius = PyT(b(0).p, b(1).p) / 2
149.  
150.     FOR bn = 0 TO 1
151.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
152.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
153.     NEXT bn
154.  
155.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
156.     B2BCollision b(0), b(1)
157.     'END OF COLLISION MATHEMATICS SECTION
158.  
159.     'graphic representation
160.     FOR grid = -_DESKTOPWIDTH / 2 TO _DESKTOPWIDTH / 2 STEP 20
161.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
162.         LINE (grid, _DESKTOPHEIGHT / 2)-(grid, -_DESKTOPHEIGHT / 2), c& 'Gray
163.         LINE (-_DESKTOPWIDTH / 2, grid)-(_DESKTOPWIDTH / 2, grid), c& ' Gray
164.     NEXT grid
165.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
166.  
167.     FOR dr = 0 TO 1
168.  
169.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , ar
170.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
171.  
172.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
173.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
174.  
175.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
176.         _PRINTSTRING (0, _DESKTOPHEIGHT - 80 + (16 * dr)), SPACE$(80)
177.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
178.  
179.         _PRINTSTRING (0, _DESKTOPHEIGHT - 80 + (16 * dr)), b$
180.  
181.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
182.     NEXT dr
183.  
184.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
185.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
186.         PUT #1, , TEXT(0) 'NOVARSEG added this line
187.         PUT #1, , TEXT(1) 'NOVARSEG added this line
188.         CLOSE 'NOVARSEG added this line
189.     END IF 'NOVARSEG added this line
190.  
191.     _LIMIT 50
192.     _DISPLAY
193. LOOP UNTIL _KEYDOWN(27)
194. END
195.  
196.  
197. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
198.  
199.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
200.     DIM un AS V2
201.     DIM ut AS V2
202.     DIM ncomp1 AS V2
203.     DIM ncomp2 AS V2
204.     DIM tcomp1 AS V2
205.     DIM tcomp2 AS V2
206.  
207.  
208.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
209.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
210.     bnci1 = VecDot(un, ball1.m) '
211.     bnci2 = VecDot(un, ball2.m) '
212.     btci1 = VecDot(ut, ball1.m) '
213.     btci2 = VecDot(ut, ball2.m) '
214.  
215.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
216.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
217.  
218.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
219.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
220.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
221.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
222.  
223.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
224.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
225.  
226. END SUB 'B2BCollision
227.  
228.  
229. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
230.  
231.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
232.  
233. END FUNCTION 'map!
234.  
235.  
236. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
237.     STATIC StartTimer AS _FLOAT
238.     STATIC ButtonDown AS INTEGER
239.     STATIC ClickCount AS INTEGER
240.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
241.     '                          Down longer counts as a HOLD event.
242.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
243.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
244.         SELECT CASE SGN(_MOUSEWHEEL)
245.             CASE 1: MBS = MBS OR 512
246.             CASE -1: MBS = MBS OR 1024
247.         END SELECT
248.     WEND
249.  
250.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
251.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
252.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
253.  
254.     IF StartTimer = 0 THEN
255.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
256.             ButtonDown = 1: StartTimer = TIMER(0.01)
257.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
258.         ELSEIF _MOUSEBUTTON(2) THEN
259.             ButtonDown = 2: StartTimer = TIMER(0.01)
260.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
261.         ELSEIF _MOUSEBUTTON(3) THEN
262.             ButtonDown = 3: StartTimer = TIMER(0.01)
263.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
264.         END IF
265.     ELSE
266.         BD = ButtonDown MOD 3
267.         IF BD = 0 THEN BD = 3
268.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
269.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
270.         ELSE
271.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
272.                 MBS = 0: ButtonDown = 0: StartTimer = 0
273.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
274.             ELSE 'We've now started the hold event
275.                 MBS = MBS OR 32 * 2 ^ ButtonDown
276.             END IF
277.         END IF
278.     END IF
279. END FUNCTION 'MBS%
280.  
281.  
282. FUNCTION PyT (var1 AS V2, var2 AS V2)
283.  
284.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
285.  
286. END FUNCTION 'PyT
287.  
288.  
289. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
290.  
291.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
292.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
293.  
294. END SUB 'Add_Vector
295.  
296.  
297. FUNCTION VecDot (var AS V2, var2 AS V2)
298.  
299.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
300.  
301. END FUNCTION 'VecDot
302.  
303.  
304. SUB VecMult (vec AS V2, multiplier AS SINGLE)
305.  
306.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
307.     vec.y = vec.y * multiplier
308.  
309. END SUB 'Vec_Mult
310.  
311. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
312.  
313.     vec.x = vec.x / divisor
314.     vec.y = vec.y / divisor
315.  
316. END SUB 'VecDIV
317.  
318.  
319. SUB VecNorm (var AS V2)
320.  
321.     m = PyT(origin, var)
322.     IF m = 0 THEN
323.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
324.     ELSE
325.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
326.     END IF
327.  
328. END SUB 'VecNorm

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 26, 2021, 08:02:12 pm

FULLSCREEN probably stretched it past the bottom of the display. Even without FULLSCREEN, I had to choke up on it a bit to keep it in my version of the display. You might have to pull it up some more on lines #176 & 179 by subtracting more from _DESKTOPHEIGHT, assuming that FULLSCREEN doesn't mess with _PRINTSTRING in some way I'm unaware of.

I've never been satisfied with FULLSCREEN whenever I've used it. It seems to render things a lot grainier than a 32 bit screen will.

Title: Re: 2D ball collisions without trigonometry.
Post by: SMcNeill on May 26, 2021, 08:21:32 pm

Instead of using full screen, why not just calculate the largest possible screen you can use and maintain the original screen ratio, and then _putimage your workscreen onto it, make it the display screen, and keep it centered on the desktop?   You'd always be working in your original screen, wouldn't need to change coordinate values or scale anything...  All you'd do is _PUTIMAGE your workscreen onto the displayscreen before your _DISPLAY statement.

Or, even easier:

Forget about _FULLSCREEN.   Just use $RESIZE:(smooth or stretch) and let the user stretch to whatever size they want for their desktop/readability.

Code: QB64: [Select]

1. SX = 400: SY = 400
2. SCREEN _NEWIMAGE(SX, SY, 32)
3. $RESIZE:SMOOTH
4. CLS , &HFF0000AA
5. FOR i = 1 TO 10
6.     PRINT i
7. NEXT
8. DO
9.     _LIMIT 30
10.     _DISPLAY
11. LOOP UNTIL _KEYHIT = 27
12.  

The above should show how simple resize is to add, and how to scales our images while maintaining aspect ratio, simply enough.  And, best of all -- all your code which you've wrote already will continue to work just like always.  mouse coordinates are automatically scaled.  screen coordinates are automatically scaled.  Your program is the same old 400 x 400 which you wrote it in, in all ways, except the user is simply resizing the final display to whatever size they want it to be on their desktop.

Honestly, I think $RESIZE:(smooth or stretch) should be included in almost all programs.  There's really very few cases where I see it as something you wouldn't want to allow.
 

Title: Re: 2D ball collisions without trigonometry.
Post by: STxAxTIC on May 26, 2021, 08:38:42 pm

When y'all get spheres figured out, you can play with this code, which works for any shape of any mass about any axis (all in 2d).

What it doesn't handle well is sustained contact between objects. (I would have to stare at this code a while to keep working on it.) Nobody tell me you were able to make an object pass through a boundary, I know! :-) This is because it's still in general mode and not optimized for any particular game.

Anyway - it completely nails the one-off collision. Have a ball... or an amoeba. PRESS SPACE DURING PLAY TO PAUSE EVERYTHING AND DRAW YOUR OWN THING. (Not sure if the instructions say this.)

Code: QB64: [Select]

1. ' Display
2. Screen _NewImage(800, 600, 32)
3. _ScreenMove (_DesktopWidth \ 2 - _Width \ 2) - 3, (_DesktopHeight \ 2 - _Height \ 2) - 29
4. _Title "Collisions - Version 9"
5. _Delay 1
6.  
7. ' Meta
8. start:
9. Clear
10. Cls
11. Randomize Timer
12.  
13. ' Data structures
14. Type Vector
15.     x As Double
16.     y As Double
17. End Type
18.  
19. Dim Shared vtemp As Vector
20.  
21. ' Object type
22. Type Object
23.     Centroid As Vector
24.     Collisions As Long
25.     CollisionSwitch As Integer
26.     DeltaO As Double
27.     DeltaV As Vector
28.     Diameter As Double
29.     Elements As Integer
30.     Fixed As Integer
31.     Mass As Double
32.     MOI As Double
33.     PartialNormal As Vector
34.     Omega As Double
35.     Shade As _Unsigned Long
36.     Velocity As Vector
37. End Type
38.  
39. ' Object storage
40. Dim Shared Shape(300) As Object
41. Dim Shared PointChain(300, 500) As Vector
42. Dim Shared TempChain(300, 500) As Vector
43. Dim Shared ShapeCount As Integer
44. Dim Shared SelectedShape As Integer
45.  
46. ' Dynamics
47. Dim Shared CollisionCount As Integer
48. Dim Shared ProximalPairs(300 / 2, 1 To 2) As Integer
49. Dim Shared ProximalPairsCount As Integer
50. Dim Shared ContactPoints As Integer
51. Dim Shared CPC, FPC, RST, VD, SV As Double
52.  
53. ' Environment
54. Dim Shared ForceField As Vector ' Ex: gravity
55.  
56. ' Initialize
57. ShapeCount = 0
58. CollisionCount = 0
59.  
60. ' Prompt
61. Cls
62. Call cprintstring(16 * 17, "WELCOME!                    ")
63. Call cprintstring(16 * 16, "Press 1 for Pool prototype  ")
64. Call cprintstring(16 * 15, "Press 2 for Wacky game      ")
65. Call cprintstring(16 * 14, "Press 3 for Concentric rings")
66. Call cprintstring(16 * 13, "Press 4 for Walls only      ")
67. Call cprintstring(16 * 12, "Press 5 for Angle pong game ")
68. _Display
69.  
70. _KeyClear
71. Do
72.     kk = _KeyHit
73.     Select Case kk
74.         Case Asc("1")
75.             Call SetupPoolGame
76.             Exit Do
77.         Case Asc("2")
78.             Call SetupWackyGame
79.             Exit Do
80.         Case Asc("3")
81.             Call SetupRings
82.             Exit Do
83.         Case Asc("4")
84.             Call SetupWallsOnly
85.             Exit Do
86.         Case Asc("5")
87.             Call SetupAnglePong
88.             Exit Do
89.         Case Else
90.             _KeyClear
91.     End Select
92.     _Limit 60
93. Loop
94.  
95. Call Graphics
96. Call cprintstring(-16 * 4, "During Play:")
97. Call cprintstring(-16 * 6, "Move mouse to select closest object (by centroid).")
98. Call cprintstring(-16 * 7, "Boost velocity with arrow keys or W/S/A/D.        ")
99. Call cprintstring(-16 * 8, "Boost angluar velocity with Q/E.                  ")
100. Call cprintstring(-16 * 9, "Drag and fling object with Mouse 1.               ")
101. Call cprintstring(-16 * 10, "Rotate selected object with Mousewheel.           ")
102. Call cprintstring(-16 * 11, "Halt all motion with ESC.                         ")
103. Call cprintstring(-16 * 12, "Create new ball with Mouse 2.                     ")
104. Call cprintstring(-16 * 13, "Initiate creative mode with SPACE.                ")
105. Call cprintstring(-16 * 14, "Restart by pressing R during motion.              ")
106. Call cprintstring(-16 * 16, "PRESS ANY KEY TO BEGIN.")
107. _Display
108. Do: Loop Until (_KeyHit > 0)
109. While (_MouseInput): Wend
110. _KeyClear
111.  
112. ' Main loop
113. Do
114.     If (UserInput = -1) Then GoTo start
115.     Call PairDynamics(CPC, FPC, RST)
116.     Call FleetDynamics(VD, SV)
117.     Call Graphics
118.     _Limit 120
119. Loop
120.  
121. End
122.  
123. Function UserInput
124.     TheReturn = 0
125.     ' Keyboard input
126.     kk = _KeyHit
127.     Select Case kk
128.         Case 32
129.             Do: Loop Until _KeyHit
130.             While _MouseInput: Wend
131.             _KeyClear
132.             Call cprintstring(16 * 17, "Drag Mouse 1 counter-clockwise to draw a new shape.")
133.             Call cprintstring(16 * 16, "Make sure centroid is inside body.                 ")
134.             Call NewMouseShape(7.5, 150, 15)
135.             Cls
136.         Case 18432, Asc("w"), Asc("W") ' Up arrow
137.             Shape(SelectedShape).Velocity.y = Shape(SelectedShape).Velocity.y * 1.05 + 1.5
138.         Case 20480, Asc("s"), Asc("S") ' Down arrow
139.             Shape(SelectedShape).Velocity.y = Shape(SelectedShape).Velocity.y * 0.95 - 1.5
140.         Case 19200, Asc("a"), Asc("A") ' Left arrow
141.             Shape(SelectedShape).Velocity.x = Shape(SelectedShape).Velocity.x * 0.95 - 1.5
142.         Case 19712, Asc("d"), Asc("D") ' Right arrow
143.             Shape(SelectedShape).Velocity.x = Shape(SelectedShape).Velocity.x * 1.05 + 1.5
144.         Case Asc("e"), Asc("E")
145.             Shape(SelectedShape).Omega = Omega * 0.5 - .02
146.         Case Asc("q"), Asc("Q")
147.             Shape(SelectedShape).Omega = Omega * 1.5 + .02
148.         Case Asc("r"), Asc("R")
149.             TheReturn = -1
150.         Case 27
151.             For k = 1 To ShapeCount
152.                 Shape(k).Velocity.x = .000001 * (Rnd - .5)
153.                 Shape(k).Velocity.y = .000001 * (Rnd - .5)
154.                 Shape(k).Omega = .000001 * (Rnd - .5)
155.             Next
156.     End Select
157.     If (kk) Then
158.         _KeyClear
159.     End If
160.  
161.     ' Mouse input
162.     mb = 0
163.     mxold = 999999999
164.     myold = 999999999
165.     Do While _MouseInput
166.         x = _MouseX
167.         y = _MouseY
168.         If (x > 0) And (x < _Width) And (y > 0) And (y < _Height) Then
169.             x = x - (_Width / 2)
170.             y = -y + (_Height / 2)
171.             rmin = 999999999
172.             For k = 1 To ShapeCount
173.                 dx = x - Shape(k).Centroid.x
174.                 dy = y - Shape(k).Centroid.y
175.                 r2 = dx * dx + dy * dy
176.                 If (r2 < rmin) Then
177.                     rmin = r2
178.                     SelectedShape = k
179.                 End If
180.             Next
181.             If (_MouseButton(1)) Then
182.                 If (mb = 0) Then
183.                     mb = 1
184.                     vtemp.x = x - Shape(SelectedShape).Centroid.x
185.                     vtemp.y = y - Shape(SelectedShape).Centroid.y
186.                     Call TranslateShape(SelectedShape, vtemp)
187.                     Shape(SelectedShape).Velocity.x = 0
188.                     Shape(SelectedShape).Velocity.y = 0
189.                     Shape(SelectedShape).Omega = 0
190.                     mxold = x
191.                     myold = y
192.                 End If
193.             End If
194.             If (_MouseButton(2)) Then
195.                 If (mb = 0) Then
196.                     mb = 1
197.                     Call NewAutoBall(x, y, 15, 0, 1, 1, 0)
198.                     _Delay .1
199.                 End If
200.             End If
201.             If (_MouseWheel > 0) Then
202.                 Call RotShape(SelectedShape, Shape(SelectedShape).Centroid, -.02 * 8 * Atn(1))
203.             End If
204.             If (_MouseWheel < 0) Then
205.                 Call RotShape(SelectedShape, Shape(SelectedShape).Centroid, .02 * 8 * Atn(1))
206.             End If
207.         End If
208.     Loop
209.     If ((mxold <> 999999999) And (myold <> 999999999)) Then
210.         Shape(SelectedShape).Velocity.x = x - mxold
211.         Shape(SelectedShape).Velocity.y = y - myold
212.     End If
213.     UserInput = TheReturn
214. End Function
215.  
216. Sub PairDynamics (CoarseProximityConstant As Double, FineProximityConstant As Double, Restitution As Double)
217.  
218.     Dim GrossJ(300) As Integer
219.     Dim GrossK(300) As Integer
220.     Dim NumJK As Integer
221.  
222.     ' Proximity detection
223.     ProximalPairsCount = 0
224.     Shape1 = 0
225.     Shape2 = 0
226.     For j = 1 To ShapeCount
227.         Shape(j).CollisionSwitch = 0
228.         Shape(j).DeltaO = 0
229.         Shape(j).DeltaV.x = 0
230.         Shape(j).DeltaV.y = 0
231.         Shape(j).PartialNormal.x = 0
232.         Shape(j).PartialNormal.y = 0
233.         For k = j + 1 To ShapeCount
234.             dx = Shape(j).Centroid.x - Shape(k).Centroid.x
235.             dy = Shape(j).Centroid.y - Shape(k).Centroid.y
236.             dr = Sqr(dx * dx + dy * dy)
237.             If (dr < (CoarseProximityConstant) * (Shape(j).Diameter + Shape(k).Diameter)) Then
238.                 ProximalPairsCount = ProximalPairsCount + 1
239.                 ProximalPairs(ProximalPairsCount, 1) = j
240.                 ProximalPairs(ProximalPairsCount, 2) = k
241.                 'Shape1 = j
242.                 'Shape2 = k
243.             End If
244.         Next
245.     Next
246.  
247.     ContactPoints = 0
248.  
249.     If (ProximalPairsCount > 0) Then
250.         For n = 1 To ProximalPairsCount
251.             Shape1 = ProximalPairs(n, 1)
252.             Shape2 = ProximalPairs(n, 2)
253.  
254.             ' Collision detection
255.             rmin = 999999999
256.             ClosestIndex1 = 0
257.             ClosestIndex2 = 0
258.             NumJK = 0
259.             For j = 1 To Shape(Shape1).Elements
260.                 For k = 1 To Shape(Shape2).Elements
261.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
262.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
263.                     r2 = dx * dx + dy * dy
264.  
265.                     If (r2 <= FineProximityConstant) Then
266.  
267.                         ContactPoints = ContactPoints + 1
268.  
269.                         ' Partial normal vector 1
270.                         nx1 = CalculateNormalY(Shape1, j)
271.                         ny1 = -CalculateNormalX(Shape1, j)
272.                         nn = Sqr(nx1 * nx1 + ny1 * ny1)
273.                         nx1 = nx1 / nn
274.                         ny1 = ny1 / nn
275.                         Shape(Shape1).PartialNormal.x = Shape(Shape1).PartialNormal.x + nx1
276.                         Shape(Shape1).PartialNormal.y = Shape(Shape1).PartialNormal.y + ny1
277.  
278.                         ' Partial normal vector 2
279.                         nx2 = CalculateNormalY(Shape2, k)
280.                         ny2 = -CalculateNormalX(Shape2, k)
281.                         nn = Sqr(nx2 * nx2 + ny2 * ny2)
282.                         nx2 = nx2 / nn
283.                         ny2 = ny2 / nn
284.                         Shape(Shape2).PartialNormal.x = Shape(Shape2).PartialNormal.x + nx2
285.                         Shape(Shape2).PartialNormal.y = Shape(Shape2).PartialNormal.y + ny2
286.  
287.                         NumJK = NumJK + 1
288.                         GrossJ(NumJK) = j
289.                         GrossK(NumJK) = k
290.  
291.                     End If
292.                     If (r2 < rmin) Then
293.                         rmin = r2
294.                         ClosestIndex1 = j
295.                         ClosestIndex2 = k
296.                     End If
297.                 Next
298.             Next
299.  
300.             If (NumJK > 1) Then
301.                 If ((GrossJ(1) - GrossJ(NumJK)) * (GrossJ(1) - GrossJ(NumJK)) > 50) Then
302.                     'ClosestIndex1 = 1
303.                 Else
304.                     ClosestIndex1 = Int(IntegrateArray(GrossJ(), NumJK) / NumJK)
305.                 End If
306.                 If ((GrossK(1) - GrossK(NumJK)) * (GrossK(1) - GrossK(NumJK)) > 50) Then
307.                     'ClosestIndex2 = 1
308.                 Else
309.                     ClosestIndex2 = Int(IntegrateArray(GrossK(), NumJK) / NumJK)
310.                 End If
311.             End If
312.  
313.             If (rmin <= FineProximityConstant) Then
314.  
315.                 CollisionCount = CollisionCount + 1
316.                 Shape(Shape1).CollisionSwitch = 1
317.                 Shape(Shape2).CollisionSwitch = 1
318.  
319.                 ' Undo previous motion
320.                 If (Shape(Shape1).Collisions = 0) Then
321.                     Call RotShape(Shape1, Shape(Shape1).Centroid, -1 * Shape(Shape1).Omega)
322.                     vtemp.x = -1 * (Shape(Shape1).Velocity.x)
323.                     vtemp.y = -1 * (Shape(Shape1).Velocity.y)
324.                     Call TranslateShape(Shape1, vtemp)
325.                 End If
326.                 If (Shape(Shape2).Collisions = 0) Then
327.                     Call RotShape(Shape2, Shape(Shape2).Centroid, -1 * Shape(Shape2).Omega)
328.                     vtemp.x = -1 * (Shape(Shape2).Velocity.x)
329.                     vtemp.y = -1 * (Shape(Shape2).Velocity.y)
330.                     Call TranslateShape(Shape2, vtemp)
331.                 End If
332.  
333.                 ' Momentum absorption
334.                 If (Shape(Shape1).Collisions = 0) Then
335.                     Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * Restitution
336.                     Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * Restitution
337.                 End If
338.                 If (Shape(Shape2).Collisions = 0) Then
339.                     Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * Restitution
340.                     Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * Restitution
341.                 End If
342.  
343.                 ' Centroid of object 1 (cx1, cy1)
344.                 cx1 = Shape(Shape1).Centroid.x
345.                 cy1 = Shape(Shape1).Centroid.y
346.  
347.                 ' Centroid of object 2 (cx2, cy2)
348.                 cx2 = Shape(Shape2).Centroid.x
349.                 cy2 = Shape(Shape2).Centroid.y
350.  
351.                 ' Contact point on object 1 (px1, py1)
352.                 px1 = PointChain(Shape1, ClosestIndex1).x
353.                 py1 = PointChain(Shape1, ClosestIndex1).y
354.  
355.                 ' Contact point on object 2 (px2, py2)
356.                 px2 = PointChain(Shape2, ClosestIndex2).x
357.                 py2 = PointChain(Shape2, ClosestIndex2).y
358.  
359.                 ' Contact-centroid differentials 1 (dx1, dy1)
360.                 dx1 = px1 - cx1
361.                 dy1 = py1 - cy1
362.  
363.                 ' Contact-centroid differentials 2 (dx2, dy2)
364.                 dx2 = px2 - cx2
365.                 dy2 = py2 - cy2
366.  
367.                 ' Normal vector 1 (nx1, ny1)
368.                 nn = Sqr(Shape(Shape1).PartialNormal.x * Shape(Shape1).PartialNormal.x + Shape(Shape1).PartialNormal.y * Shape(Shape1).PartialNormal.y)
369.                 nx1 = Shape(Shape1).PartialNormal.x / nn
370.                 ny1 = Shape(Shape1).PartialNormal.y / nn
371.  
372.                 ' Normal vector 2 (nx2, ny2)
373.                 nn = Sqr(Shape(Shape2).PartialNormal.x * Shape(Shape2).PartialNormal.x + Shape(Shape2).PartialNormal.y * Shape(Shape2).PartialNormal.y)
374.                 nx2 = Shape(Shape2).PartialNormal.x / nn
375.                 ny2 = Shape(Shape2).PartialNormal.y / nn
376.  
377.                 '''
378.                 'nx1 = CalculateNormalY(Shape1, ClosestIndex1)
379.                 'ny1 = -CalculateNormalX(Shape1, ClosestIndex1)
380.                 'nn = SQR(nx1 * nx1 + ny1 * ny1)
381.                 'nx1 = nx1 / nn
382.                 'ny1 = ny1 / nn
383.  
384.                 'nx2 = CalculateNormalY(Shape2, ClosestIndex2)
385.                 'ny2 = -CalculateNormalX(Shape2, ClosestIndex2)
386.                 'nn = SQR(nx2 * nx2 + ny2 * ny2)
387.                 'nx2 = nx2 / nn
388.                 'ny2 = ny2 / nn
389.                 '''
390.  
391.                 ' Perpendicular vector 1 (prx1, pry1)
392.                 prx1 = -1 * dy1
393.                 pry1 = dx1
394.                 pp = Sqr(prx1 * prx1 + pry1 * pry1)
395.                 prx1 = prx1 / pp
396.                 pry1 = pry1 / pp
397.  
398.                 ' Perpendicular vector 2 (prx2, pry2)
399.                 prx2 = -1 * dy2
400.                 pry2 = dx2
401.                 pp = Sqr(prx2 * prx2 + pry2 * pry2)
402.                 prx2 = prx2 / pp
403.                 pry2 = pry2 / pp
404.  
405.                 ' Angular velocity vector 1 (w1, r1, vx1, vy1)
406.                 w1 = Shape(Shape1).Omega
407.                 r1 = Sqr(dx1 * dx1 + dy1 * dy1)
408.                 vx1 = w1 * r1 * prx1
409.                 vy1 = w1 * r1 * pry1
410.  
411.                 ' Angular velocity vector 2 (w2, r2, vx2, vy2)
412.                 w2 = Shape(Shape2).Omega
413.                 r2 = Sqr(dx2 * dx2 + dy2 * dy2)
414.                 vx2 = w2 * r2 * prx2
415.                 vy2 = w2 * r2 * pry2
416.  
417.                 ' Mass terms (m1, m2, mu)
418.                 m1 = Shape(Shape1).Mass
419.                 m2 = Shape(Shape2).Mass
420.                 mu = 1 / (1 / m1 + 1 / m2)
421.  
422.                 ' Re-Calculate moment of inertia (i1, i2)
423.                 vtemp.x = px1
424.                 vtemp.y = py1
425.                 Call CalculateMOI(Shape1, vtemp)
426.                 vtemp.x = px2
427.                 vtemp.y = py2
428.                 Call CalculateMOI(Shape2, vtemp)
429.                 i1 = Shape(Shape1).MOI
430.                 i2 = Shape(Shape2).MOI
431.  
432.                 ' Velocity differentials (v1, v2, dvtx, dvty)
433.                 vcx1 = Shape(Shape1).Velocity.x
434.                 vcy1 = Shape(Shape1).Velocity.y
435.                 vcx2 = Shape(Shape2).Velocity.x
436.                 vcy2 = Shape(Shape2).Velocity.y
437.                 vtx1 = vcx1 + vx1
438.                 vty1 = vcy1 + vy1
439.                 vtx2 = vcx2 + vx2
440.                 vty2 = vcy2 + vy2
441.                 v1 = Sqr(vtx1 * vtx1 + vty1 * vty1)
442.                 v2 = Sqr(vtx2 * vtx2 + vty2 * vty2)
443.                 dvtx = vtx2 - vtx1
444.                 dvty = vty2 - vty1
445.  
446.                 ' Geometry (n1dotdvt, n2dotdvt)
447.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
448.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
449.  
450.                 ' Momentum exchange (qx1, qy1, qx2, qy2)
451.                 qx1 = nx1 * 2 * mu * n1dotdvt
452.                 qy1 = ny1 * 2 * mu * n1dotdvt
453.                 qx2 = nx2 * 2 * mu * n2dotdvt
454.                 qy2 = ny2 * 2 * mu * n2dotdvt
455.  
456.                 ' Momentum exchange unit vector (qhat)
457.                 qq = Sqr(qx1 * qx1 + qy1 * qy1)
458.                 If (qx1 * qx1 > 0.01) Then
459.                     qhatx1 = qx1 / qq
460.                 Else
461.                     qx1 = 0
462.                     qhatx1 = 0
463.                 End If
464.                 If (qy1 * qy1 > 0.01) Then
465.                     qhaty1 = qy1 / qq
466.                 Else
467.                     qy1 = 0
468.                     qhaty1 = 0
469.                 End If
470.                 qq = Sqr(qx2 * qx2 + qy2 * qy2)
471.                 If (qx2 * qx2 > 0.01) Then
472.                     qhatx2 = qx2 / qq
473.                 Else
474.                     qx2 = 0
475.                     qhatx2 = 0
476.                 End If
477.                 If (qy2 * qy2 > 0.01) Then
478.                     qhaty2 = qy2 / qq
479.                 Else
480.                     qy2 = 0
481.                     qhaty2 = 0
482.                 End If
483.  
484.                 ' Angular impulse (qdotp)
485.                 q1dotp1 = qx1 * prx1 + qy1 * pry1
486.                 q2dotp2 = qx2 * prx2 + qy2 * pry2
487.  
488.                 ' Translational impulse (qdotn, ndotrhat, f)
489.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
490.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
491.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
492.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
493.                 f1 = -q1dotn1 * n1dotr1hat
494.                 f2 = -q2dotn2 * n2dotr2hat
495.  
496.                 ' Special case for shape within shape.
497.                 np = nx1 * nx2 + ny1 * ny2
498.                 If (np > 0) Then
499.                     dcx = cx1 - cx2
500.                     dcy = cy1 - cy2
501.                     dc = Sqr(dcx * dcx + dcy * dcy)
502.                     If (dc < (r1 + r2)) Then
503.                         If (m1 > m2) Then ' This criteria may be bullshit in general but works now.
504.                             q1dotp1 = -q1dotp1
505.                             f1 = -f1
506.                         Else
507.                             q2dotp2 = -q2dotp2
508.                             f2 = -f2
509.                         End If
510.                     End If
511.                 End If
512.  
513.                 ' Angular impulse update (edits omega)
514.                 Shape(Shape1).DeltaO = Shape(Shape1).DeltaO + r1 * q1dotp1 / i1
515.                 Shape(Shape2).DeltaO = Shape(Shape2).DeltaO - r2 * q2dotp2 / i2
516.  
517.                 ' Linear impulse update (edits velocity)
518.                 dvx1 = f1 * qx1 / m1
519.                 dvy1 = f1 * qy1 / m1
520.                 dvx2 = f2 * qx2 / m2
521.                 dvy2 = f2 * qy2 / m2
522.                 dvx1s = dvx1 * dvx1
523.                 dvy1s = dvy1 * dvy1
524.                 dvx2s = dvx2 * dvx2
525.                 dvy2s = dvy2 * dvy2
526.                 If ((dvx1s > .001) And (dvx1s < 50)) Then
527.                     Shape(Shape1).DeltaV.x = Shape(Shape1).DeltaV.x + dvx1
528.                 End If
529.                 If ((dvy1s > .001) And (dvy1s < 50)) Then
530.                     Shape(Shape1).DeltaV.y = Shape(Shape1).DeltaV.y + dvy1
531.                 End If
532.                 If ((dvx2s > .001) And (dvx2s < 50)) Then
533.                     Shape(Shape2).DeltaV.x = Shape(Shape2).DeltaV.x + dvx2
534.                 End If
535.                 If ((dvy2s > .001) And (dvy2s < 50)) Then
536.                     Shape(Shape2).DeltaV.y = Shape(Shape2).DeltaV.y + dvy2
537.                 End If
538.  
539.                 ' External torque (edits omega)
540.                 torque1 = m1 * (dx1 * ForceField.y - dy1 * ForceField.x)
541.                 torque2 = m2 * (dx2 * ForceField.y - dy2 * ForceField.x)
542.                 Shape(Shape1).DeltaO = Shape(Shape1).DeltaO - torque1 / i1
543.                 Shape(Shape2).DeltaO = Shape(Shape2).DeltaO - torque2 / i2
544.  
545.                 ' Separate along normal (edits position)
546.                 If (Shape(Shape1).Collisions < 2) Then ' changed from = 0
547.                     vtemp.x = -nx1 * (.5 / m1) * (1 * v1 ^ 2 + 1 * w1 ^ 2)
548.                     vtemp.y = -ny1 * (.5 / m1) * (1 * v1 ^ 2 + 1 * w1 ^ 2)
549.                     Call TranslateShape(Shape1, vtemp)
550.                 End If
551.                 If (Shape(Shape2).Collisions < 2) Then
552.                     vtemp.x = -nx2 * (.5 / m2) * (1 * v2 ^ 2 + 1 * w2 ^ 2)
553.                     vtemp.y = -ny2 * (.5 / m2) * (1 * v2 ^ 2 + 1 * w2 ^ 2)
554.                     Call TranslateShape(Shape2, vtemp)
555.                 End If
556.  
557.                 ' Dent along normal
558.                 'PointChain(Shape1, ClosestIndex1).x = PointChain(Shape1, ClosestIndex1).x - v1 * nx1 / 2
559.                 'PointChain(Shape1, ClosestIndex1).y = PointChain(Shape1, ClosestIndex1).y - v1 * ny1 / 2
560.                 'PointChain(Shape2, ClosestIndex2).x = PointChain(Shape2, ClosestIndex2).x - v2 * nx2 / 2
561.                 'PointChain(Shape2, ClosestIndex2).y = PointChain(Shape2, ClosestIndex2).y - v2 * ny2 / 2
562.  
563.                 ' Feedback
564.                 If ((Shape(Shape1).Collisions = 0) And (Shape(Shape2).Collisions = 0)) Then
565.                     Call snd(100 * (v1 + v2) / 2, .5)
566.                 End If
567.  
568.             End If
569.         Next
570.     End If
571. End Sub
572.  
573. Sub FleetDynamics (MotionDamping As Double, LowLimitVelocity As Double)
574.  
575.     For ShapeIndex = 1 To ShapeCount
576.  
577.         ' Contact update
578.         If (Shape(ShapeIndex).CollisionSwitch = 1) Then
579.             Shape(ShapeIndex).Collisions = Shape(ShapeIndex).Collisions + 1
580.         Else
581.             Shape(ShapeIndex).Collisions = 0
582.         End If
583.  
584.         If (Shape(ShapeIndex).Fixed = 0) Then
585.  
586.             ' Angular velocity update
587.             Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + Shape(ShapeIndex).DeltaO
588.  
589.             ' Linear velocity update
590.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Shape(ShapeIndex).DeltaV.x
591.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Shape(ShapeIndex).DeltaV.y
592.  
593.             If (Shape(ShapeIndex).Collisions = 0) Then
594.                 ' Freefall (if airborne)
595.                 Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + ForceField.x
596.                 Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + ForceField.y
597.             End If
598.  
599.             If (Shape(ShapeIndex).Collisions > 2) Then
600.                 ' Static friction
601.                 If ((Shape(ShapeIndex).Velocity.x * Shape(ShapeIndex).Velocity.x) < LowLimitVelocity) Then
602.                     Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .05
603.                 End If
604.                 If ((Shape(ShapeIndex).Velocity.y * Shape(ShapeIndex).Velocity.y) < LowLimitVelocity) Then
605.                     Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .05
606.                 End If
607.                 If ((Shape(ShapeIndex).Omega * Shape(ShapeIndex).Omega) < .000015 * LowLimitVelocity) Then
608.                     Shape(ShapeIndex).Omega = 0
609.                 End If
610.             End If
611.  
612.             ' Rotation update
613.             Call RotShape(ShapeIndex, Shape(ShapeIndex).Centroid, Shape(ShapeIndex).Omega)
614.  
615.             ' Position update
616.             Call TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
617.  
618.             ' Motion Damping
619.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * MotionDamping
620.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * MotionDamping
621.             Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * MotionDamping
622.  
623.         Else
624.  
625.             ' Lock all motion
626.             Shape(ShapeIndex).Velocity.x = 0
627.             Shape(ShapeIndex).Velocity.y = 0
628.             Shape(ShapeIndex).Omega = 0
629.  
630.         End If
631.     Next
632.  
633. End Sub
634.  
635. Sub Graphics
636.     Line (0, 0)-(_Width, _Height), _RGBA(0, 0, 0, 200), BF
637.     Locate 1, 1: Print ProximalPairsCount, CollisionCount, ContactPoints
638.     For ShapeIndex = 1 To ShapeCount
639.         For i = 1 To Shape(ShapeIndex).Elements - 1
640.             Call cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
641.             Call cline(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, PointChain(ShapeIndex, i + 1).x, PointChain(ShapeIndex, i + 1).y, Shape(ShapeIndex).Shade)
642.             If (ShapeIndex = SelectedShape) Then
643.                 Call ccircle(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, 1, Shape(ShapeIndex).Shade)
644.             End If
645.         Next
646.         Call cpset(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, Shape(ShapeIndex).Shade)
647.         Call cline(PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, Shape(ShapeIndex).Shade)
648.         Call cline(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
649.         If (ShapeIndex = SelectedShape) Then
650.             Call ccircle(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, 3, Shape(ShapeIndex).Shade)
651.             Call cpaint(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, Shape(ShapeIndex).Shade, Shape(ShapeIndex).Shade)
652.         End If
653.     Next
654.     _Display
655. End Sub
656.  
657. Function IntegrateArray (arr() As Integer, lim As Integer)
658.     t = 0
659.     For j = 1 To lim
660.         t = t + arr(j)
661.     Next
662.     IntegrateArray = t
663. End Function
664.  
665. Function CalculateNormalX (k As Integer, i As Integer)
666.     Dim l As Vector
667.     Dim r As Vector
668.     li = i - 1
669.     ri = i + 1
670.     If (i = 1) Then li = Shape(k).Elements
671.     If (i = Shape(k).Elements) Then ri = 1
672.     l.x = PointChain(k, li).x
673.     r.x = PointChain(k, ri).x
674.     dx = r.x - l.x
675.     CalculateNormalX = dx
676. End Function
677.  
678. Function CalculateNormalY (k As Integer, i As Integer)
679.     Dim l As Vector
680.     Dim r As Vector
681.     li = i - 1
682.     ri = i + 1
683.     If (i = 1) Then li = Shape(k).Elements
684.     If (i = Shape(k).Elements) Then ri = 1
685.     l.y = PointChain(k, li).y
686.     r.y = PointChain(k, ri).y
687.     dy = r.y - l.y
688.     CalculateNormalY = dy
689. End Function
690.  
691. Sub CalculateCentroid (k As Integer)
692.     xx = 0
693.     yy = 0
694.     For i = 1 To Shape(k).Elements
695.         xx = xx + PointChain(k, i).x
696.         yy = yy + PointChain(k, i).y
697.     Next
698.     Shape(k).Centroid.x = xx / Shape(k).Elements
699.     Shape(k).Centroid.y = yy / Shape(k).Elements
700. End Sub
701.  
702. Sub CalculateDiameter (k As Integer)
703.     r2max = -1
704.     For i = 1 To Shape(k).Elements
705.         xx = Shape(k).Centroid.x - PointChain(k, i).x
706.         yy = Shape(k).Centroid.y - PointChain(k, i).y
707.         r2 = xx * xx + yy * yy
708.         If (r2 > r2max) Then
709.             r2max = r2
710.         End If
711.     Next
712.     Shape(k).Diameter = Sqr(r2max)
713. End Sub
714.  
715. Sub CalculateMass (k As Integer, factor As Double)
716.     aa = 0
717.     For i = 2 To Shape(k).Elements
718.         x = PointChain(k, i).x - Shape(k).Centroid.x
719.         y = PointChain(k, i).y - Shape(k).Centroid.y
720.         dx = (PointChain(k, i).x - PointChain(k, i - 1).x)
721.         dy = (PointChain(k, i).y - PointChain(k, i - 1).y)
722.         da = .5 * (x * dy - y * dx)
723.         aa = aa + da
724.     Next
725.     Shape(k).Mass = factor * Sqr(aa * aa)
726. End Sub
727.  
728. Sub CalculateMOI (k As Integer, ctrvec As Vector)
729.     xx = 0
730.     yy = 0
731.     For i = 1 To Shape(k).Elements
732.         a = ctrvec.x - PointChain(k, i).x
733.         b = ctrvec.y - PointChain(k, i).y
734.         xx = xx + a * a
735.         yy = yy + b * b
736.     Next
737.     Shape(k).MOI = Sqr((xx + yy) * (xx + yy)) * (Shape(k).Mass / Shape(k).Elements)
738. End Sub
739.  
740. Sub TranslateShape (k As Integer, c As Vector)
741.     For i = 1 To Shape(k).Elements
742.         PointChain(k, i).x = PointChain(k, i).x + c.x
743.         PointChain(k, i).y = PointChain(k, i).y + c.y
744.     Next
745.     Shape(k).Centroid.x = Shape(k).Centroid.x + c.x
746.     Shape(k).Centroid.y = Shape(k).Centroid.y + c.y
747. End Sub
748.  
749. Sub RotShape (k As Integer, c As Vector, da As Double)
750.     For i = 1 To Shape(k).Elements
751.         xx = PointChain(k, i).x - c.x
752.         yy = PointChain(k, i).y - c.y
753.         PointChain(k, i).x = c.x + xx * Cos(da) - yy * Sin(da)
754.         PointChain(k, i).y = c.y + yy * Cos(da) + xx * Sin(da)
755.     Next
756. End Sub
757.  
758. Sub NewAutoBall (x1 As Double, y1 As Double, r1 As Double, r2 As Double, pa As Double, pb As Double, fx As Integer)
759.     ShapeCount = ShapeCount + 1
760.     Shape(ShapeCount).Fixed = fx
761.     Shape(ShapeCount).Collisions = 0
762.     i = 0
763.     For j = 0 To (8 * Atn(1)) Step .02 * 8 * Atn(1)
764.         i = i + 1
765.         r = r1 + r2 * Cos(pa * j) ^ pb
766.         PointChain(ShapeCount, i).x = x1 + r * Cos(j)
767.         PointChain(ShapeCount, i).y = y1 + r * Sin(j)
768.     Next
769.     Shape(ShapeCount).Elements = i
770.     Call CalculateCentroid(ShapeCount)
771.     If (fx = 0) Then
772.         Call CalculateMass(ShapeCount, 1)
773.     Else
774.         Call CalculateMass(ShapeCount, 999999)
775.     End If
776.     Call CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
777.     Call CalculateDiameter(ShapeCount)
778.     Shape(ShapeCount).Velocity.x = 0
779.     Shape(ShapeCount).Velocity.y = 0
780.     Shape(ShapeCount).Omega = 0
781.     If (fx = 0) Then
782.         Shape(ShapeCount).Shade = _RGB(100 + Int(Rnd * 155), 100 + Int(Rnd * 155), 100 + Int(Rnd * 155))
783.     Else
784.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
785.     End If
786.     SelectedShape = ShapeCount
787. End Sub
788.  
789. Sub NewAutoBrick (x1 As Double, y1 As Double, wx As Double, wy As Double, ang As Double)
790.     ShapeCount = ShapeCount + 1
791.     Shape(ShapeCount).Fixed = 1
792.     Shape(ShapeCount).Collisions = 0
793.     i = 0
794.     For j = -wy / 2 To wy / 2 Step 5
795.         i = i + 1
796.         PointChain(ShapeCount, i).x = x1 + wx / 2
797.         PointChain(ShapeCount, i).y = y1 + j
798.     Next
799.     For j = wx / 2 To -wx / 2 Step -5
800.         i = i + 1
801.         PointChain(ShapeCount, i).x = x1 + j
802.         PointChain(ShapeCount, i).y = y1 + wy / 2
803.     Next
804.     For j = wy / 2 To -wy / 2 Step -5
805.         i = i + 1
806.         PointChain(ShapeCount, i).x = x1 - wx / 2
807.         PointChain(ShapeCount, i).y = y1 + j
808.     Next
809.     For j = -wx / 2 To wx / 2 Step 5
810.         i = i + 1
811.         PointChain(ShapeCount, i).x = x1 + j
812.         PointChain(ShapeCount, i).y = y1 - wy / 2
813.     Next
814.     Shape(ShapeCount).Elements = i
815.     Call CalculateCentroid(ShapeCount)
816.     Call CalculateMass(ShapeCount, 99999)
817.     Call CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
818.     Call CalculateDiameter(ShapeCount)
819.     Shape(ShapeCount).Velocity.x = 0
820.     Shape(ShapeCount).Velocity.y = 0
821.     Shape(ShapeCount).Omega = 0
822.     Shape(ShapeCount).Shade = _RGB(100, 100, 100)
823.     SelectedShape = ShapeCount
824.     Call RotShape(ShapeCount, Shape(ShapeCount).Centroid, ang)
825. End Sub
826.  
827. Sub NewBrickLine (xi As Double, yi As Double, xf As Double, yf As Double, wx As Double, wy As Double)
828.     d1 = Sqr((xf - xi) ^ 2 + (yf - yi) ^ 2)
829.     d2 = Sqr(wx ^ 2 + wy ^ 2)
830.     ang = Atn((yf - yi) / (xf - xi))
831.     f = 1.2 * d2 / d1
832.     For t = 0 To 1 + f Step f
833.         Call NewAutoBrick(xi * (1 - t) + xf * t, yi * (1 - t) + yf * t, wx, wy, ang)
834.     Next
835. End Sub
836.  
837. Sub NewMouseShape (rawresolution As Double, targetpoints As Integer, smoothiterations As Integer)
838.     ShapeCount = ShapeCount + 1
839.     Shape(ShapeCount).Fixed = 0
840.     Shape(ShapeCount).Collisions = 0
841.     numpoints = 0
842.     xold = 999 ^ 999
843.     yold = 999 ^ 999
844.     Do
845.         Do While _MouseInput
846.             x = _MouseX
847.             y = _MouseY
848.             If (x > 0) And (x < _Width) And (y > 0) And (y < _Height) Then
849.                 If _MouseButton(1) Then
850.                     x = x - (_Width / 2)
851.                     y = -y + (_Height / 2)
852.                     delta = Sqr((x - xold) ^ 2 + (y - yold) ^ 2)
853.                     If (delta > rawresolution) And (numpoints < targetpoints - 1) Then
854.                         numpoints = numpoints + 1
855.                         PointChain(ShapeCount, numpoints).x = x
856.                         PointChain(ShapeCount, numpoints).y = y
857.                         Call cpset(x, y, _RGB(0, 255, 255))
858.                         xold = x
859.                         yold = y
860.                     End If
861.                 End If
862.             End If
863.         Loop
864.         _Display
865.     Loop Until Not _MouseButton(1) And (numpoints > 1)
866.  
867.     Do While (numpoints < targetpoints)
868.         rad2max = -1
869.         kmax = -1
870.         For k = 1 To numpoints - 1
871.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
872.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
873.             rad2 = xfac ^ 2 + yfac ^ 2
874.             If rad2 > rad2max Then
875.                 kmax = k
876.                 rad2max = rad2
877.             End If
878.         Next
879.         edgecase = 0
880.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
881.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
882.         rad2 = xfac ^ 2 + yfac ^ 2
883.         If (rad2 > rad2max) Then
884.             kmax = numpoints
885.             rad2max = rad2
886.             edgecase = 1
887.         End If
888.         numpoints = numpoints + 1
889.         If (edgecase = 0) Then
890.             For j = numpoints To kmax + 1 Step -1
891.                 PointChain(ShapeCount, j + 1).x = PointChain(ShapeCount, j).x
892.                 PointChain(ShapeCount, j + 1).y = PointChain(ShapeCount, j).y
893.             Next
894.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
895.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
896.         Else
897.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + PointChain(ShapeCount, numpoints - 1).x)
898.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + PointChain(ShapeCount, numpoints - 1).y)
899.         End If
900.     Loop
901.  
902.     For j = 1 To smoothiterations
903.         For k = 2 To numpoints - 1
904.             TempChain(ShapeCount, k).x = (1 / 2) * (PointChain(ShapeCount, k - 1).x + PointChain(ShapeCount, k + 1).x)
905.             TempChain(ShapeCount, k).y = (1 / 2) * (PointChain(ShapeCount, k - 1).y + PointChain(ShapeCount, k + 1).y)
906.         Next
907.         For k = 2 To numpoints - 1
908.             PointChain(ShapeCount, k).x = TempChain(ShapeCount, k).x
909.             PointChain(ShapeCount, k).y = TempChain(ShapeCount, k).y
910.         Next
911.         TempChain(ShapeCount, 1).x = (1 / 2) * (PointChain(ShapeCount, numpoints).x + PointChain(ShapeCount, 2).x)
912.         TempChain(ShapeCount, 1).y = (1 / 2) * (PointChain(ShapeCount, numpoints).y + PointChain(ShapeCount, 2).y)
913.         PointChain(ShapeCount, 1).x = TempChain(ShapeCount, 1).x
914.         PointChain(ShapeCount, 1).y = TempChain(ShapeCount, 1).y
915.         TempChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + PointChain(ShapeCount, numpoints - 1).x)
916.         TempChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + PointChain(ShapeCount, numpoints - 1).y)
917.         PointChain(ShapeCount, numpoints).x = TempChain(ShapeCount, numpoints).x
918.         PointChain(ShapeCount, numpoints).y = TempChain(ShapeCount, numpoints).y
919.     Next
920.  
921.     Shape(ShapeCount).Elements = numpoints
922.     Call CalculateCentroid(ShapeCount)
923.     Call CalculateMass(ShapeCount, 1)
924.     Call CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
925.     Call CalculateDiameter(ShapeCount)
926.     Shape(ShapeCount).Velocity.x = 0
927.     Shape(ShapeCount).Velocity.y = 0
928.     Shape(ShapeCount).Omega = 0
929.     Shape(ShapeCount).Shade = _RGB(100 + Int(Rnd * 155), 100 + Int(Rnd * 155), 100 + Int(Rnd * 155))
930.     SelectedShape = ShapeCount
931. End Sub
932.  
933. Sub cline (x1 As Double, y1 As Double, x2 As Double, y2 As Double, col As _Unsigned Long)
934.     Line (_Width / 2 + x1, -y1 + _Height / 2)-(_Width / 2 + x2, -y2 + _Height / 2), col
935. End Sub
936.  
937. Sub ccircle (x1 As Double, y1 As Double, rad As Double, col As _Unsigned Long)
938.     Circle (_Width / 2 + x1, -y1 + _Height / 2), rad, col
939. End Sub
940.  
941. Sub cpset (x1 As Double, y1 As Double, col As _Unsigned Long)
942.     PSet (_Width / 2 + x1, -y1 + _Height / 2), col
943. End Sub
944.  
945. Sub cpaint (x1 As Double, y1 As Double, col1 As _Unsigned Long, col2 As _Unsigned Long)
946.     Paint (_Width / 2 + x1, -y1 + _Height / 2), col1, col2
947. End Sub
948.  
949. Sub cprintstring (y As Double, a As String)
950.     _PrintString (_Width / 2 - (Len(a) * 8) / 2, -y + _Height / 2), a
951. End Sub
952.  
953. Sub snd (frq As Double, dur As Double)
954.     If ((frq >= 37) And (frq <= 2000)) Then
955.         Sound frq, dur
956.     End If
957. End Sub
958.  
959. Sub SetupPoolGame
960.     ' Set external field
961.     ForceField.x = 0
962.     ForceField.y = 0
963.  
964.     ' Rectangular border
965.     wx = 42
966.     wy = 10
967.     Call NewBrickLine(-_Width / 2 + wx, _Height / 2 - wy, _Width / 2 - wx, _Height / 2 - wy, wx, wy)
968.     Call NewBrickLine(-_Width / 2 + wx, -_Height / 2 + wy, _Width / 2 - wx, -_Height / 2 + wy, wx, wy)
969.     wx = 40
970.     wy = 10
971.     Call NewBrickLine(-_Width / 2 + wy, -_Height / 2 + 2 * wx, -_Width / 2 + wy, _Height / 2 - 2 * wx, wx, wy)
972.     Call NewBrickLine(_Width / 2 - wy, -_Height / 2 + 2 * wx, _Width / 2 - wy, _Height / 2 - 2 * wx, wx, wy)
973.  
974.     ' Balls (billiard setup)
975.     x0 = 160
976.     y0 = 0
977.     r = 15
978.     gg = 2 * r + 4
979.     gx = gg * Cos(30 * 3.14159 / 180)
980.     gy = gg * Sin(30 * 3.14159 / 180)
981.     Call NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, r, 0, 1, 1, 0)
982.     Call NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, r, 0, 1, 1, 0)
983.     Call NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, r, 0, 1, 1, 0)
984.     Call NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, r, 0, 1, 1, 0)
985.     Call NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, r, 0, 1, 1, 0)
986.     Call NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, r, 0, 1, 1, 0)
987.     Call NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, r, 0, 1, 1, 0)
988.     Call NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, r, 0, 1, 1, 0)
989.     Call NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, r, 0, 1, 1, 0)
990.     Call NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, r, 0, 1, 1, 0)
991.     Call NewAutoBall(x0 + 4 * gx, y0 + 4 * gy, r, 0, 1, 1, 0)
992.     Call NewAutoBall(x0 + 4 * gx, y0 + 2 * gy, r, 0, 1, 1, 0)
993.     Call NewAutoBall(x0 + 4 * gx, y0 - 0 * gy, r, 0, 1, 1, 0)
994.     Call NewAutoBall(x0 + 4 * gx, y0 - 2 * gy, r, 0, 1, 1, 0)
995.     Call NewAutoBall(x0 + 4 * gx, y0 - 4 * gy, r, 0, 1, 1, 0)
996.  
997.     ' Cue ball
998.     Call NewAutoBall(-220, 0, r, 0, 1, 1, 0)
999.     Shape(ShapeCount).Velocity.x = 10 + 2 * Rnd
1000.     Shape(ShapeCount).Velocity.y = 1 * (Rnd - .5)
1001.     Shape(ShapeCount).Shade = _RGB(255, 255, 255)
1002.  
1003.     ' Parameters
1004.     CPC = 1.15
1005.     FPC = 8
1006.     RST = 0.75
1007.     VD = 0.995
1008.     SV = 0
1009. End Sub
1010.  
1011. Sub SetupWackyGame
1012.     ' Set external field
1013.     ForceField.x = 0
1014.     ForceField.y = -.08
1015.  
1016.     ' Rectangular border
1017.     wx = 42
1018.     wy = 10
1019.     Call NewBrickLine(-_Width / 2 + wx, _Height / 2 - wy, _Width / 2 - wx, _Height / 2 - wy, wx, wy)
1020.     Call NewBrickLine(-_Width / 2 + wx, -_Height / 2 + wy, _Width / 2 - wx, -_Height / 2 + wy, wx, wy)
1021.     wx = 40
1022.     wy = 10
1023.     Call NewBrickLine(-_Width / 2 + wy, -_Height / 2 + 2 * wx, -_Width / 2 + wy, _Height / 2 - 2 * wx, wx, wy)
1024.     Call NewBrickLine(_Width / 2 - wy, -_Height / 2 + 2 * wx, _Width / 2 - wy, _Height / 2 - 2 * wx, wx, wy)
1025.  
1026.     ' Wacky balls
1027.     x0 = -70
1028.     y0 = 120
1029.     r1 = 15
1030.     r2 = 2.5
1031.     gg = 2.5 * (r1 + r2) + 3.5
1032.     gx = gg * Cos(30 * 3.14159 / 180)
1033.     gy = gg * Sin(30 * 3.14159 / 180)
1034.     Call NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1035.     Call NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1036.     Call NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1037.     Call NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1038.     Call NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1039.     Call NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1040.     Call NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1041.     Call NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1042.     Call NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1043.     Call NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, r1, r2, Int(Rnd * 3) + 1, Int(Rnd * 1) + 2, 0)
1044.  
1045.     ' Slanted bricks
1046.     wx = 60
1047.     wy = 10
1048.     ww = Sqr(wx * wx + wy * wy) * .85
1049.     Call NewBrickLine(ww, 0, 100 + ww, 100, wx, wy)
1050.     Call NewBrickLine(-ww, 0, -100 - ww, 100, wx, wy)
1051.  
1052.     ' Fidget spinner
1053.     Call NewAutoBall(-220, 0, 20, 15, 1.5, 2, 0)
1054.     Shape(ShapeCount).Shade = _RGB(255, 255, 255)
1055.  
1056.     ' Parameters
1057.     CPC = 1.15
1058.     FPC = 8
1059.     RST = 0.70
1060.     VD = 0.995
1061.     SV = 0.025
1062. End Sub
1063.  
1064. Sub SetupRings
1065.     ' Set external field
1066.     ForceField.x = 0
1067.     ForceField.y = 0
1068.  
1069.     ' Rectangular border
1070.     wx = 42
1071.     wy = 10
1072.     Call NewBrickLine(-_Width / 2 + wx, _Height / 2 - wy, _Width / 2 - wx, _Height / 2 - wy, wx, wy)
1073.     Call NewBrickLine(-_Width / 2 + wx, -_Height / 2 + wy, _Width / 2 - wx, -_Height / 2 + wy, wx, wy)
1074.     wx = 40
1075.     wy = 10
1076.     Call NewBrickLine(-_Width / 2 + wy, -_Height / 2 + 2 * wx, -_Width / 2 + wy, _Height / 2 - 2 * wx, wx, wy)
1077.     Call NewBrickLine(_Width / 2 - wy, -_Height / 2 + 2 * wx, _Width / 2 - wy, _Height / 2 - 2 * wx, wx, wy)
1078.  
1079.     For r = 25 To 175 Step 25
1080.         Call NewAutoBall(0, 0, r, 0, 1, 1, 0)
1081.     Next
1082.  
1083.     ' Parameters
1084.     CPC = 1.15
1085.     FPC = 8
1086.     RST = 0.75
1087.     VD = 0.995
1088.     SV = 0.025
1089. End Sub
1090.  
1091. Sub SetupWallsOnly
1092.     ' Set external field
1093.     ForceField.x = 0
1094.     ForceField.y = 0 - .08
1095.  
1096.     ' Fidget spinner
1097.     Call NewAutoBall(-220, 0, 20, 15, 1.5, 2, 0)
1098.     Shape(ShapeCount).Shade = _RGB(255, 255, 255)
1099.  
1100.     ' Rectangular border
1101.     wx = 42
1102.     wy = 10
1103.     Call NewBrickLine(-_Width / 2 + wx, _Height / 2 - wy, _Width / 2 - wx, _Height / 2 - wy, wx, wy)
1104.     Call NewBrickLine(-_Width / 2 + wx, -_Height / 2 + wy, _Width / 2 - wx, -_Height / 2 + wy, wx, wy)
1105.     wx = 40
1106.     wy = 10
1107.     Call NewBrickLine(-_Width / 2 + wy, -_Height / 2 + 2 * wx, -_Width / 2 + wy, _Height / 2 - 2 * wx, wx, wy)
1108.     Call NewBrickLine(_Width / 2 - wy, -_Height / 2 + 2 * wx, _Width / 2 - wy, _Height / 2 - 2 * wx, wx, wy)
1109.  
1110.     ' Parameters
1111.     CPC = 1.15
1112.     FPC = 8
1113.     RST = 0.75
1114.     VD = 0.995
1115.     SV = 0.025
1116. End Sub
1117.  
1118. Sub SetupAnglePong
1119.     ' Set external field
1120.     ForceField.x = 0
1121.     ForceField.y = 0
1122.  
1123.     ' Rectangular border
1124.     wx = 42
1125.     wy = 10
1126.     Call NewBrickLine(-_Width / 2 + wx, _Height / 2 - wy, _Width / 2 - wx, _Height / 2 - wy, wx, wy)
1127.     Call NewBrickLine(-_Width / 2 + wx, -_Height / 2 + wy, _Width / 2 - wx, -_Height / 2 + wy, wx, wy)
1128.     wx = 40
1129.     wy = 10
1130.     Call NewBrickLine(-_Width / 2 + wy, -_Height / 2 + 2 * wx, -_Width / 2 + wy, _Height / 2 - 2 * wx, wx, wy)
1131.     Call NewBrickLine(_Width / 2 - wy, -_Height / 2 + 2 * wx, _Width / 2 - wy, _Height / 2 - 2 * wx, wx, wy)
1132.  
1133.     ' Pong ball
1134.     Call NewAutoBall(0, 200, 20, 0, 1, 1, 0)
1135.     Shape(ShapeCount).Velocity.x = -1
1136.     Shape(ShapeCount).Velocity.y = -3
1137.     Shape(ShapeCount).Shade = _RGB(255, 255, 255)
1138.  
1139.     ' Pong Paddle
1140.     Call NewAutoBrick(-100, 10, 100, -10, -.02 * 8 * Atn(1))
1141.     vtemp.x = 0
1142.     vtemp.y = -200
1143.     Call TranslateShape(ShapeCount, vtemp)
1144.     Shape(ShapeCount).Shade = _RGB(200, 200, 200)
1145.  
1146.     ' Parameters
1147.     CPC = 1.15
1148.     FPC = 8
1149.     RST = 1 '0.75
1150.     VD = 1 '0.995
1151.     SV = 0.025
1152. End Sub

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 27, 2021, 02:28:17 am

several coffees later

was having problems with ball contact and I thought FULLSCREEN was to blame. Actually the FULLSCREEN is very precise.   Run the code and try the arrow keys. See how the balls maintain perfect contact at all positions.

Keys to rotate vector are z or x
keys to adjust vector magnitude (ball velocity) are c or v
Key to toggle red or cyan ball is b

As in the original code, the arrow keys move the ball positions.

rotate vector has an auto fine / coarse control.   hold down key longer, for coarse rotation and momentary for fine rotation.

Code shows how WINDOW, FULLSCREEN and NEWIMAGE can work together to make graphics larger on the computer display. This method fills the entire screen automatically.  This should work on any size of computer display.

Everyone puts down FULLSCREEN  but it has it's uses.  There are probably even better ways to do this.

Code: QB64: [Select]

1. 'Original code by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   position
14.     m AS V2 '                                                   movement (pre-contact) incoming
15.     x AS V2 '                                                   vector of post contact movement
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18.  
19. DIM TEXT(1) AS STRING
20. DIM RAD AS SINGLE
21. RAD = 0
22. DIM c(1) AS STRING
23. DIM AR AS SINGLE
24. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
25. DIM mouse AS V2
26. DIM b(1) AS ball
27. 'DIM SHARED AS V2 origin
28. DIM SHARED origin AS V2
29. origin.x = 0: origin.y = 0
30. b(0).c = Red: b(0).cn = "red"
31. b(1).c = Cyan: b(1).cn = "cyan"
32.  
33. SCREEN _NEWIMAGE(600, 600, 32) ' this will (should) allow the magnify effect of fullscreen
34. DO: LOOP UNTIL _SCREENEXISTS
35. _SCREENMOVE 10, 10
36.  
37. AR = _DESKTOPWIDTH / _DESKTOPHEIGHT 'Aspect ratio
38.  
39. y1 = (600 / ((_DESKTOPWIDTH / _DESKTOPHEIGHT) + 1))
40.  
41. x1 = (600 / ((_DESKTOPHEIGHT / _DESKTOPWIDTH) + 1))
42.  
43. WINDOW (-x1, y1)-(x1, -y1) 'correct fullscreen x , y  distortion etc
44.  
45. _FULLSCREEN
46.  
47. 'starting state
48. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
49. b(0).s = PyT(origin, b(0).m)
50. 'b(0).s = _HYPOT(origin.x - b(0).m.x, origin.y - b(0).m.y) ' reds magnitude (speed or force)
51.  
52. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
53. b(1).s = PyT(origin, b(1).m)
54. 'b(1).s = _HYPOT(origin.x - b(1).m.x, origin.y - b(1).m.y) ' cyans magnitude (speed or force)
55.  
56. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
57. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
58.  
59. DO
60.     CLS
61.     ms = MBS '                                                  process mouse actions dragging endpoints
62.     IF ms AND 64 THEN
63.  
64.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
65.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
66.  
67.         FOR x = 0 TO 1
68.             FOR y = 0 TO 1
69.                 ds! = PyT(vertex(x, y), mouse)
70.                 IF ds! < ballradius * .5 THEN i = x: j = y
71.             NEXT y
72.         NEXT x
73.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
74.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
75.                 b(i).p = mouse
76.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
77.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
78.         END SELECT
79.     END IF
80.  
81.     'IF _KEYDOWN(114) THEN i = 0
82.     'IF _KEYDOWN(99) THEN i = 1
83.     IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
84.     IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
85.     IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
86.     IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
87.  
88.     'IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
89.     'IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
90.     'IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
91.     'IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
92.  
93.     '**************Code added by Novarseg
94.     'Vector rotation and vector magnitude adjustment using keyboard input
95.  
96.     I$ = INKEY$
97.  
98.     _DELAY .04 'allows enough time for keyboard buffer to accumulate characters
99.     '           so the vector rotation (fast / slow) operates properly
100.     '           there is probably a better way to do this
101.     IF I$ = "" THEN f1 = 0
102.  
103.     IF f3 = 0 THEN I$ = "b": f3 = 1
104.     IF I$ = "b" AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
105.     IF I$ = "b" AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
106.     LL1:
107.  
108.     IF I$ = "c" THEN 'increase vector magnitude
109.         mult = 1.01
110.         VecMult b(i).m, mult
111.     END IF
112.  
113.     IF I$ = "v" THEN 'decrease vector magnitude
114.         div = 1.01
115.         VecDIV b(i).m, div 'added a new sub
116.     END IF
117.  
118.     IF I$ = "z" THEN 'rotate vector counter clockwise
119.         IF RAD > _PI * 2 THEN RAD = 0
120.  
121.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
122.         IF TIMER - t1 > 1.5 THEN RAD = RAD + .05
123.         IF TIMER - t1 <= 1.5 THEN RAD = RAD + .005
124.  
125.         signC = COS(RAD) * 1 / ABS(COS(RAD))
126.         signS = SIN(RAD) * 1 / ABS(SIN(RAD))
127.         b(i).s = PyT(origin, b(i).m)
128.         b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
129.         b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
130.  
131.     END IF
132.  
133.     IF I$ = "x" THEN 'rotate vector clockwise
134.         IF RAD < 0 THEN RAD = _PI * 2
135.  
136.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
137.         IF TIMER - t1 > 1.5 THEN RAD = RAD - .05
138.         IF TIMER - t1 <= 1.5 THEN RAD = RAD - .005
139.  
140.         signC = COS(RAD) * 1 / ABS(COS(RAD))
141.         signS = SIN(RAD) * 1 / ABS(SIN(RAD))
142.         b(i).s = PyT(origin, b(i).m)
143.         b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
144.         b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
145.  
146.  
147.     END IF
148.     '**************END Code added Novarseg
149.  
150.  
151.     'START OF COLLISION MATHEMATICS SECTION
152.     ballradius = bPyT(b(0).p, b(1).p, AR) / 2 'the only time this function is used
153.  
154.     FOR bn = 0 TO 1
155.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
156.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
157.     NEXT bn
158.  
159.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
160.     B2BCollision b(0), b(1)
161.     'END OF COLLISION MATHEMATICS SECTION
162.  
163.     'graphic representation
164.     FOR grid = -300 TO 300 STEP 20
165.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
166.         LINE (grid, 300)-(grid, -300), c& 'Gray  'vertical lines
167.         LINE (-300, grid)-(300, grid), c& ' Gray  'horizontal lines
168.     NEXT grid
169.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
170.  
171.     FOR dr = 0 TO 1
172.  
173.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , AR
174.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
175.  
176.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
177.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
178.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
179.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
180.  
181.         _PRINTSTRING (0, 567 + (16 * dr)), b$
182.  
183.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
184.     NEXT dr
185.  
186.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
187.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
188.         PUT #1, , TEXT(0) 'NOVARSEG added this line
189.         PUT #1, , TEXT(1) 'NOVARSEG added this line
190.         CLOSE 'NOVARSEG added this line
191.     END IF 'NOVARSEG added this line
192.  
193.     ' _LIMIT 500
194.     _DISPLAY
195. LOOP UNTIL _KEYDOWN(27)
196. END
197.  
198.  
199. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
200.  
201.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
202.     DIM un AS V2
203.     DIM ut AS V2
204.     DIM ncomp1 AS V2
205.     DIM ncomp2 AS V2
206.     DIM tcomp1 AS V2
207.     DIM tcomp2 AS V2
208.  
209.  
210.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
211.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
212.     bnci1 = VecDot(un, ball1.m) '
213.     bnci2 = VecDot(un, ball2.m) '
214.     btci1 = VecDot(ut, ball1.m) '
215.     btci2 = VecDot(ut, ball2.m) '
216.  
217.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
218.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
219.  
220.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
221.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
222.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
223.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
224.  
225.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
226.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
227.  
228. END SUB 'B2BCollision
229.  
230.  
231. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
232.  
233.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
234.  
235. END FUNCTION 'map!
236.  
237.  
238. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
239.     STATIC StartTimer AS _FLOAT
240.     STATIC ButtonDown AS INTEGER
241.     STATIC ClickCount AS INTEGER
242.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
243.     '                          Down longer counts as a HOLD event.
244.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
245.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
246.         SELECT CASE SGN(_MOUSEWHEEL)
247.             CASE 1: MBS = MBS OR 512
248.             CASE -1: MBS = MBS OR 1024
249.         END SELECT
250.     WEND
251.  
252.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
253.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
254.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
255.  
256.     IF StartTimer = 0 THEN
257.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
258.             ButtonDown = 1: StartTimer = TIMER(0.01)
259.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
260.         ELSEIF _MOUSEBUTTON(2) THEN
261.             ButtonDown = 2: StartTimer = TIMER(0.01)
262.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
263.         ELSEIF _MOUSEBUTTON(3) THEN
264.             ButtonDown = 3: StartTimer = TIMER(0.01)
265.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
266.         END IF
267.     ELSE
268.         BD = ButtonDown MOD 3
269.         IF BD = 0 THEN BD = 3
270.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
271.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
272.         ELSE
273.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
274.                 MBS = 0: ButtonDown = 0: StartTimer = 0
275.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
276.             ELSE 'We've now started the hold event
277.                 MBS = MBS OR 32 * 2 ^ ButtonDown
278.             END IF
279.         END IF
280.     END IF
281. END FUNCTION 'MBS%
282.  
283.  
284. FUNCTION PyT (var1 AS V2, var2 AS V2)
285.  
286.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
287.  
288. END FUNCTION 'PyT
289.  
290. FUNCTION bPyT (var1 AS V2, var2 AS V2, var3) 'to calulate ball radius only
291.     'var1.x = var1.x * 1.6384
292.     bPyT = _HYPOT((var1.x - var2.x) * var3, (var1.y - var2.y) * var3)
293.  
294. END FUNCTION 'bPyT
295.  
296.  
297.  
298. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
299.  
300.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
301.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
302.  
303. END SUB 'Add_Vector
304.  
305.  
306. FUNCTION VecDot (var AS V2, var2 AS V2)
307.  
308.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
309.  
310. END FUNCTION 'VecDot
311.  
312.  
313. SUB VecMult (vec AS V2, multiplier AS SINGLE)
314.  
315.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
316.     vec.y = vec.y * multiplier
317.  
318. END SUB 'Vec_Mult
319.  
320. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
321.  
322.     vec.x = vec.x / divisor
323.     vec.y = vec.y / divisor
324.  
325. END SUB 'VecDIV
326.  
327.  
328. SUB VecNorm (var AS V2)
329.  
330.     m = PyT(origin, var)
331.     IF m = 0 THEN
332.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
333.     ELSE
334.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
335.     END IF
336.  
337. END SUB 'VecNorm

@STxAxTIC
realistic effects

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 27, 2021, 09:06:33 pm

I think I may have solved my magnetic ball issue. This latest version even seems to break well. At least I haven't been able to "break" it yet... and I'm amazed at how much the code distilled down. I'm starting to feel like I can now invest time and stress in the table details.

Also fixed the cue strike so that it strikes clean and doesn't "thrust" the cueball if you're slow releasing the button.

A couple control pointers:

It uses all mouse buttons and wheel.
roll the wheel back like you're pulling back a pinball spring. A force number will show in the cueball up to a max of 35
roll the wheel the other way and the force will "reduce" to a max of -35. Click the wheel button sets force at max positive.

Why negative force? you might ask...
positive force accelerates the ball away from the  mouse cursor
negative force accelerates the ball toward the mouse cursor
very useful for aiming when you're scrunched up against the table edge.

left click to shoot
click the right mouse button to reset the rack for a new break.

Code: QB64: [Select]

1. $COLOR:32
2. 'ball colors 1 yellow 2 blue 3 red 4 purple 5 orange 6 green 7 maroon 8 black
3. '9 yellow/s 10 blue/s 11 red/s 12 purple/s 13 orange/s 14 green/s 15 maroon/s
4.  
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     sunk AS _BYTE '                                             has ball been sunk true/false
12.     c AS _UNSIGNED LONG '                                       ball color
13.     p AS V2 '                                                   position vector
14.     d AS V2 '                                                   direction vector
15.     n AS V2 '                                                   normalized direction vector
16.     s AS SINGLE '                                               speed
17.     r AS _BYTE '                                                rack position
18. END TYPE
19.  
20. DIM SHARED xtable AS INTEGER
21. DIM SHARED ytable AS INTEGER
22. DIM SHARED xt5 AS INTEGER
23. DIM SHARED bsiz AS INTEGER '                                    radius of ball
24. DIM SHARED bsiz2 AS INTEGER '                                   ball diameter or sphere of contact
25. DIM SHARED bl(15) AS ball '                                     ball data
26. DIM SHARED bnum(15) AS LONG
27. DIM SHARED tbl AS LONG
28. DIM SHARED origin AS V2
29. origin.x = 0: origin.y = 0
30.  
31. 'Set the table size
32. IF _DESKTOPWIDTH > _DESKTOPHEIGHT * 1.6 THEN
33.     xtable = _DESKTOPWIDTH - 100: ytable = xtable / 2
34. ELSE
35.     ytable = _DESKTOPHEIGHT - 80: xtable = ytable * 2
36. END IF
37.  
38.  
39. bsiz = INT(((xtable / 118.1102) * 2.375) / 2) '                 size balls to table
40. bsiz2 = bsiz * 2
41. xt5 = xtable * .05
42.  
43. RANDOMIZE TIMER
44. RESTORE hue
45. FOR x = 0 TO 15
46.     READ bl(x).c
47. NEXT x
48.  
49. MakeTable
50. MakeBalls
51. RackEmUp
52. bl(0).p.y = INT(ytable * .5) '                                  position the cue
53. bl(0).p.x = INT(xtable * .75)
54.  
55. a& = _NEWIMAGE(xtable, ytable, 32)
56. _DEST a&: SCREEN a&
57. DO: LOOP UNTIL _SCREENEXISTS
58. _SCREENMOVE 5, 5
59.  
60. COLOR , &HFF007632
61. CLS
62.  
63. DO
64.     CLS
65.     _PUTIMAGE , tbl, a&
66.  
67.     FOR x = 0 TO 15
68.         IF bl(x).sunk THEN
69.             IF x = 0 THEN
70.                 'scratch
71.                 bl(0).p.y = INT(ytable * .5) '                  position the cue
72.                 bl(0).p.x = INT(xtable * .75)
73.             ELSE
74.                 _CONTINUE
75.             END IF
76.         END IF
77.         VecAdd bl(x).p, bl(x).d, 1
78.         VecMult bl(x).d, .99
79.         IF PyT(origin, bl(x).d) < .05 THEN bl(x).d = origin
80.         ColCheck x
81.         _PUTIMAGE (INT(bl(x).p.x) - CINT(_WIDTH(bnum(x)) / 2), INT(bl(x).p.y) - CINT(_HEIGHT(bnum(x)) / 2)), bnum(x), a&
82.     NEXT x
83.  
84.     ms = MBS%
85.     IF ms AND 1 THEN
86.         IF (origin.x = bl(0).d.x) AND (origin.y = bl(0).d.y) THEN
87.             bl(0).d.x = bl(0).p.x - _MOUSEX '                   get the cue strike vector
88.             bl(0).d.y = bl(0).p.y - _MOUSEY
89.             VecNorm bl(0).d '                                   shrink it
90.             VecMult bl(0).d, su '                               grow it
91.             DO UNTIL NOT _MOUSEBUTTON(1) '                      prevents cue thrusting,
92.                 WHILE _MOUSEINPUT: WEND '                       i.e. constant acceleration across table
93.             LOOP '                                              while holding down mouse button
94.             su = 0 '                                            reset strike units
95.         END IF
96.     END IF
97.     IF ms AND 2 THEN '                                          if mouse right button reset the rack
98.         BallStop '                                              all displacements to = origin
99.         bl(0).p.y = INT(ytable * .5)
100.         bl(0).p.x = INT(xtable * .75)
101.         RackEmUp
102.     END IF
103.     IF ms AND 4 THEN '                                          if mouse center button, set full strike
104.         IF su = 35 THEN su = 0
105.         IF su = 0 THEN su = 35
106.     END IF
107.     IF ms AND 512 THEN '                                        roll mousewheel back, accelerate away from mouse cursor
108.         su = Limit%(35, su + 1) '                               like pulling back a pinball spring
109.     END IF
110.     IF ms AND 1024 THEN '                                       roll mousewheel frw'd, accelerate towards mouse cursor
111.         su = su + 1 * (su > -35) '                              helpful in aiming from table edge
112.     END IF
113.  
114.     LINE (_MOUSEX, _MOUSEY)-(CINT(bl(0).p.x), CINT(bl(0).p.y))
115.     'slope of target line
116.     pathx = CINT(bl(0).p.x) - _MOUSEX: pathy = CINT(bl(0).p.y) - _MOUSEY
117.     LINE (bl(0).p.x, bl(0).p.y)-(pathx * 1000, pathy * 1000), Blue
118.     IF (bl(0).d.x = 0) AND (bl(0).d.y = 0) THEN
119.         _PRINTSTRING (bl(0).p.x - 8, bl(0).p.y - 8), STR$(su)
120.     END IF
121.     _DISPLAY
122.     _LIMIT 100
123. LOOP UNTIL _KEYDOWN(27)
124.  
125. END
126.  
127. '                                                               DATA SECTION
128. hue:
129. DATA 4294967295,4294967040,4278190335,4294901760,4286578816,4294944000,4278222848,4286578688
130. DATA 4278190080,4294967040,4278190335,4294901760,4286578816,4294944000,4278222848,4286578688
131.  
132. start:
133. DATA 1,2,15,14,8,3,4,6,11,13,12,7,9,10,5,0
134.  
135. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
136.  
137.     DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
138.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
139.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
140.     bnci1 = VecDot(un, ball1.d) '                               ball 1 normal component of input velocity
141.     bnci2 = VecDot(un, ball2.d) '                               ball 2 normal component of input velocity
142.     btci1 = VecDot(ut, ball1.d) '                               ball 1 tangent component of input velocity
143.     btci2 = VecDot(ut, ball2.d) '                               ball 2 tangent component of input velocity
144.  
145.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
146.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
147.  
148.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
149.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
150.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
151.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
152.  
153.     ball1.d = ncomp1: VecAdd ball1.d, tcomp1, 1 '               add normal and tangent exit vectors
154.     ball2.d = ncomp2: VecAdd ball2.d, tcomp2, 1 '               add normal and tangent exit vectors
155.  
156.     VecMult ball1.d, .95 '                                      lets take 5% of energy in entropic factors
157.     VecMult ball2.d, .95
158.  
159. END SUB 'B2BCollision
160.  
161.  
162. SUB BallStop
163.  
164.     FOR x = 0 TO 15
165.         bl(x).d = origin
166.     NEXT x
167.  
168. END SUB 'BallStop
169.  
170.  
171. SUB ColCheck (var AS INTEGER)
172.  
173.     'check for ball in displacement radius
174.     disp = SQR(bl(var).d.x * bl(var).d.x + bl(var).d.y * bl(var).d.y) 'vector magnitude for this iteration
175.     FOR x = 0 TO 15 '
176.         IF x = var THEN _CONTINUE
177.         dist = PyT(bl(var).p, bl(x).p) '                calculate distance between var and x
178.         IF dist < bsiz2 THEN '                          are they closer than two radii, i.e. stuck together
179.             DIM AS V2 un
180.             un = bl(var).p: VecAdd un, bl(x).p, -1 '    get a normal vector between them
181.             VecNorm un '                                shrink it to a unit vector
182.             VecMult un, (bsiz2 - dist) '                grow it by the amount they intersect
183.             VecAdd bl(var).p, un, 1 '                   add it to the position
184.         END IF
185.         IF dist - bsiz2 < disp THEN '                   if ball x is within reach of magnitude
186.             dx = bl(var).p.x - bl(x).p.x
187.             dy = bl(var).p.y - bl(x).p.y
188.             A## = (bl(var).d.x * bl(var).d.x) + (bl(var).d.y * bl(var).d.y) 'displacement range
189.             B## = 2 * bl(var).d.x * dx + 2 * bl(var).d.y * dy
190.                 C## = (bl(x).p.x * bl(x).p.x) + (bl(x).p.y * bl(x).p.y) + (bl(var).p.x * bl(var).p.x)_
191.                      + (bl(var).p.y * bl(var).p.y) + -2 * (bl(x).p.x * bl(var).p.x + bl(x).p.y * bl(var).p.y) - (bsiz2 * bsiz2)
192.             disabc## = (B## * B##) - 4 * A## * C##
193.             IF disabc## > 0 THEN '                          ray intersects ball x position
194.                 B2BCollision bl(var), bl(x)
195.             END IF '                                        end: disabc <= 0  aka ball missed
196.         END IF '                                            end: dist < disp test
197.     NEXT x
198.  
199.     'wall bounces - now we need to work in pocket corners which we will tentatively treat like immobile balls flanking the holes
200.     IF bl(var).p.x < bsiz + xt5 OR bl(var).p.x > xtable - bsiz - xt5 THEN
201.         bl(var).d.x = -bl(var).d.x
202.         IF bl(var).p.x < bsiz + xt5 THEN '                            if beyond left edge
203.             bl(var).p.x = bl(var).p.x + (2 * (bsiz + xt5 - bl(var).p.x))
204.         END IF
205.         IF bl(var).p.x > xtable - bsiz - xt5 THEN '                   if beyond right edge
206.             bl(var).p.x = bl(var).p.x - (2 * (bl(var).p.x - (xtable - bsiz - xt5)))
207.         END IF
208.     END IF
209.     IF bl(var).p.y < bsiz + xt5 OR bl(var).p.y > ytable - bsiz - xt5 THEN
210.         bl(var).d.y = -bl(var).d.y
211.         IF bl(var).p.y < bsiz + xt5 THEN '                            if beyond top edge
212.             bl(var).p.y = bl(var).p.y + (2 * (bsiz + xt5 - bl(var).p.y))
213.         END IF
214.         IF bl(var).p.y > ytable - bsiz - xt5 THEN '                   if beyond bottom edge
215.             bl(var).p.y = bl(var).p.y - (2 * (bl(var).p.y - (ytable - bsiz - xt5)))
216.         END IF
217.     END IF
218.  
219. END SUB 'ColCheck
220.  
221.  
222. SUB FCirc (CX AS INTEGER, CY AS INTEGER, RR AS INTEGER, C AS _UNSIGNED LONG, C2 AS _UNSIGNED LONG)
223.     DIM R AS INTEGER, RError AS INTEGER '                       SMcNeill's circle fill
224.     DIM X AS INTEGER, Y AS INTEGER
225.  
226.     R = ABS(RR)
227.     RError = -R
228.     X = R
229.     Y = 0
230.     IF R = 0 THEN PSET (CX, CY), C: EXIT SUB
231.     LINE (CX - X, CY)-(CX + X, CY), C, BF
232.     WHILE X > Y
233.         RError = RError + Y * 2 + 1
234.         IF RError >= 0 THEN
235.             IF X <> Y + 1 THEN
236.                 LINE (CX - Y, CY - X)-(CX + Y, CY - X), C2, BF 'these two need white here for 9-15 balls
237.                 LINE (CX - Y, CY + X)-(CX + Y, CY + X), C2, BF
238.             END IF
239.             X = X - 1
240.             RError = RError - X * 2
241.         END IF
242.         Y = Y + 1
243.         LINE (CX - X, CY - Y)-(CX + X, CY - Y), C, BF
244.         LINE (CX - X, CY + Y)-(CX + X, CY + Y), C, BF
245.     WEND
246. END SUB 'FCirc
247.  
248.  
249. FUNCTION Limit% (lim AS INTEGER, var AS INTEGER)
250.  
251.     Limit% = lim - ((var - lim) * (var < lim + 1))
252.  
253. END FUNCTION 'Limit%
254.  
255.  
256. SUB MakeBalls
257.  
258.     FOR x = 0 TO 15
259.         'make ball images here
260.         bnum(x) = _NEWIMAGE(bsiz * 2 + 4, bsiz * 2 + 4, 32)
261.         _DEST bnum(x)
262.         IF x = 0 THEN '                                         Cue ball
263.             FCirc INT(_WIDTH(bnum(x)) / 2), INT(_HEIGHT(bnum(x)) / 2), bsiz, bl(x).c, bl(x).c
264.             CIRCLE (_WIDTH(bnum(x)) / 2, _HEIGHT(bnum(x)) / 2), bsiz + 1, Black
265.         ELSE
266.             'Solids or stripes
267.             IF x <= 8 THEN
268.                 FCirc INT(_WIDTH(bnum(x)) / 2), INT(_HEIGHT(bnum(x)) / 2), bsiz, bl(x).c, bl(x).c ' solid
269.             ELSE
270.                 FCirc INT(_WIDTH(bnum(x)) / 2), INT(_HEIGHT(bnum(x)) / 2), bsiz, bl(x).c, White '   stripe
271.             END IF
272.             FCirc INT(_WIDTH(bnum(x)) / 2), INT(_HEIGHT(bnum(x)) / 2), bsiz - 5, White, White 'number circle
273.             CIRCLE (_WIDTH(bnum(x)) / 2, _HEIGHT(bnum(x)) / 2), bsiz + 1, Black
274.             n$ = _TRIM$(STR$(x))
275.             t& = _NEWIMAGE(16, 16, 32)
276.             _DEST t&
277.             COLOR Black
278.             _PRINTMODE _KEEPBACKGROUND
279.             IF LEN(n$) > 1 THEN a = 0 ELSE a = 4
280.             _PRINTSTRING (a, 0), n$, t&
281.             _DEST bnum(x)
282.             _PUTIMAGE (8, 8)-(_WIDTH(bnum(x)) - 8, _HEIGHT(bnum(x)) - 8), t&, bnum(x)
283.             _FREEIMAGE t&
284.         END IF
285.     NEXT x
286.  
287. END SUB 'MakeBalls
288.  
289.  
290. SUB MakeTable
291.  
292.     tbl = _NEWIMAGE(xtable, ytable, 32)
293.     _DEST tbl
294.     COLOR , &HFF007632
295.     CLS
296.     FOR x = 0 TO 2
297.         LINE (x, x)-(xtable - x, ytable - x), Black, B
298.     NEXT x
299.     FCirc xtable * .75, ytable * .5, 5, Gray, Gray
300.     FCirc xtable * .75, ytable * .5, 2, White, White
301.     LINE (xt5, xt5)-(xtable - xt5, ytable - xt5), &HFFFF0000, B , &HF0F0
302.  
303. END SUB 'MakeTable
304.  
305.  
306. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
307.  
308.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
309.  
310. END FUNCTION 'map!
311.  
312.  
313. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
314.     STATIC StartTimer AS _FLOAT
315.     STATIC ButtonDown AS INTEGER
316.     STATIC ClickCount AS INTEGER
317.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
318.     '                          Down longer counts as a HOLD event.
319.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
320.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
321.         SELECT CASE SGN(_MOUSEWHEEL)
322.             CASE 1: MBS = MBS OR 512
323.             CASE -1: MBS = MBS OR 1024
324.         END SELECT
325.     WEND
326.  
327.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
328.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
329.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
330.  
331.     IF StartTimer = 0 THEN
332.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
333.             ButtonDown = 1: StartTimer = TIMER(0.01)
334.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
335.         ELSEIF _MOUSEBUTTON(2) THEN
336.             ButtonDown = 2: StartTimer = TIMER(0.01)
337.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
338.         ELSEIF _MOUSEBUTTON(3) THEN
339.             ButtonDown = 3: StartTimer = TIMER(0.01)
340.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
341.         END IF
342.     ELSE
343.         BD = ButtonDown MOD 3
344.         IF BD = 0 THEN BD = 3
345.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
346.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
347.         ELSE
348.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
349.                 MBS = 0: ButtonDown = 0: StartTimer = 0
350.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
351.             ELSE 'We've now started the hold event
352.                 MBS = MBS OR 32 * 2 ^ ButtonDown
353.             END IF
354.         END IF
355.     END IF
356. END FUNCTION 'MBS%
357.  
358.  
359. FUNCTION PyT (var1 AS V2, var2 AS V2)
360.  
361.     PyT = _HYPOT(ABS(var1.x - var2.x), ABS(var1.y - var2.y)) '  distances and magnitudes
362.  
363. END FUNCTION 'PyT
364.  
365.  
366. SUB RackEmUp
367.  
368.     yoff = bsiz2 + 4
369.     xoff = SQR((yoff / 2) * (yoff / 2) + yoff * yoff) - 4
370.  
371.     RESTORE start
372.     FOR rank = 1 TO 5
373.         FOR b = 1 TO rank
374.             READ k
375.             bl(k).p.x = (.25 * xtable) - (xoff * (rank - 1))
376.             bl(k).p.y = (.5 * ytable) - ((rank - 1) * (.5 * yoff)) + ((b - 1) * yoff)
377.     NEXT b, rank
378.  
379. END SUB 'RackEmUp
380.  
381.  
382. SUB VecAdd (var AS V2, var2 AS V2, var3 AS INTEGER)
383.  
384.     var.x = var.x + (var2.x * var3) '                           add (or subtract) two vectors defined by unitpoint
385.     var.y = var.y + (var2.y * var3) '                           var= base vector, var2= vector to add
386.  
387. END SUB 'VecAdd
388.  
389.  
390. FUNCTION VecDot (var AS V2, var2 AS V2)
391.  
392.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
393.  
394. END FUNCTION 'VecDot
395.  
396.  
397. SUB VecMult (vec AS V2, multiplier AS SINGLE)
398.  
399.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
400.     vec.y = vec.y * multiplier
401.  
402. END SUB 'VecMult
403.  
404. SUB VecNorm (var AS V2)
405.  
406.     m = SQR(var.x * var.x + var.y * var.y) '                    convert var to unit vector
407.     var.x = var.x / m
408.     var.y = var.y / m
409.  
410. END SUB 'VecNorm
411.  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 27, 2021, 09:22:26 pm

Graphics look better. Still uses FULLSCREEN .

Code: QB64: [Select]

1. 'Original code by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   position
14.     m AS V2 '                                                   movement (pre-contact) incoming
15.     x AS V2 '                                                   vector of post contact movement
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18.  
19.  
20. DIM TEXT(1) AS STRING
21. DIM RAD AS SINGLE
22. RAD = 0
23. DIM c(1) AS STRING
24. DIM AR AS SINGLE
25. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
26. DIM mouse AS V2
27. DIM b(1) AS ball
28.  
29. 'DIM SHARED AS V2 origin
30. DIM SHARED origin AS V2
31. origin.x = 0: origin.y = 0
32. b(0).c = Red: b(0).cn = "red"
33. b(1).c = Cyan: b(1).cn = "cyan"
34.  
35. SCREEN _NEWIMAGE(_DESKTOPWIDTH, _DESKTOPHEIGHT, 32) 'prevents FULLSCREEN distortion
36.  
37. DO: LOOP UNTIL _SCREENEXISTS
38. ' _SCREENMOVE 10, 10
39.  
40. MAG = _DESKTOPHEIGHT / 300 'this 300 is from the grid drawing code.
41.  
42. WINDOW (-_DESKTOPWIDTH / MAG, _DESKTOPHEIGHT / MAG)-(_DESKTOPWIDTH / MAG, -_DESKTOPHEIGHT / MAG)
43.  
44. _FULLSCREEN 'gives a full screen - not a window!
45.  
46. 'starting state
47. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
48. b(0).s = PyT(origin, b(0).m)
49. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
50. b(1).s = PyT(origin, b(1).m)
51. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
52. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
53.  
54. DO
55.     CLS
56.     ms = MBS '                                                  process mouse actions dragging endpoints
57.     IF ms AND 64 THEN
58.  
59.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
60.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
61.  
62.         FOR x = 0 TO 1
63.             FOR y = 0 TO 1
64.                 ds! = PyT(vertex(x, y), mouse)
65.                 IF ds! < ballradius * .5 THEN i = x: j = y
66.             NEXT y
67.         NEXT x
68.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
69.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
70.                 b(i).p = mouse
71.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
72.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
73.         END SELECT
74.     END IF
75.  
76.     'IF _KEYDOWN(114) THEN i = 0
77.     'IF _KEYDOWN(99) THEN i = 1
78.     IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
79.     IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
80.     IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
81.     IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
82.  
83.     'IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
84.     'IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
85.     'IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
86.     'IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
87.  
88.     '**************Code added by Novarseg
89.     'Vector rotation and vector magnitude adjustment using keyboard input
90.  
91.     I$ = INKEY$
92.  
93.     _DELAY .04 'allows enough time for keyboard buffer to accumulate characters
94.     '           so the vector rotation (fast / slow) operates properly
95.     '           there is probably a better way to do this
96.     IF I$ = "" THEN f1 = 0
97.  
98.     IF f3 = 0 THEN I$ = "b": f3 = 1
99.     IF I$ = "b" AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
100.     IF I$ = "b" AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
101.     LL1:
102.  
103.     IF I$ = "c" THEN 'increase vector magnitude
104.         mult = 1.01
105.         VecMult b(i).m, mult
106.     END IF
107.  
108.     IF I$ = "v" THEN 'decrease vector magnitude
109.         div = 1.01
110.         VecDIV b(i).m, div 'added a new sub
111.     END IF
112.  
113.     IF I$ = "z" THEN 'rotate vector counter clockwise
114.         IF RAD > _PI * 2 THEN RAD = 0
115.  
116.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
117.         IF TIMER - t1 > 1.5 THEN RAD = RAD + .05
118.         IF TIMER - t1 <= 1.5 THEN RAD = RAD + .005
119.  
120.         signC = COS(RAD) * 1 / ABS(COS(RAD))
121.         signS = SIN(RAD) * 1 / ABS(SIN(RAD))
122.         b(i).s = PyT(origin, b(i).m)
123.         b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
124.         b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
125.  
126.     END IF
127.  
128.     IF I$ = "x" THEN 'rotate vector clockwise
129.         IF RAD < 0 THEN RAD = _PI * 2
130.  
131.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
132.         IF TIMER - t1 > 1.5 THEN RAD = RAD - .05
133.         IF TIMER - t1 <= 1.5 THEN RAD = RAD - .005
134.  
135.         signC = COS(RAD) * 1 / ABS(COS(RAD))
136.         signS = SIN(RAD) * 1 / ABS(SIN(RAD))
137.         b(i).s = PyT(origin, b(i).m)
138.         b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5) * signS
139.         b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5) * signC
140.  
141.  
142.     END IF
143.     '**************END Code added Novarseg
144.  
145.  
146.     'START OF COLLISION MATHEMATICS SECTION
147.  
148.     ballradius = PyT(b(0).p, b(1).p) / 2
149.  
150.     FOR bn = 0 TO 1
151.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
152.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
153.     NEXT bn
154.  
155.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
156.     B2BCollision b(0), b(1)
157.     'END OF COLLISION MATHEMATICS SECTION
158.  
159.     'graphic representation
160.     FOR grid = -300 TO 300 STEP 20
161.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
162.         LINE (grid, 300)-(grid, -300), c& 'Gray  'vertical lines
163.         LINE (-300, grid)-(300, grid), c& ' Gray  'horizontal lines
164.     NEXT grid
165.  
166.  
167.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
168.  
169.     FOR dr = 0 TO 1
170.  
171.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , 1 'AR
172.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
173.  
174.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
175.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
176.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
177.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
178.  
179.         _PRINTSTRING (0, 567 + (16 * dr)), b$
180.  
181.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
182.     NEXT dr
183.  
184.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
185.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
186.         PUT #1, , TEXT(0) 'NOVARSEG added this line
187.         PUT #1, , TEXT(1) 'NOVARSEG added this line
188.         CLOSE 'NOVARSEG added this line
189.     END IF 'NOVARSEG added this line
190.  
191.     _LIMIT 500
192.     _DISPLAY
193. LOOP UNTIL _KEYDOWN(27)
194. END
195.  
196.  
197. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
198.  
199.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
200.     DIM un AS V2
201.     DIM ut AS V2
202.     DIM ncomp1 AS V2
203.     DIM ncomp2 AS V2
204.     DIM tcomp1 AS V2
205.     DIM tcomp2 AS V2
206.  
207.  
208.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
209.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
210.     bnci1 = VecDot(un, ball1.m) '
211.     bnci2 = VecDot(un, ball2.m) '
212.     btci1 = VecDot(ut, ball1.m) '
213.     btci2 = VecDot(ut, ball2.m) '
214.  
215.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
216.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
217.  
218.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
219.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
220.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
221.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
222.  
223.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
224.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
225.  
226. END SUB 'B2BCollision
227.  
228.  
229. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
230.  
231.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
232.  
233. END FUNCTION 'map!
234.  
235.  
236. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
237.     STATIC StartTimer AS _FLOAT
238.     STATIC ButtonDown AS INTEGER
239.     STATIC ClickCount AS INTEGER
240.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
241.     '                          Down longer counts as a HOLD event.
242.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
243.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
244.         SELECT CASE SGN(_MOUSEWHEEL)
245.             CASE 1: MBS = MBS OR 512
246.             CASE -1: MBS = MBS OR 1024
247.         END SELECT
248.     WEND
249.  
250.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
251.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
252.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
253.  
254.     IF StartTimer = 0 THEN
255.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
256.             ButtonDown = 1: StartTimer = TIMER(0.01)
257.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
258.         ELSEIF _MOUSEBUTTON(2) THEN
259.             ButtonDown = 2: StartTimer = TIMER(0.01)
260.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
261.         ELSEIF _MOUSEBUTTON(3) THEN
262.             ButtonDown = 3: StartTimer = TIMER(0.01)
263.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
264.         END IF
265.     ELSE
266.         BD = ButtonDown MOD 3
267.         IF BD = 0 THEN BD = 3
268.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
269.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
270.         ELSE
271.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
272.                 MBS = 0: ButtonDown = 0: StartTimer = 0
273.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
274.             ELSE 'We've now started the hold event
275.                 MBS = MBS OR 32 * 2 ^ ButtonDown
276.             END IF
277.         END IF
278.     END IF
279. END FUNCTION 'MBS%
280.  
281.  
282. FUNCTION PyT (var1 AS V2, var2 AS V2)
283.  
284.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
285.  
286. END FUNCTION 'PyT
287.  
288. FUNCTION bPyT (var1 AS V2, var2 AS V2, var3) 'to calulate ball radius only
289.     'var1.x = var1.x * 1.6384
290.     bPyT = _HYPOT((var1.x - var2.x) * var3, (var1.y - var2.y) * var3)
291.  
292. END FUNCTION 'bPyT
293.  
294.  
295.  
296. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
297.  
298.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
299.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
300.  
301. END SUB 'Add_Vector
302.  
303.  
304. FUNCTION VecDot (var AS V2, var2 AS V2)
305.  
306.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
307.  
308. END FUNCTION 'VecDot
309.  
310.  
311. SUB VecMult (vec AS V2, multiplier AS SINGLE)
312.  
313.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
314.     vec.y = vec.y * multiplier
315.  
316. END SUB 'Vec_Mult
317.  
318. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
319.  
320.     vec.x = vec.x / divisor
321.     vec.y = vec.y / divisor
322.  
323. END SUB 'VecDIV
324.  
325.  
326. SUB VecNorm (var AS V2)
327.  
328.     m = PyT(origin, var)
329.     IF m = 0 THEN
330.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
331.     ELSE
332.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
333.     END IF
334.  
335. END SUB 'VecNorm

simplified code

changed

 

Quote

  signC = COS(RAD) * 1 / ABS(COS(RAD))
    signS = SIN(RAD) * 1 / ABS(SIN(RAD))
   b(i).s = PyT(origin, b(i).m)
b(i).m.y = ((b(i).s ^ 2 / (((COS(RAD)) ^ 2 / (SIN(RAD)) ^ 2) + 1)) ^ .5)* signS
b(i).m.x = -((b(i).s ^ 2 / (((SIN(RAD)) ^ 2 / (COS(RAD)) ^ 2) + 1)) ^ .5)* signC

to
     

Quote

   b(i).s = PyT(origin, b(i).m)
        b(i).m.y = b(i).s * COS(RAD(i))
        b(i).m.x = b(i).s * SIN(RAD(i))

Code: QB64: [Select]

1. 'Original code by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   position
14.     m AS V2 '                                                   movement (pre-contact) incoming
15.     x AS V2 '                                                   vector of post contact movement
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18.  
19.  
20. DIM TEXT(1) AS STRING
21. DIM RAD(1) AS SINGLE
22. RAD = 0
23. DIM c(1) AS STRING
24. DIM AR AS SINGLE
25. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
26. DIM mouse AS V2
27. DIM b(1) AS ball
28.  
29. 'DIM SHARED AS V2 origin
30. DIM SHARED origin AS V2
31. origin.x = 0: origin.y = 0
32. b(0).c = Red: b(0).cn = "red"
33. b(1).c = Cyan: b(1).cn = "cyan"
34.  
35. SCREEN _NEWIMAGE(_DESKTOPWIDTH, _DESKTOPHEIGHT, 32) 'prevents FULLSCREEN distortion
36.  
37. DO: LOOP UNTIL _SCREENEXISTS
38. ' _SCREENMOVE 10, 10
39.  
40. MAG = _DESKTOPHEIGHT / 300 'this 300 is from the grid drawing code.
41.  
42. WINDOW (-_DESKTOPWIDTH / MAG, _DESKTOPHEIGHT / MAG)-(_DESKTOPWIDTH / MAG, -_DESKTOPHEIGHT / MAG)
43.  
44. _FULLSCREEN 'gives a full screen - not a window!
45.  
46. 'starting state
47. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
48. b(0).s = PyT(origin, b(0).m)
49. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
50. RAD(1) = 3 * _PI / 2
51. b(1).s = PyT(origin, b(1).m)
52. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
53. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
54.  
55. DO
56.     CLS
57.     ms = MBS '                                                  process mouse actions dragging endpoints
58.     IF ms AND 64 THEN
59.  
60.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
61.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
62.  
63.         FOR x = 0 TO 1
64.             FOR y = 0 TO 1
65.                 ds! = PyT(vertex(x, y), mouse)
66.                 IF ds! < ballradius * .5 THEN i = x: j = y
67.             NEXT y
68.         NEXT x
69.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
70.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
71.                 b(i).p = mouse
72.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
73.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
74.         END SELECT
75.     END IF
76.  
77.     'IF _KEYDOWN(114) THEN i = 0
78.     'IF _KEYDOWN(99) THEN i = 1
79.     IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
80.     IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
81.     IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
82.     IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
83.  
84.     'IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
85.     'IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
86.     'IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
87.     'IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
88.  
89.     '**************Code added by Novarseg
90.     'Vector rotation and vector magnitude adjustment using keyboard input
91.  
92.     I$ = INKEY$
93.  
94.     _DELAY .04 'allows enough time for keyboard buffer to accumulate characters
95.     '           so the vector rotation (fast / slow) operates properly
96.     '           there is probably a better way to do this
97.     IF I$ = "" THEN f1 = 0
98.  
99.     IF f3 = 0 THEN I$ = "b": f3 = 1
100.     IF I$ = "b" AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
101.     IF I$ = "b" AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
102.     LL1:
103.  
104.     IF I$ = "c" THEN 'increase vector magnitude
105.         mult = 1.01
106.         VecMult b(i).m, mult
107.     END IF
108.  
109.     IF I$ = "v" THEN 'decrease vector magnitude
110.         div = 1.01
111.         VecDIV b(i).m, div 'added a new sub
112.     END IF
113.  
114.     IF I$ = "z" THEN 'rotate vector counter clockwise
115.         IF RAD(i) > _PI * 2 THEN RAD(i) = 0
116.  
117.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
118.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) + .05
119.         IF TIMER - t1 <= 1.5 THEN RAD(i) = RAD(i) + .005
120.  
121.  
122.         b(i).s = PyT(origin, b(i).m)
123.         b(i).m.y = b(i).s * COS(RAD(i))
124.         b(i).m.x = b(i).s * SIN(RAD(i))
125.  
126.     END IF
127.  
128.     IF I$ = "x" THEN 'rotate vector clockwise
129.         IF RAD(i) < 0 THEN RAD(i) = _PI * 2
130.  
131.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
132.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) - .05
133.         IF TIMER - t1 <= 1.5 THEN RAD(i) = RAD(i) - .005
134.  
135.         b(i).s = PyT(origin, b(i).m)
136.         b(i).m.y = b(i).s * COS(RAD(i))
137.         b(i).m.x = b(i).s * SIN(RAD(i))
138.     END IF
139.     '**************END Code added Novarseg
140.  
141.  
142.     'START OF COLLISION MATHEMATICS SECTION
143.  
144.     ballradius = PyT(b(0).p, b(1).p) / 2
145.  
146.     FOR bn = 0 TO 1
147.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
148.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
149.     NEXT bn
150.  
151.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
152.     B2BCollision b(0), b(1)
153.     'END OF COLLISION MATHEMATICS SECTION
154.  
155.     'graphic representation
156.     FOR grid = -300 TO 300 STEP 20
157.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
158.         LINE (grid, 300)-(grid, -300), c& 'Gray  'vertical lines
159.         LINE (-300, grid)-(300, grid), c& ' Gray  'horizontal lines
160.     NEXT grid
161.  
162.  
163.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
164.  
165.     FOR dr = 0 TO 1
166.  
167.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , 1 'AR
168.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
169.  
170.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
171.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
172.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
173.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
174.  
175.         _PRINTSTRING (0, 567 + (16 * dr)), b$
176.  
177.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
178.     NEXT dr
179.  
180.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
181.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
182.         PUT #1, , TEXT(0) 'NOVARSEG added this line
183.         PUT #1, , TEXT(1) 'NOVARSEG added this line
184.         CLOSE 'NOVARSEG added this line
185.     END IF 'NOVARSEG added this line
186.  
187.     _LIMIT 500
188.     _DISPLAY
189. LOOP UNTIL _KEYDOWN(27)
190. END
191.  
192.  
193. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
194.  
195.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
196.     DIM un AS V2
197.     DIM ut AS V2
198.     DIM ncomp1 AS V2
199.     DIM ncomp2 AS V2
200.     DIM tcomp1 AS V2
201.     DIM tcomp2 AS V2
202.  
203.  
204.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
205.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
206.     bnci1 = VecDot(un, ball1.m) '
207.     bnci2 = VecDot(un, ball2.m) '
208.     btci1 = VecDot(ut, ball1.m) '
209.     btci2 = VecDot(ut, ball2.m) '
210.  
211.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
212.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
213.  
214.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
215.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
216.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
217.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
218.  
219.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
220.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
221.  
222. END SUB 'B2BCollision
223.  
224.  
225. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
226.  
227.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
228.  
229. END FUNCTION 'map!
230.  
231.  
232. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
233.     STATIC StartTimer AS _FLOAT
234.     STATIC ButtonDown AS INTEGER
235.     STATIC ClickCount AS INTEGER
236.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
237.     '                          Down longer counts as a HOLD event.
238.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
239.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
240.         SELECT CASE SGN(_MOUSEWHEEL)
241.             CASE 1: MBS = MBS OR 512
242.             CASE -1: MBS = MBS OR 1024
243.         END SELECT
244.     WEND
245.  
246.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
247.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
248.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
249.  
250.     IF StartTimer = 0 THEN
251.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
252.             ButtonDown = 1: StartTimer = TIMER(0.01)
253.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
254.         ELSEIF _MOUSEBUTTON(2) THEN
255.             ButtonDown = 2: StartTimer = TIMER(0.01)
256.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
257.         ELSEIF _MOUSEBUTTON(3) THEN
258.             ButtonDown = 3: StartTimer = TIMER(0.01)
259.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
260.         END IF
261.     ELSE
262.         BD = ButtonDown MOD 3
263.         IF BD = 0 THEN BD = 3
264.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
265.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
266.         ELSE
267.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
268.                 MBS = 0: ButtonDown = 0: StartTimer = 0
269.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
270.             ELSE 'We've now started the hold event
271.                 MBS = MBS OR 32 * 2 ^ ButtonDown
272.             END IF
273.         END IF
274.     END IF
275. END FUNCTION 'MBS%
276.  
277.  
278. FUNCTION PyT (var1 AS V2, var2 AS V2)
279.  
280.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
281.  
282. END FUNCTION 'PyT
283.  
284. FUNCTION bPyT (var1 AS V2, var2 AS V2, var3) 'to calulate ball radius only
285.     'var1.x = var1.x * 1.6384
286.     bPyT = _HYPOT((var1.x - var2.x) * var3, (var1.y - var2.y) * var3)
287.  
288. END FUNCTION 'bPyT
289.  
290.  
291.  
292. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
293.  
294.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
295.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
296.  
297. END SUB 'Add_Vector
298.  
299.  
300. FUNCTION VecDot (var AS V2, var2 AS V2)
301.  
302.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
303.  
304. END FUNCTION 'VecDot
305.  
306.  
307. SUB VecMult (vec AS V2, multiplier AS SINGLE)
308.  
309.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
310.     vec.y = vec.y * multiplier
311.  
312. END SUB 'Vec_Mult
313.  
314. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
315.  
316.     vec.x = vec.x / divisor
317.     vec.y = vec.y / divisor
318.  
319. END SUB 'VecDIV
320.  
321.  
322. SUB VecNorm (var AS V2)
323.  
324.     m = PyT(origin, var)
325.     IF m = 0 THEN
326.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
327.     ELSE
328.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
329.     END IF
330.  
331. END SUB 'VecNorm

Title: Re: 2D ball collisions without trigonometry.
Post by: STxAxTIC on May 27, 2021, 11:30:59 pm

Looks good Moses!

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 28, 2021, 01:19:04 am

Looking at OldMoses code now.  Great work.

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 28, 2021, 10:30:54 am

@OldMoses Yes! I am a little confused by cue stick (not the wheel, that's good!) but really nice ball action.

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 28, 2021, 07:00:39 pm

Probably with the addition of a cue stick image I could make it less confusing, it would then provide an orientation aid. I just can't figure out a natural way of cue handling that doesn't come with various aiming and/or force issues, particularly when shooting from a wall. Aim gets really coarse when the mouse cursor is close to the ball, for mathematically obvious reasons.

And speaking of mathematics; I actually realized that for all its nice appearance, it is not mathematically correct. It doesn't compute ball vectors at the point of impact, but rather from the point at which it's ray tracing equation detects a future collision in the present main loop iteration. It's close, but no cigar, as they say... This is more pronounced at faster speeds. By slowing down the _LIMIT 100 to a _LIMIT 10, the effect can then be easily seen, with faster balls shearing away from each other before actually touching. Updating the striking ball's position reintroduced the magnetic effect. So, back to the drawing board yet again...

Still, I'll consider this a usable baseline from which to tweak things.

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 28, 2021, 08:49:03 pm

Quote

And speaking of mathematics; I actually realized that for all its nice appearance, it is not mathematically correct. It doesn't compute ball vectors at the point of impact, but rather from the point at which it's ray tracing equation detects a future collision in the present main loop iteration.

@OldMoses About backing up balls to collision kiss point see last code block below

This (from my Pool 3.1, Steve's forum) backs up 2 balls just detected as having deepest collision for ball i, saveJ was the other ball index.

Code: QB64: [Select]

1.         For i = 0 To topBall
2.             minDist = 100000: saveJ = -1
3.             For j = 0 To topBall 'find deepest collision in case more than one we want earliest = deepest penetration
4.                 If i <> j And b(i).x <> -1000 Then
5.                     dist = Sqr((b(i).x - b(j).x) * (b(i).x - b(j).x) + (b(i).y - b(j).y) * (b(i).y - b(j).y))
6.                     If dist < BDia Then ' collision but is it first or deepest collision
7.                         If dist < minDist Then minDist = dist: saveJ = j
8.                     End If
9.                 End If
10.             Next
11.             If saveJ <> -1 Then ' found collision change ball i dx, dy   calc new course for ball i
12.                 ''reflection  from circle  using Vectors  from JB, thanks tsh73
13.                 v1$ = vect$(b(i).x, b(i).y) ' circle i
14.                 v2$ = vect$(b(saveJ).x, b(saveJ).y) ' the other circle j
15.                 dv1$ = vect$(b(i).dx, b(i).dy) ' change in velocity vector
16.                 dv2$ = vect$(b(saveJ).dx, b(saveJ).dy)
17.                 dv1u$ = vectUnit$(dv1$) '1 pixel
18.                 dv2u$ = vectUnit$(dv2$)
19.  
20.                 ' Here is the place where code hangs, make sure at least 1 vector has a decent length to change
21.                 If vectLen(dv1u$) > .00001 Or vectLen(dv2u$) > .00001 Then
22.                     Do ' this should back up the balls to kiss point thanks tsh73
23.                         v1$ = vectSub$(v1$, dv1u$)
24.                         v2$ = vectSub(v2$, dv2u$)
25.                     Loop While vectLen(vectSub$(v1$, v2$)) < BDia 'back up our circle i to point on kiss
26.                 End If
27.  
28.  

The rest of the code is from that 2D Collision paper you gave us a link to.

I made 2 arrays to hold ball data one for current frame, b(i), and one for next frame, nf(i) that way all ball data gets changed at once for next frame without changing ball data of current frame, so all balls of current frame work on same set of data.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 28, 2021, 09:37:38 pm

@bplus

Quote

I made 2 arrays to hold ball data one for current frame, b(i), and one for next frame, nf(i) that way all ball data gets changed at once for next frame without changing ball data of current frame, so all balls of current frame work on same set of data.

So for frame b(i) check every ball for collisions and if there are any calculate new data and save it in frame nf(i). At what point is the switch made to frame nf(i)?

Title: Re: 2D ball collisions without trigonometry.
Post by: bplus on May 28, 2021, 10:16:44 pm

Quote from: NOVARSEG on May 28, 2021, 09:37:38 pm

@bplus
So for frame b(i) check every ball for collisions and if there are any calculate new data and save it in frame nf(i). At what point is the switch made to frame nf(i)?

Just before the loop back. In this program, I broke my normal routine of drawing everything last to drawing everything first, then recalculating new locations.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 29, 2021, 01:10:01 am

I still don't know how 2d ball collisions work.  That's OK, about 99.999999% of the world's population don't know either.

I will try to do a step by step calculation of the following ball data to arrive at the exit vectors shown.

red  @ (0, 0)  along <0, 100>  exits along <79, 60>           
cyan @ (-100, 50)  along <-100, 100>  exits along <20, 140>  SELECTED

So there is the unit tangent and unit normal vector.  The unit normal vector is also known as the strike vector.  The unit tangent vector is at a right angle to the unit normal vector.

un = unit normal vector
ut = unit tangent vector

lets calculate un

un =  er wait .. what the hek is that again ........
cyan ball position -100x  50y
red ball position        0x     0y

normal vector (strike vector) is -100x   50y

unit normal vector =
(-100^2+ 50^2 )^.5 = 111.8033

-100x / 111.8033 = -.8944x
50y / 111.8033 = .4472y

un =   -.8944x    .4472y   
ut is easy to calculate because it is at right angle to un
multiply y by -1
swap x with y and y with x

ut  = -.4472x   -.8944y 


The literature says that UT is tangent to both balls but with the red ball centered at 0x  0y,  the above math indicates that ut can be in any position and still be the same vector

Ok from this point there are probably more than one way to solve for exit vectors of both balls.

STxAxTIC supplied an interesting equation:

q = 2( un. cyan ball vector  - un . red ball vector )

lets sidetrack and look at a straight on collision

red  @ (0, 0)  along <120, 60>  exits along <139, -70>           
cyan @ (-100, 50)  along <-140, -70>  exits along <-121, 60>  SELECTED

the unit normal vector is the same as before

un =   -.894427x    .447213y   


The cyan ball heading before collision -140x   -70y

actually the display for y should be 70y will fix  that later

divide cyan vector x ,y by cyan vector magnitude to obtain cyan unit vector

unit cyan vector = -.8944x,   .4472y

the dot product of unit normal (un)  with unit cyan  (uc)
 un . uc = -.8944  *  -.8944 +  .4472 *.4472  = .8   +  .2  = 1

The dot product for red ball =1.

un . uc - un . ur = 0

both balls come to a complete stop and rebound at the same velocity then arrived at. 
What happens if the cyan ball heads in a direction that is right angle to un?

red  @ (0, 0)  along <120, 60>  exits along <0, -1>           
cyan @ (-100, 50)  along <56, -115>  exits along <-178, -55>  SELECTED

unit cyan vector (uc)
(56^2 = 115^2 )^.5 = 127.9101

56 / 127.9101 =.4378
115 / 127.9101 = .89906

un . uc = -.8944  *.4378 + 44721 *.89906  = -.3915 + .4 = approx zero

not exactly zero due to small errors in graph output. 

RULE:  The dot product of 2 unit vectors ranges from 0 to 1

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 29, 2021, 07:55:46 am

Quote from: NOVARSEG on May 29, 2021, 01:10:01 am

I still don't know how 2d ball collisions work.  That's OK, about 99.999999% of the world's population don't know either.

But you want to know, which is the point of all this.

Quote

I will try to do a step by step calculation of the following ball data to arrive at the exit vectors shown.

red  @ (0, 0)  along <0, 100>  exits along <79, 60>           
cyan @ (-100, 50)  along <-100, 100>  exits along <20, 140>  SELECTED

I set this up (hopefully I did this right) using the version of the test program that I posted at reply #63
https://www.qb64.org/forum/index.php?topic=3866.msg132698#msg132698
(play with this one some and see how unit normal component and unit tangent component vectors mirror around the incoming vectors, they're colored according to where they get their influence)

  [ This attachment cannot be displayed inline in 'Print Page' view ]  

The first thing that jumps out at me is not so much that it arrives at different exit vectors, but that the scenario, as presented, would not happen in a properly designed application. The balls, if I interpret your scenario correctly, would be starting from an overlapping state, and a slower ball would be colliding from behind with a faster ball. We can't expect plausible outputs from implausible inputs. I believe that such things were the reason my billiard balls were acting magnet like, because they had overlapped into a situation where the calculations could no longer output physically tenable data. It was a garbage in/garbage out situation.

The test bed assumes that balls are in an impacting state after having traveled in on a given vector, it doesn't make judgements as to whether the travel vectors and starting positions can happen in a proper physics model. It only forces an impact point by adjusting ball radii, then gives exit vectors.

Quote

So there is the unit tangent and unit normal vector.  The unit normal vector is also known as the strike vector.  The unit tangent vector is at a right angle to the unit normal vector.

un = unit normal vector
ut = unit tangent vector

lets calculate un

un =  er wait .. what the hek is that again ........
cyan ball position -100x  50y
red ball position        0x     0y

normal vector (strike vector) is -100x   50y

unit normal vector =
(-100^2+ 50^2 )^.5 = 111.8033

-100x / 111.8033 = -.8944x
50y / 111.8033 = .4472y

un =   -.8944x    .4472y   
ut is easy to calculate because it is at right angle to un
multiply y by -1
swap x with y and y with x

ut  = -.4472x   -.8944y 

All looks good to me.

Quote

The literature says that UT is tangent to both balls but with the red ball centered at 0x  0y,  the above math indicates that ut can be in any position and still be the same vector

That's how vectors work. They can be anywhere in the universe, but it doesn't change their direction and magnitude, and the math will still work the same. It doesn't matter where red ball is except for obtaining the UN vector. After that you've got UT vector as you did above. It's at this point that the Dot Product calculations step in and determine where the balls will deflect based upon which way they came in. The unit normal (UN) is how the opposite ball influences the collision and the unit tangent (UT) is how a ball's incoming affects itself upon exit. Those two are added together to get the final exit vector.

Title: Re: 2D ball collisions without trigonometry.
Post by: STxAxTIC on May 29, 2021, 11:33:36 am

Whenever I need to think about balls touching, I use these notes. Same thing Moses is saying:

  [ This attachment cannot be displayed inline in 'Print Page' view ]  
  [ This attachment cannot be displayed inline in 'Print Page' view ]  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 29, 2021, 06:17:12 pm

@OldMoses
Im using this version.

The image you showed is not the one I'm working on.

 If you type the "f" key the ball data is saved to a file called BALL STUFF.txt.  That lets you copy and paste data.

If you want to minimize the program simply comment out _FULLSCREEN,   it'll still work but you won't get that nice DOS look.

Code: QB64: [Select]

1. 'Original code by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   position
14.     m AS V2 '                                                   movement (pre-contact) incoming
15.     x AS V2 '                                                   vector of post contact movement
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18.  
19.  
20. DIM TEXT(1) AS STRING
21. DIM RAD(1) AS SINGLE
22. RAD = 0
23. DIM c(1) AS STRING
24. DIM AR AS SINGLE
25. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
26. DIM mouse AS V2
27. DIM b(1) AS ball
28.  
29. 'DIM SHARED AS V2 origin
30. DIM SHARED origin AS V2
31. origin.x = 0: origin.y = 0
32. b(0).c = Red: b(0).cn = "red"
33. b(1).c = Cyan: b(1).cn = "cyan"
34.  
35. SCREEN _NEWIMAGE(_DESKTOPWIDTH, _DESKTOPHEIGHT, 32) 'prevents FULLSCREEN distortion
36.  
37. DO: LOOP UNTIL _SCREENEXISTS
38. ' _SCREENMOVE 10, 10
39.  
40. MAG = _DESKTOPHEIGHT / 300 'this 300 is from the grid drawing code.
41.  
42. WINDOW (-_DESKTOPWIDTH / MAG, _DESKTOPHEIGHT / MAG)-(_DESKTOPWIDTH / MAG, -_DESKTOPHEIGHT / MAG)
43.  
44. _FULLSCREEN 'gives a full screen - not a window!
45.  
46. 'starting state
47. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
48. b(0).s = PyT(origin, b(0).m)
49. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
50. RAD(1) = 3 * _PI / 2
51. b(1).s = PyT(origin, b(1).m)
52. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
53. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
54.  
55. DO
56.     CLS
57.     ms = MBS '                                                  process mouse actions dragging endpoints
58.     IF ms AND 64 THEN
59.  
60.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
61.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
62.  
63.         FOR x = 0 TO 1
64.             FOR y = 0 TO 1
65.                 ds! = PyT(vertex(x, y), mouse)
66.                 IF ds! < ballradius * .5 THEN i = x: j = y
67.             NEXT y
68.         NEXT x
69.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
70.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
71.                 b(i).p = mouse
72.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
73.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
74.         END SELECT
75.     END IF
76.  
77.     'IF _KEYDOWN(114) THEN i = 0
78.     'IF _KEYDOWN(99) THEN i = 1
79.     IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
80.     IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
81.     IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
82.     IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
83.  
84.     'IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
85.     'IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
86.     'IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
87.     'IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
88.  
89.     '**************Code added by Novarseg
90.     'Vector rotation and vector magnitude adjustment using keyboard input
91.  
92.     I$ = INKEY$
93.  
94.     _DELAY .04 'allows enough time for keyboard buffer to accumulate characters
95.     '           so the vector rotation (fast / slow) operates properly
96.     '           there is probably a better way to do this
97.     IF I$ = "" THEN f1 = 0
98.  
99.     IF f3 = 0 THEN I$ = "b": f3 = 1
100.     IF I$ = "b" AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
101.     IF I$ = "b" AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
102.     LL1:
103.  
104.     IF I$ = "c" THEN 'increase vector magnitude
105.         mult = 1.01
106.         VecMult b(i).m, mult
107.     END IF
108.  
109.     IF I$ = "v" THEN 'decrease vector magnitude
110.         div = 1.01
111.         VecDIV b(i).m, div 'added a new sub
112.     END IF
113.  
114.     IF I$ = "z" THEN 'rotate vector counter clockwise
115.         IF RAD(i) > _PI * 2 THEN RAD(i) = 0
116.  
117.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
118.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) + .05
119.         IF TIMER - t1 <= 1.5 THEN RAD(i) = RAD(i) + .005
120.  
121.  
122.         b(i).s = PyT(origin, b(i).m)
123.         b(i).m.y = b(i).s * COS(RAD(i))
124.         b(i).m.x = b(i).s * SIN(RAD(i))
125.  
126.     END IF
127.  
128.     IF I$ = "x" THEN 'rotate vector clockwise
129.         IF RAD(i) < 0 THEN RAD(i) = _PI * 2
130.  
131.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
132.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) - .05
133.         IF TIMER - t1 <= 1.5 THEN RAD(i) = RAD(i) - .005
134.  
135.         b(i).s = PyT(origin, b(i).m)
136.         b(i).m.y = b(i).s * COS(RAD(i))
137.         b(i).m.x = b(i).s * SIN(RAD(i))
138.     END IF
139.     '**************END Code added Novarseg
140.  
141.  
142.     'START OF COLLISION MATHEMATICS SECTION
143.  
144.     ballradius = PyT(b(0).p, b(1).p) / 2
145.  
146.     FOR bn = 0 TO 1
147.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
148.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
149.     NEXT bn
150.  
151.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
152.     B2BCollision b(0), b(1)
153.     'END OF COLLISION MATHEMATICS SECTION
154.  
155.     'graphic representation
156.     FOR grid = -300 TO 300 STEP 20
157.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
158.         LINE (grid, 300)-(grid, -300), c& 'Gray  'vertical lines
159.         LINE (-300, grid)-(300, grid), c& ' Gray  'horizontal lines
160.     NEXT grid
161.  
162.  
163.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
164.  
165.     FOR dr = 0 TO 1
166.  
167.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , 1 'AR
168.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y - b(dr).m.y), b(dr).c 'incoming
169.  
170.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
171.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
172.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
173.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
174.  
175.         _PRINTSTRING (0, 567 + (16 * dr)), b$
176.  
177.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
178.     NEXT dr
179.  
180.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
181.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
182.         PUT #1, , TEXT(0) 'NOVARSEG added this line
183.         PUT #1, , TEXT(1) 'NOVARSEG added this line
184.         CLOSE 'NOVARSEG added this line
185.     END IF 'NOVARSEG added this line
186.  
187.     _LIMIT 500
188.     _DISPLAY
189. LOOP UNTIL _KEYDOWN(27)
190. END
191.  
192.  
193. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
194.  
195.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
196.     DIM un AS V2
197.     DIM ut AS V2
198.     DIM ncomp1 AS V2
199.     DIM ncomp2 AS V2
200.     DIM tcomp1 AS V2
201.     DIM tcomp2 AS V2
202.  
203.  
204.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
205.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
206.     bnci1 = VecDot(un, ball1.m) '
207.     bnci2 = VecDot(un, ball2.m) '
208.     btci1 = VecDot(ut, ball1.m) '
209.     btci2 = VecDot(ut, ball2.m) '
210.  
211.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
212.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
213.  
214.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
215.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
216.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
217.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
218.  
219.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
220.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
221.  
222. END SUB 'B2BCollision
223.  
224.  
225. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
226.  
227.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
228.  
229. END FUNCTION 'map!
230.  
231.  
232. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
233.     STATIC StartTimer AS _FLOAT
234.     STATIC ButtonDown AS INTEGER
235.     STATIC ClickCount AS INTEGER
236.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
237.     '                          Down longer counts as a HOLD event.
238.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
239.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
240.         SELECT CASE SGN(_MOUSEWHEEL)
241.             CASE 1: MBS = MBS OR 512
242.             CASE -1: MBS = MBS OR 1024
243.         END SELECT
244.     WEND
245.  
246.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
247.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
248.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
249.  
250.     IF StartTimer = 0 THEN
251.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
252.             ButtonDown = 1: StartTimer = TIMER(0.01)
253.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
254.         ELSEIF _MOUSEBUTTON(2) THEN
255.             ButtonDown = 2: StartTimer = TIMER(0.01)
256.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
257.         ELSEIF _MOUSEBUTTON(3) THEN
258.             ButtonDown = 3: StartTimer = TIMER(0.01)
259.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
260.         END IF
261.     ELSE
262.         BD = ButtonDown MOD 3
263.         IF BD = 0 THEN BD = 3
264.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
265.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
266.         ELSE
267.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
268.                 MBS = 0: ButtonDown = 0: StartTimer = 0
269.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
270.             ELSE 'We've now started the hold event
271.                 MBS = MBS OR 32 * 2 ^ ButtonDown
272.             END IF
273.         END IF
274.     END IF
275. END FUNCTION 'MBS%
276.  
277.  
278. FUNCTION PyT (var1 AS V2, var2 AS V2)
279.  
280.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
281.  
282. END FUNCTION 'PyT
283.  
284. FUNCTION bPyT (var1 AS V2, var2 AS V2, var3) 'to calulate ball radius only
285.     'var1.x = var1.x * 1.6384
286.     bPyT = _HYPOT((var1.x - var2.x) * var3, (var1.y - var2.y) * var3)
287.  
288. END FUNCTION 'bPyT
289.  
290.  
291.  
292. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
293.  
294.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
295.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
296.  
297. END SUB 'Add_Vector
298.  
299.  
300. FUNCTION VecDot (var AS V2, var2 AS V2)
301.  
302.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
303.  
304. END FUNCTION 'VecDot
305.  
306.  
307. SUB VecMult (vec AS V2, multiplier AS SINGLE)
308.  
309.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
310.     vec.y = vec.y * multiplier
311.  
312. END SUB 'Vec_Mult
313.  
314. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
315.  
316.     vec.x = vec.x / divisor
317.     vec.y = vec.y / divisor
318.  
319. END SUB 'VecDIV
320.  
321.  
322. SUB VecNorm (var AS V2)
323.  
324.     m = PyT(origin, var)
325.     IF m = 0 THEN
326.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
327.     ELSE
328.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
329.     END IF
330.  
331. END SUB 'VecNorm

@STxAxTIC

your notes solve with unit normal vector.  Looks like unit tangent vector is not necessary?

Title: Re: 2D ball collisions without trigonometry.
Post by: OldMoses on May 29, 2021, 06:37:16 pm

If you add the four LINE statements to the end of SUB B2BCollision, as shown below, that will show how the vector components react to changes in ball position and velocity. It should work with your version and you can comment them out if you don't want or need them any more. It may help with visualizing the dot product interaction when you can see what component of the exit velocity comes from a ball's own velocity and what comes from the other ball.

Code: QB64: [Select]

1. SUB B2BCollision (ball1 AS ball, ball2 AS ball)
2.  
3.     DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
4.     un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
5.     ut.x = -un.y: ut.y = un.x '                                 establish unit tangent
6.     bnci1 = VecDot(un, ball1.m) '                               ball 1 normal component of input velocity
7.     bnci2 = VecDot(un, ball2.m) '                               ball 2 normal component of input velocity
8.     btci1 = VecDot(ut, ball1.m) '                               ball 1 tangent component of input velocity
9.     btci2 = VecDot(ut, ball2.m) '                               ball 2 tangent component of input velocity
10.  
11.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
12.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
13.  
14.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
15.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
16.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
17.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
18.  
19.     ball1.x = ncomp1: VecAdd ball1.x, tcomp1, 1 '               add normal and tangent exit vectors
20.     ball2.x = ncomp2: VecAdd ball2.x, tcomp2, 1 '               add normal and tangent exit vectors
21.  
22.     'The following is for graphic representation only and can be removed without affecting the SUB's purpose
23.     LINE (ball1.p.x, ball1.p.y)-(ball1.p.x + ncomp1.x, ball1.p.y + ncomp1.y), &H9F00FFFF, , &B0011001100110011
24.     LINE (ball1.p.x, ball1.p.y)-(ball1.p.x + tcomp1.x, ball1.p.y + tcomp1.y), &H9FFF7F7F, , &B0011001100110011
25.     LINE (ball2.p.x, ball2.p.y)-(ball2.p.x + ncomp2.x, ball2.p.y + ncomp2.y), &H9FFF7F7F, , &B0011001100110011
26.     LINE (ball2.p.x, ball2.p.y)-(ball2.p.x + tcomp2.x, ball2.p.y + tcomp2.y), &H9F00FFFF, , &B0011001100110011
27.  
28. END SUB 'B2BCollision
29.  

Title: Re: 2D ball collisions without trigonometry.
Post by: STxAxTIC on May 29, 2021, 10:01:44 pm

Quote from: NOVARSEG on May 29, 2021, 06:17:12 pm

@STxAxTIC
your notes solve with unit normal vector.  Looks like unit tangent vector is not necessary?

Correct. Tangent vector is superfluous.

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 29, 2021, 11:43:26 pm

OldMoses
I added the 4 lines - looking at it now

STxAxTIC
That is interesting!.   

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on May 30, 2021, 12:38:57 am

STxAxTIC

looking at your notes and there is the key observation

 vector q = magnitude of vector q * unit normal vector (un)

magnitude of vector q is found by

2 (un . vector v1   - un . vector v2)

where vec v1 and vec v2 are not unit vectors.

If that is the correct interpretation then how is vector q used?

Title: Re: 2D ball collisions without trigonometry.
Post by: STxAxTIC on May 30, 2021, 11:18:13 am

@NOVARSEG

Hey - yeah I've been meaning to type those notes for a few years but I'm not "on that chapter" yet (long story). Anyway... I did a fairly-ok job of distinguishing between full vectors (with the arrow) and unit vectors (with the hat). Throughout the whole thing, the vectors v1 and v2 are always full vectors, never unit vectors.

Keep in mind too I use the reduced mass term (greek mu) to calculate q

\mu = (m1 + m2) / (m1 * m2)

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on June 02, 2021, 12:10:05 am

Getting close to a solution. Thanks to everyone on this thread. So much information to distill.

Program shows the normal and tangent vectors as dashed lines.  The code is mess but at least I got some results.  The code still does not show the exit vectors.

Well, there are some ball angles that don't make sense at all.

example
red  @ (0, 0)  along <100, 0>  exits along <0, 0>
cyan @ (-100, 100)  along <-100, 0>  exits along <0, 0>

Does not seem correct.

****************
Looking at STxAxTIC's notes about momentum exchange

****************
Looking at this paper again  https://www.vobarian.com/collisions/2dcollisions2.pdf

I looked at that paper before, but it was of no use to me at the time, because I did not understand the math.

Code: QB64: [Select]

1. 'Original code by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   ball position
14.     m AS V2 '                                                   heading vector
15.     x AS V2 '                                                   exit vector
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18.  
19. DIM Nvec(1) AS V2
20. DIM Tvec(1) AS V2
21. DIM TEXT(1) AS STRING
22. DIM RAD(1) AS SINGLE
23. RAD = 0
24. DIM c(1) AS STRING
25. DIM AR AS SINGLE
26. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
27. DIM mouse AS V2
28. DIM b(1) AS ball
29.  
30. 'DIM SHARED AS V2 origin
31. DIM SHARED origin AS V2
32. origin.x = 0: origin.y = 0
33. b(0).c = Red: b(0).cn = "red"
34. b(1).c = Cyan: b(1).cn = "cyan"
35.  
36. SCREEN _NEWIMAGE(_DESKTOPWIDTH, _DESKTOPHEIGHT, 32) 'prevents FULLSCREEN distortion
37.  
38. DO: LOOP UNTIL _SCREENEXISTS
39. ' _SCREENMOVE 10, 10
40.  
41. MAG = _DESKTOPHEIGHT / 300 'this 300 is from the grid drawing code.
42. 'MAG = 4
43. WINDOW (-_DESKTOPWIDTH / MAG, -_DESKTOPHEIGHT / MAG)-(_DESKTOPWIDTH / MAG, _DESKTOPHEIGHT / MAG)
44.  
45. _FULLSCREEN 'gives a full screen - not a window!
46.  
47. 'starting state
48. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
49. RAD(0) = 2 * _PI / 2
50. b(0).s = PyT(origin, b(0).m)
51.  
52. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
53. RAD(1) = 3 * _PI / 2
54. b(1).s = PyT(origin, b(1).m)
55.  
56. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
57. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
58.  
59. DO
60.     CLS
61.     ms = MBS '                                                  process mouse actions dragging endpoints
62.     IF ms AND 64 THEN
63.  
64.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
65.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
66.  
67.         FOR x = 0 TO 1
68.             FOR y = 0 TO 1
69.                 ds! = PyT(vertex(x, y), mouse)
70.                 IF ds! < ballradius * .5 THEN i = x: j = y
71.             NEXT y
72.         NEXT x
73.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
74.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
75.                 b(i).p = mouse
76.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
77.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
78.         END SELECT
79.     END IF
80.  
81.     'IF _KEYDOWN(114) THEN i = 0
82.     'IF _KEYDOWN(99) THEN i = 1
83.     IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
84.     IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
85.     IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
86.     IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
87.  
88.     'IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
89.     'IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
90.     'IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
91.     'IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
92.  
93.     '**************Code added by Novarseg
94.     'Vector rotation and vector magnitude adjustment using keyboard input
95.  
96.     IF f4 = 0 THEN
97.         f4 = 1
98.         FOR i = 0 TO 1
99.  
100.             b(i).s = PyT(origin, b(i).m)
101.             b(i).m.y = b(i).s * COS(RAD(i))
102.             b(i).m.x = b(i).s * SIN(RAD(i))
103.         NEXT i
104.         i = 0
105.     END IF
106.  
107.     I$ = INKEY$
108.  
109.     _DELAY .04 'allows enough time for keyboard buffer to accumulate characters
110.     '           so the vector rotation (fast / slow) operates properly
111.     '           there is probably a better way to do this
112.     IF I$ = "" THEN f1 = 0
113.  
114.     'IF f3 = 0 THEN I$ = "b": f3 = 1
115.     IF I$ = "b" AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
116.     IF I$ = "b" AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
117.     LL1:
118.  
119.     IF I$ = "c" THEN 'increase vector magnitude
120.         mult = 1.01
121.         VecMult b(i).m, mult
122.     END IF
123.  
124.     IF I$ = "v" THEN 'decrease vector magnitude
125.         div = 1.01
126.         VecDIV b(i).m, div 'added a new sub
127.     END IF
128.  
129.     IF I$ = "z" THEN 'rotate vector counter clockwise
130.         IF RAD(i) > _PI * 2 THEN RAD(i) = 0
131.  
132.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
133.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) + .05
134.         IF TIMER - t1 <= 1.5 THEN RAD(i) = RAD(i) + .005
135.  
136.  
137.         b(i).s = PyT(origin, b(i).m)
138.         b(i).m.y = b(i).s * COS(RAD(i))
139.         b(i).m.x = b(i).s * SIN(RAD(i))
140.  
141.     END IF
142.  
143.     IF I$ = "x" THEN 'rotate vector clockwise
144.         IF RAD(i) < 0 THEN RAD(i) = _PI * 2
145.  
146.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
147.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) - .05
148.         IF TIMER - t1 <= 1.5 THEN RAD(i) = RAD(i) - .005
149.  
150.         b(i).s = PyT(origin, b(i).m)
151.         b(i).m.y = b(i).s * COS(RAD(i))
152.         b(i).m.x = b(i).s * SIN(RAD(i))
153.     END IF
154.     '**************END Code added Novarseg
155.  
156.  
157.     'START OF COLLISION MATHEMATICS SECTION
158.  
159.     ballradius = PyT(b(0).p, b(1).p) / 2
160.  
161.     FOR bn = 0 TO 1
162.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
163.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
164.     NEXT bn
165.  
166.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
167.     B2BCollision b(0), b(1), Nvec(), Tvec()
168.     'END OF COLLISION MATHEMATICS SECTION
169.  
170.     'graphic representation
171.     FOR grid = -300 TO 300 STEP 20
172.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
173.         LINE (grid, 300)-(grid, -300), c& 'Gray  'vertical lines
174.         LINE (-300, grid)-(300, grid), c& ' Gray  'horizontal lines
175.     NEXT grid
176.  
177.  
178.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
179.  
180.     FOR dr = 0 TO 1
181.  
182.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , 1 'AR
183.  
184.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y + b(dr).m.y), b(dr).c 'incoming
185.  
186.         'LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
187.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Nvec(dr).x, b(dr).p.y + Nvec(dr).y), b(dr).c, , &B1111000011110000 'exit vector
188.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Tvec(dr).x, b(dr).p.y + Tvec(dr).y), b(dr).c, , &B1111000011110000 'exit vector
189.  
190.  
191.  
192.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
193.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
194.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
195.  
196.         _PRINTSTRING (0, 567 + (16 * dr)), b$
197.  
198.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
199.     NEXT dr
200.  
201.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
202.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
203.         PUT #1, , TEXT(0) 'NOVARSEG added this line
204.         PUT #1, , TEXT(1) 'NOVARSEG added this line
205.         CLOSE 'NOVARSEG added this line
206.     END IF 'NOVARSEG added this line
207.  
208.     _LIMIT 500
209.     _DISPLAY
210. LOOP UNTIL _KEYDOWN(27)
211. END
212.  
213.  
214. SUB B2BCollision (ball0 AS ball, ball1 AS ball, Nvec() AS V2, Tvec() AS V2)
215.  
216.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
217.     DIM un AS V2
218.     DIM ut AS V2
219.     DIM ncomp1 AS V2
220.     DIM ncomp2 AS V2
221.     DIM tcomp1 AS V2
222.     DIM tcomp2 AS V2
223.     DIM MAG AS SINGLE
224.  
225.     DIM unDOT0 AS SINGLE 'unit normal vector "dot" pre collision heading ball0
226.     DIM unDOT1 AS SINGLE 'unit normal vector "dot" pre collision heading ball1
227.     DIM utDOT0 AS SINGLE 'unit tangent vector "dot" pre collision heading ball0
228.     DIM utDOT1 AS SINGLE ' unit tangent vector "dot" pre collision heading ball1
229.  
230.     DIM unVec0 AS V2
231.     DIM utVec0 AS V2
232.     DIM unVec1 AS V2
233.     DIM utVec1 AS V2
234.     ' DIM nvec(1) AS V2
235.     ' DIM Tvec(1) AS V2
236.  
237.  
238.     '  GOSUB getUnitNormal uses  ball1.p ball2.p
239.  
240.     'calculate unit normql vector from ball positions
241.     'ball0 = red, ball1 =cyan
242.     un.x = ball1.p.x - ball0.p.x
243.     un.y = ball1.p.y - ball0.p.y
244.     MAG = (un.x ^ 2 + un.y ^ 2) ^ .5
245.     un.x = un.x / MAG
246.     un.y = un.y / MAG
247.  
248.     'un = ball0.p: VecAdd un, ball1.p, -1: VecNorm un '
249.     'un = ball1.p
250.     'VecAdd un, ball1.p, -1
251.     ' VecNorm un '          establish unit normal
252.  
253.  
254.     ut.x = -un.y: ut.y = un.x '     establish unit tangent
255.  
256.  
257.     unDOT0 = un.x * ball0.m.x + un.y * ball0.m.y 'unit normal vector DOT ball vector
258.     unDOT1 = un.x * ball1.m.x + un.y * ball1.m.y 'unit normal vector DOT ball vector
259.     utDOT0 = ut.x * ball0.m.x + ut.y * ball0.m.y 'unit tangent vector DOT ball vector
260.     utDOT1 = ut.x * ball1.m.x + ut.y * ball1.m.y 'unit tangent vector DOT ball vector
261.  
262.  
263.     'bnci1 = VecDot(un, ball0.m) '
264.     'bnci2 = VecDot(un, ball1.m) '
265.     'btci1 = VecDot(ut, ball0.m) '
266.     'btci2 = VecDot(ut, ball1.m) '
267.  
268.     ' bncx1 = bnci2 '                                   compute normal component of ball 1 exit velocity
269.     ' bncx2 = bnci1 '                                   compute normal component of ball 2 exit velocity
270.  
271.  
272.  
273.  
274.     ' ncomp1 = un:
275.  
276.     VecMult2 un, unDOT0, unVec0 '    first two parameters are inputs, the 3rd is output vector
277.     VecMult2 ut, utDOT0, utVec0 '
278.     VecMult2 un, unDOT1, unVec1 '
279.     VecMult2 ut, utDOT1, utVec1 '
280.  
281.     LOCATE 30, 10: PRINT "unvec0.x"; unVec0.x
282.     LOCATE 31, 10: PRINT "unvec0.y"; unVec0.y
283.  
284.     LOCATE 32, 10: PRINT "utvec0.x"; utVec0.x
285.     LOCATE 33, 10: PRINT "utvec0.y"; utVec0.y
286.  
287.  
288.     'ncomp1 = un: VecMult ncomp1, bncx2 '
289.     'tcomp1 = ut: VecMult tcomp1, btci1 '               unit tangent exit vector x tangent component of exit vector
290.     'ncomp2 = un: VecMult ncomp2, bncx2 '               same for ball2, unit normal...
291.     'tcomp2 = ut: VecMult tcomp2, btci2 '               same for ball2, unit tangent...
292.  
293.     'ball0.x = ncomp1: VecAdd ball0.x, tcomp1, 1 '      add normal and tangent exit vectors
294.     'ball1.x = ncomp2: VecAdd ball1.x, tcomp2, 1 '      add normal and tangent exit vectors
295.  
296.     'VecAdd2 unVec1, utVec1, Nvec(1) '
297.     'VecAdd2 unVec0, utVec0, Nvec(0) '
298.     Nvec(0).x = unVec0.x
299.     Nvec(0).y = unVec0.y
300.  
301.     Nvec(1).x = unVec1.x
302.     Nvec(1).y = unVec1.y
303.  
304.     Tvec(1).x = -utVec0.x
305.     Tvec(1).y = -utVec0.y
306.  
307.     Tvec(0).x = -utVec1.x
308.     Tvec(0).y = -utVec1.y
309.  
310.  
311. END SUB 'B2BCollision
312.  
313.  
314. SUB B2B2Collision (ball0 AS ball, ball1 AS ball)
315.  
316.     ' DIM AS V2 un, ut, ncomp1, ncomp2, tcomp1, tcomp2
317.     DIM un AS V2
318.     DIM ut AS V2
319.     DIM ncomp1 AS V2
320.     DIM ncomp2 AS V2
321.     DIM tcomp1 AS V2
322.     DIM tcomp2 AS V2
323.  
324.     DIM MAG AS SINGLE
325.  
326.     DIM unDOT0 AS SINGLE 'unit normal vector "dot" pre collision heading ball0
327.     DIM unDOT1 AS SINGLE 'unit normal vector "dot" pre collision heading ball1
328.     DIM utDOT0 AS SINGLE 'unit tangent vector "dot" pre collision heading ball0
329.     DIM utDOT1 AS SINGLE ' unit tangent vector "dot" pre collision heading ball1
330.  
331.     DIM unVec0 AS V2
332.     DIM utVec0 AS V2
333.     DIM unVec1 AS V2
334.     DIM utVec1 AS V2
335.  
336.  
337.     '  GOSUB getUnitNormal uses  ball1.p ball2.p
338.  
339.     'calculate unit normql vector from ball positions
340.     'ball0 = red, ball1 =cyan
341.     un.x = ball1.p.x - ball0.p.x
342.     un.y = ball1.p.y - ball0.p.y
343.     MAG = (un.x ^ 2 + un.y ^ 2) ^ .5
344.     un.x = un.x / MAG
345.     un.y = un.y / MAG
346.  
347.  
348.     ' un = ball2.p: VecAdd un, ball1.p, -1: VecNorm un '          establish unit normal
349.     ut.x = un.y: ut.y = un.x '                                 establish unit tangent
350.     bnci1 = VecDot(un, ball0.m) '
351.     bnci2 = VecDot(un, ball1.m) '
352.     btci1 = VecDot(ut, ball0.m) '
353.     btci2 = VecDot(ut, ball1.m) '
354.  
355.     bncx1 = bnci2 '                                             compute normal component of ball 1 exit velocity
356.     bncx2 = bnci1 '                                             compute normal component of ball 2 exit velocity
357.  
358.     ncomp1 = un: VecMult ncomp1, bncx1 '                        unit normal exit vector x normal component of exit vector ball1
359.     tcomp1 = ut: VecMult tcomp1, btci1 '                        unit tangent exit vector x tangent component of exit vector
360.     ncomp2 = un: VecMult ncomp2, bncx2 '                        same for ball2, unit normal...
361.     tcomp2 = ut: VecMult tcomp2, btci2 '                        same for ball2, unit tangent...
362.  
363.     ball0.x = ncomp1: VecAdd ball0.x, tcomp1, 1 '               add normal and tangent exit vectors
364.     ball1.x = ncomp2: VecAdd ball1.x, tcomp2, 1 '               add normal and tangent exit vectors
365.  
366. END SUB 'B2BCollision
367.  
368.  
369.  
370. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
371.  
372.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
373.  
374. END FUNCTION 'map!
375.  
376.  
377. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
378.     STATIC StartTimer AS _FLOAT
379.     STATIC ButtonDown AS INTEGER
380.     STATIC ClickCount AS INTEGER
381.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
382.     '                          Down longer counts as a HOLD event.
383.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
384.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
385.         SELECT CASE SGN(_MOUSEWHEEL)
386.             CASE 1: MBS = MBS OR 512
387.             CASE -1: MBS = MBS OR 1024
388.         END SELECT
389.     WEND
390.  
391.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
392.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
393.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
394.  
395.     IF StartTimer = 0 THEN
396.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
397.             ButtonDown = 1: StartTimer = TIMER(0.01)
398.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
399.         ELSEIF _MOUSEBUTTON(2) THEN
400.             ButtonDown = 2: StartTimer = TIMER(0.01)
401.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
402.         ELSEIF _MOUSEBUTTON(3) THEN
403.             ButtonDown = 3: StartTimer = TIMER(0.01)
404.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
405.         END IF
406.     ELSE
407.         BD = ButtonDown MOD 3
408.         IF BD = 0 THEN BD = 3
409.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
410.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
411.         ELSE
412.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
413.                 MBS = 0: ButtonDown = 0: StartTimer = 0
414.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
415.             ELSE 'We've now started the hold event
416.                 MBS = MBS OR 32 * 2 ^ ButtonDown
417.             END IF
418.         END IF
419.     END IF
420. END FUNCTION 'MBS%
421.  
422.  
423. FUNCTION PyT (var1 AS V2, var2 AS V2)
424.  
425.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
426.  
427. END FUNCTION 'PyT
428.  
429. FUNCTION bPyT (var1 AS V2, var2 AS V2, var3) 'to calulate ball radius only
430.     'var1.x = var1.x * 1.6384
431.     bPyT = _HYPOT((var1.x - var2.x) * var3, (var1.y - var2.y) * var3)
432.  
433. END FUNCTION 'bPyT
434.  
435.  
436.  
437. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
438.  
439.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
440.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
441.  
442. END SUB 'Add_Vector
443.  
444. SUB VecAdd2 (var1 AS V2, var2 AS V2, var3 AS V2)
445.  
446.     'var3.x = var1.x + var2.x '                           add vector (or a scalar multiple of) var2 to var)
447.     'var3.y = var1.y + var2.y '                           use var3 = -1 to subtract var2 from var
448.  
449.     var3.x = var1.x '+ var2.x '                           add vector (or a scalar multiple of) var2 to var)
450.     var3.y = var1.y '+ var2.y '                           use var3 = -1 to subtract var2 from var
451.  
452. END SUB 'Add_Vector
453.  
454.  
455. FUNCTION VecDot (var AS V2, var2 AS V2)
456.  
457.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
458.  
459. END FUNCTION 'VecDot
460.  
461.  
462. SUB VecMult (vec AS V2, multiplier AS SINGLE)
463.  
464.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
465.     vec.y = vec.y * multiplier
466.  
467. END SUB 'Vec_Mult
468.  
469. SUB VecMult2 (var1 AS V2, var2 AS SINGLE, out1 AS V2)
470.  
471.     out1.x = var1.x * var2
472.     out1.y = var1.y * var2
473.  
474. END SUB 'Vec_Mult
475.  
476.  
477.  
478.  
479.  
480.  
481.  
482. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
483.  
484.     vec.x = vec.x / divisor
485.     vec.y = vec.y / divisor
486.  
487. END SUB 'VecDIV
488.  
489.  
490. SUB VecNorm (var AS V2)
491.  
492.     m = PyT(origin, var)
493.     IF m = 0 THEN
494.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
495.     ELSE
496.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
497.     END IF
498.  
499. END SUB 'VecNorm
500.  
501.  
502.  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on June 02, 2021, 11:14:25 pm

The code seems to work now. Have a look.

Math from https://www.vobarian.com/collisions/2dcollisions2.pdf

Again much thanks to everyone on this thread.

Code: QB64: [Select]

1.  'Original code by OldMoses
2. 'Additional code by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   ball position
14.     m AS V2 '                                                   heading vector
15.     x AS V2 '                                                   exit vector
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18.  
19. DIM Nvec(1) AS V2 'normal velocity vectors
20. DIM Tvec(1) AS V2 'tangential velocity vectors
21. DIM Fvec(1) AS V2 'Final or exit vectors
22.  
23. DIM TEXT(1) AS STRING
24. DIM RAD(1) AS SINGLE
25. RAD = 0
26. DIM c(1) AS STRING
27. DIM AR AS SINGLE
28. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
29. DIM mouse AS V2
30. DIM b(1) AS ball
31.  
32. 'DIM SHARED AS V2 origin
33. DIM SHARED origin AS V2
34. origin.x = 0: origin.y = 0
35. b(0).c = Red: b(0).cn = "red"
36. b(1).c = Cyan: b(1).cn = "cyan"
37.  
38. SCREEN _NEWIMAGE(_DESKTOPWIDTH, _DESKTOPHEIGHT, 32) 'prevents FULLSCREEN distortion
39.  
40. DO: LOOP UNTIL _SCREENEXISTS
41. ' _SCREENMOVE 10, 10
42.  
43. MAG = _DESKTOPHEIGHT / 300 'this 300 is from the grid drawing code.
44. 'MAG = 4
45. WINDOW (-_DESKTOPWIDTH / MAG, -_DESKTOPHEIGHT / MAG)-(_DESKTOPWIDTH / MAG, _DESKTOPHEIGHT / MAG)
46.  
47. _FULLSCREEN 'gives a full screen - not a window!
48.  
49. 'starting state
50. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
51. RAD(0) = 2 * _PI / 2
52. b(0).s = PyT(origin, b(0).m)
53.  
54. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
55. RAD(1) = 3 * _PI / 2
56. b(1).s = PyT(origin, b(1).m)
57.  
58. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
59. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
60.  
61. DO
62.     CLS
63.     ms = MBS '                                                  process mouse actions dragging endpoints
64.     IF ms AND 64 THEN
65.  
66.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
67.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
68.  
69.         FOR x = 0 TO 1
70.             FOR y = 0 TO 1
71.                 ds! = PyT(vertex(x, y), mouse)
72.                 IF ds! < ballradius * .5 THEN i = x: j = y
73.             NEXT y
74.         NEXT x
75.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
76.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
77.                 b(i).p = mouse
78.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
79.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
80.         END SELECT
81.     END IF
82.  
83.     'IF _KEYDOWN(114) THEN i = 0
84.     'IF _KEYDOWN(99) THEN i = 1
85.     IF _KEYDOWN(18432) THEN b(i).p.y = b(i).p.y + 1
86.     IF _KEYDOWN(20480) THEN b(i).p.y = b(i).p.y - 1
87.     IF _KEYDOWN(19200) THEN b(i).p.x = b(i).p.x - 1
88.     IF _KEYDOWN(19712) THEN b(i).p.x = b(i).p.x + 1
89.  
90.     'IF _KEYDOWN(119) THEN b(i).m.y = b(i).m.y - 1
91.     'IF _KEYDOWN(115) THEN b(i).m.y = b(i).m.y + 1
92.     'IF _KEYDOWN(97) THEN b(i).m.x = b(i).m.x + 1
93.     'IF _KEYDOWN(100) THEN b(i).m.x = b(i).m.x - 1
94.  
95.     '**************Code added by Novarseg
96.     'Vector rotation and vector magnitude adjustment using keyboard input
97.  
98.     IF f4 = 0 THEN
99.         f4 = 1
100.         FOR i = 0 TO 1
101.  
102.             b(i).s = PyT(origin, b(i).m)
103.             b(i).m.y = b(i).s * COS(RAD(i))
104.             b(i).m.x = b(i).s * SIN(RAD(i))
105.         NEXT i
106.         i = 0
107.     END IF
108.  
109.     I$ = INKEY$
110.  
111.     _DELAY .04 'allows enough time for keyboard buffer to accumulate characters
112.     '           so the vector rotation (fast / slow) operates properly
113.     '           there is probably a better way to do this
114.     IF I$ = "" THEN f1 = 0
115.  
116.     'IF f3 = 0 THEN I$ = "b": f3 = 1
117.     IF I$ = "b" AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
118.     IF I$ = "b" AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
119.     LL1:
120.  
121.     IF I$ = "c" THEN 'increase vector magnitude
122.         mult = 1.01
123.         VecMult b(i).m, mult
124.     END IF
125.  
126.     IF I$ = "v" THEN 'decrease vector magnitude
127.         div = 1.01
128.         VecDIV b(i).m, div 'added a new sub
129.     END IF
130.  
131.     IF I$ = "z" THEN 'rotate vector counter clockwise
132.         IF RAD(i) > _PI * 2 THEN RAD(i) = 0
133.  
134.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
135.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) + .05
136.         IF TIMER - t1 <= 1.5 THEN RAD(i) = RAD(i) + .005
137.  
138.  
139.         b(i).s = PyT(origin, b(i).m)
140.         b(i).m.y = b(i).s * COS(RAD(i))
141.         b(i).m.x = b(i).s * SIN(RAD(i))
142.  
143.     END IF
144.  
145.     IF I$ = "x" THEN 'rotate vector clockwise
146.         IF RAD(i) < 0 THEN RAD(i) = _PI * 2
147.  
148.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
149.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) - .05
150.         IF TIMER - t1 <= 1.5 THEN RAD(i) = RAD(i) - .005
151.  
152.         b(i).s = PyT(origin, b(i).m)
153.         b(i).m.y = b(i).s * COS(RAD(i))
154.         b(i).m.x = b(i).s * SIN(RAD(i))
155.     END IF
156.     '**************END Code added Novarseg
157.  
158.  
159.     'START OF COLLISION MATHEMATICS SECTION
160.  
161.     ballradius = PyT(b(0).p, b(1).p) / 2
162.  
163.     FOR bn = 0 TO 1
164.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
165.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
166.     NEXT bn
167.  
168.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
169.     B2BCollision b(0), b(1), Nvec(), Tvec(), Fvec()
170.     'END OF COLLISION MATHEMATICS SECTION
171.  
172.     'graphic representation
173.     FOR grid = -300 TO 300 STEP 20
174.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
175.         LINE (grid, 300)-(grid, -300), c& 'Gray  'vertical lines
176.         LINE (-300, grid)-(300, grid), c& ' Gray  'horizontal lines
177.     NEXT grid
178.  
179.  
180.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
181.  
182.     FOR dr = 0 TO 1
183.  
184.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , 1 'AR
185.  
186.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y + b(dr).m.y), b(dr).c 'incoming
187.  
188.         'LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).x.x, b(dr).p.y + b(dr).x.y), b(dr).c, , &B1111000011110000 'exit vector
189.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Fvec(dr).x, b(dr).p.y + Fvec(dr).y), b(dr).c, , &B1111000011110000 'exit vector
190.  
191.         ' LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Nvec(dr).x, b(dr).p.y + Nvec(dr).y), b(dr).c, , &B1111000011110000 'exit vector
192.         ' LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Tvec(dr).x, b(dr).p.y + Tvec(dr).y), b(dr).c, , &B1111000011110000 'exit vector
193.  
194.  
195.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
196.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
197.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(b(dr).x.x))) + ", " + _TRIM$(STR$(INT(b(dr).x.y))) + ">" + c(dr)
198.  
199.         _PRINTSTRING (0, 567 + (16 * dr)), b$
200.  
201.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
202.     NEXT dr
203.  
204.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
205.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
206.         PUT #1, , TEXT(0) 'NOVARSEG added this line
207.         PUT #1, , TEXT(1) 'NOVARSEG added this line
208.         CLOSE 'NOVARSEG added this line
209.     END IF 'NOVARSEG added this line
210.  
211.     _LIMIT 500
212.     _DISPLAY
213. LOOP UNTIL _KEYDOWN(27)
214. END
215.  
216.  
217. SUB B2BCollision (ball0 AS ball, ball1 AS ball, Nvec() AS V2, Tvec() AS V2, Fvec() AS V2)
218.  
219.     DIM un AS V2
220.     DIM ut AS V2
221.     DIM MAG AS SINGLE
222.  
223.     DIM unDOT0 AS SINGLE 'unit normal vector "dot" pre collision heading ball0
224.     DIM unDOT1 AS SINGLE 'unit normal vector "dot" pre collision heading ball1
225.     DIM utDOT0 AS SINGLE 'unit tangent vector "dot" pre collision heading ball0
226.     DIM utDOT1 AS SINGLE 'unit tangent vector "dot" pre collision heading ball1
227.  
228.     DIM unVec0 AS V2
229.     DIM utVec0 AS V2
230.     DIM unVec1 AS V2
231.     DIM utVec1 AS V2
232.  
233.     'calculate unit normql vector from ball positions
234.     'ball0 = red, ball1 =cyan
235.     un.x = ball1.p.x - ball0.p.x
236.     un.y = ball1.p.y - ball0.p.y
237.     MAG = (un.x ^ 2 + un.y ^ 2) ^ .5
238.     un.x = un.x / MAG
239.     un.y = un.y / MAG
240.  
241.     ut.x = -un.y: ut.y = un.x '     establish unit tangent
242.  
243.     unDOT0 = un.x * ball0.m.x + un.y * ball0.m.y 'unit normal vector DOT ball vector
244.     unDOT1 = un.x * ball1.m.x + un.y * ball1.m.y 'unit normal vector DOT ball vector
245.     utDOT0 = ut.x * ball0.m.x + ut.y * ball0.m.y 'unit tangent vector DOT ball vector
246.     utDOT1 = ut.x * ball1.m.x + ut.y * ball1.m.y 'unit tangent vector DOT ball vector
247.  
248.     'swap "unit normal" scaled ball vectors (pre collision)   according to https://www.vobarian.com/collisions/2dcollisions2.pdf
249.     A = unDOT0
250.     B = unDOT1
251.     unDOT0 = B: unDOT1 = A
252.  
253.     'Convert the scalar normal and tangential velocities into vectors
254.     'according to https://www.vobarian.com/collisions/2dcollisions2.pdf
255.     VecMult2 un, unDOT0, unVec0 '  third parameter is output
256.     VecMult2 ut, utDOT0, utVec0 '  third parameter is output
257.     VecMult2 un, unDOT1, unVec1 '  third parameter is output
258.     VecMult2 ut, utDOT1, utVec1 '  third parameter is output
259.  
260.     VecAdd2 unVec1, utVec1, Fvec(1) 'vector addition to calculate final ball vectors
261.     VecAdd2 unVec0, utVec0, Fvec(0) 'vector addition to calculate final ball vectors
262.  
263.     Nvec(0).x = -unVec0.x 'not necessary code - for display only
264.     Nvec(0).y = -unVec0.y 'not necessary code - for display only
265.  
266.     Nvec(1).x = -unVec1.x 'not necessary code - for display only
267.     Nvec(1).y = -unVec1.y 'not necessary code - for display only
268.  
269.     Tvec(0).x = -utVec0.x 'not necessary code - for display only
270.     Tvec(0).y = -utVec0.y 'not necessary code - for display only
271.  
272.     Tvec(1).x = -utVec1.x 'not necessary code - for display only
273.     Tvec(1).y = -utVec1.y 'not necessary code - for display only
274.  
275. END SUB 'B2BCollision
276.  
277.  
278. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
279.  
280.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
281.  
282. END FUNCTION 'map!
283.  
284.  
285. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
286.     STATIC StartTimer AS _FLOAT
287.     STATIC ButtonDown AS INTEGER
288.     STATIC ClickCount AS INTEGER
289.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
290.     '                          Down longer counts as a HOLD event.
291.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
292.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
293.         SELECT CASE SGN(_MOUSEWHEEL)
294.             CASE 1: MBS = MBS OR 512
295.             CASE -1: MBS = MBS OR 1024
296.         END SELECT
297.     WEND
298.  
299.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
300.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
301.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
302.  
303.     IF StartTimer = 0 THEN
304.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
305.             ButtonDown = 1: StartTimer = TIMER(0.01)
306.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
307.         ELSEIF _MOUSEBUTTON(2) THEN
308.             ButtonDown = 2: StartTimer = TIMER(0.01)
309.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
310.         ELSEIF _MOUSEBUTTON(3) THEN
311.             ButtonDown = 3: StartTimer = TIMER(0.01)
312.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
313.         END IF
314.     ELSE
315.         BD = ButtonDown MOD 3
316.         IF BD = 0 THEN BD = 3
317.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
318.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
319.         ELSE
320.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
321.                 MBS = 0: ButtonDown = 0: StartTimer = 0
322.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
323.             ELSE 'We've now started the hold event
324.                 MBS = MBS OR 32 * 2 ^ ButtonDown
325.             END IF
326.         END IF
327.     END IF
328. END FUNCTION 'MBS%
329.  
330.  
331. FUNCTION PyT (var1 AS V2, var2 AS V2)
332.  
333.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
334.  
335. END FUNCTION 'PyT
336.  
337. FUNCTION bPyT (var1 AS V2, var2 AS V2, var3) 'to calulate ball radius only
338.  
339.     bPyT = _HYPOT((var1.x - var2.x) * var3, (var1.y - var2.y) * var3)
340.  
341. END FUNCTION 'bPyT
342.  
343.  
344.  
345. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
346.  
347.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
348.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
349.  
350. END SUB 'Add_Vector
351.  
352. SUB VecAdd2 (var1 AS V2, var2 AS V2, var3 AS V2)
353.  
354.     var3.x = -var1.x + -var2.x '
355.     var3.y = -var1.y + -var2.y '
356.  
357. END SUB 'Add_Vector
358.  
359.  
360. FUNCTION VecDot (var AS V2, var2 AS V2)
361.  
362.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
363.  
364. END FUNCTION 'VecDot
365.  
366.  
367. SUB VecMult (vec AS V2, multiplier AS SINGLE)
368.  
369.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
370.     vec.y = vec.y * multiplier
371.  
372. END SUB 'Vec_Mult
373.  
374. SUB VecMult2 (var1 AS V2, var2 AS SINGLE, out1 AS V2)
375.  
376.     out1.x = var1.x * var2
377.     out1.y = var1.y * var2
378.  
379. END SUB 'Vec_Mult
380.  
381. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
382.  
383.     vec.x = vec.x / divisor
384.     vec.y = vec.y / divisor
385.  
386. END SUB 'VecDIV
387.  
388.  
389. SUB VecNorm (var AS V2)
390.  
391.     m = PyT(origin, var)
392.     IF m = 0 THEN
393.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
394.     ELSE
395.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
396.     END IF
397.  
398. END SUB 'VecNorm
399.  

The previous code was  annoying when rotating the vectors. The vector kept rotating when the key was released.  fixed with 3 speed rotation now.

Keys to rotate vector are z or x
keys to adjust vector magnitude (ball velocity) are c or v
Key to toggle red or cyan ball is b

As in the original code, the arrow keys move the ball positions.

rotate vector has an auto  - fine / medium / coarse control.   hold down key longer to obtain effect.

Code: QB64: [Select]

1. 'Original code and concept by OldMoses
2. 'additional code and mods by Novarseg
3.  
4. $COLOR:32
5. TYPE V2
6.     x AS SINGLE
7.     y AS SINGLE
8. END TYPE
9.  
10. TYPE ball
11.     cn AS STRING * 4 '                                          ball name by color
12.     c AS _UNSIGNED LONG '                                       color
13.     p AS V2 '                                                   ball position
14.     m AS V2 '                                                   heading vector
15.     x AS V2 '                                                   exit vector
16.     s AS INTEGER '                                              magnitude of movement
17. END TYPE
18.  
19. DIM Nvec(1) AS V2 'normal velocity vectors
20. DIM Tvec(1) AS V2 'tangential velocity vectors
21. DIM Fvec(1) AS V2 'Final or exit vectors
22. DIM kh AS LONG
23.  
24. DIM TEXT(1) AS STRING
25. DIM RAD(1) AS SINGLE
26.  
27. DIM c(1) AS STRING
28.  
29. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
30. DIM mouse AS V2
31. DIM b(1) AS ball
32.  
33. 'DIM SHARED AS V2 origin
34. DIM SHARED origin AS V2
35. origin.x = 0: origin.y = 0
36. b(0).c = Red: b(0).cn = "red"
37. b(1).c = Cyan: b(1).cn = "cyan"
38.  
39. SCREEN _NEWIMAGE(_DESKTOPWIDTH, _DESKTOPHEIGHT, 32) 'prevents FULLSCREEN distortion
40.  
41. MAG = _DESKTOPHEIGHT / 300 'this 300 is from the grid drawing code.
42.  
43. WINDOW (-_DESKTOPWIDTH / MAG, -_DESKTOPHEIGHT / MAG)-(_DESKTOPWIDTH / MAG, _DESKTOPHEIGHT / MAG)
44.  
45. _FULLSCREEN 'gives a full screen - not a window!
46. 'advantage:  only one position - the screen!
47. 'disadvantage: can't be minimized - or can it?
48.  
49. 'starting state
50. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
51. RAD(0) = 2 * _PI / 2
52. b(0).s = PyT(origin, b(0).m)
53.  
54. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
55. RAD(1) = 3 * _PI / 2
56. b(1).s = PyT(origin, b(1).m)
57.  
58. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
59. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
60.  
61. f4 = 0 'initial ball select flag
62. f5 = 0 'inital ball display flag
63.  
64. DO
65.  
66.     CLS
67.     ms = MBS '                                                  process mouse actions dragging endpoints
68.     IF ms AND 64 THEN
69.  
70.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
71.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
72.  
73.         FOR x = 0 TO 1
74.             FOR y = 0 TO 1
75.                 ds! = PyT(vertex(x, y), mouse)
76.                 IF ds! < ballradius * .5 THEN i = x: j = y
77.             NEXT y
78.         NEXT x
79.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
80.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
81.                 b(i).p = mouse
82.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
83.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
84.         END SELECT
85.     END IF
86.  
87.     IF kh = 18432 THEN b(i).p.y = b(i).p.y + 1
88.     IF kh = 20480 THEN b(i).p.y = b(i).p.y - 1
89.     IF kh = 19200 THEN b(i).p.x = b(i).p.x - 1
90.     IF kh = 19712 THEN b(i).p.x = b(i).p.x + 1
91.  
92.  
93.     'Vector rotation and vector magnitude adjustment using keyboard input
94.  
95.     IF f5 = 0 THEN
96.         f5 = 1
97.         FOR i = 0 TO 1
98.             b(i).s = PyT(origin, b(i).m)
99.             b(i).m.y = b(i).s * COS(RAD(i))
100.             b(i).m.x = b(i).s * SIN(RAD(i))
101.         NEXT i
102.         i = 1
103.     END IF
104.  
105.     IF kh = 122 OR kh = 120 THEN f3 = 1
106.  
107.     IF (kh = -122 OR kh = -120) AND f3 = 1 THEN f1 = 0: f3 = 0
108.  
109.     IF f4 = 0 THEN kh = 98: f4 = 1
110.     IF kh = 98 AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
111.     IF kh = 98 AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
112.     LL1:
113.  
114.     IF kh = 99 THEN 'increase vector magnitude  press c
115.         mult = 1.01
116.         VecMult b(i).m, mult
117.     END IF
118.  
119.     IF kh = 118 THEN 'decrease vector magnitude     press v
120.         div = 1.01
121.         VecDIV b(i).m, div 'added a new sub
122.     END IF
123.  
124.     IF kh = 122 THEN 'rotate vector counter clockwise  'press z
125.         IF RAD(i) > _PI * 2 THEN RAD(i) = 0
126.  
127.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
128.  
129.         IF TIMER - t1 <= 1 THEN RAD(i) = RAD(i) + .005
130.         IF TIMER - t1 > 1 THEN RAD(i) = RAD(i) + .020
131.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) + .05
132.  
133.         b(i).s = PyT(origin, b(i).m)
134.         b(i).m.y = b(i).s * COS(RAD(i))
135.         b(i).m.x = b(i).s * SIN(RAD(i))
136.  
137.     END IF
138.  
139.     IF kh = 120 THEN 'rotate vector clockwise   'press x
140.         IF RAD(i) < 0 THEN RAD(i) = _PI * 2
141.  
142.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
143.  
144.         IF TIMER - t1 <= 1 THEN RAD(i) = RAD(i) - .005
145.         IF TIMER - t1 > 1 THEN RAD(i) = RAD(i) - .020
146.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) - .05
147.  
148.         b(i).s = PyT(origin, b(i).m)
149.         b(i).m.y = b(i).s * COS(RAD(i))
150.         b(i).m.x = b(i).s * SIN(RAD(i))
151.     END IF
152.  
153.     'START OF COLLISION MATHEMATICS SECTION
154.  
155.     ballradius = PyT(b(0).p, b(1).p) / 2
156.  
157.     FOR bn = 0 TO 1
158.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
159.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
160.     NEXT bn
161.  
162.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
163.     B2BCollision b(0), b(1), Nvec(), Tvec(), Fvec()
164.     'END OF COLLISION MATHEMATICS SECTION
165.  
166.     'graphic representation
167.     FOR grid = -300 TO 300 STEP 20
168.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
169.         LINE (grid, 300)-(grid, -300), c& 'Gray  'vertical lines
170.         LINE (-300, grid)-(300, grid), c& ' Gray  'horizontal lines
171.     NEXT grid
172.  
173.  
174.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
175.  
176.     FOR dr = 0 TO 1
177.  
178.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , 1 'AR
179.  
180.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y + b(dr).m.y), b(dr).c 'incoming
181.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Fvec(dr).x, b(dr).p.y + Fvec(dr).y), b(dr).c, , &B1111000011110000 'exit vector
182.  
183.         ' LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Nvec(dr).x, b(dr).p.y + Nvec(dr).y), b(dr).c, , &B1111000011110000 ' for testing
184.         ' LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Tvec(dr).x, b(dr).p.y + Tvec(dr).y), b(dr).c, , &B1111000011110000 ' for testing
185.  
186.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
187.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
188.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(Fvec(dr).x))) + ", " + _TRIM$(STR$(INT(Fvec(dr).y))) + ">" + c(dr)
189.  
190.         _PRINTSTRING (0, 567 + (16 * dr)), b$
191.  
192.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
193.     NEXT dr
194.  
195.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
196.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
197.         PUT #1, , TEXT(0) 'NOVARSEG added this line
198.         PUT #1, , TEXT(1) 'NOVARSEG added this line
199.         CLOSE 'NOVARSEG added this line
200.     END IF 'NOVARSEG added this line
201.  
202.     _DISPLAY
203.  
204.     DO
205.         _LIMIT 500
206.         kh = _KEYHIT
207.         IF kh > 0 OR kh < 0 THEN EXIT DO
208.     LOOP
209.  
210. LOOP UNTIL _KEYDOWN(27)
211.  
212. END
213.  
214.  
215. SUB B2BCollision (ball0 AS ball, ball1 AS ball, Nvec() AS V2, Tvec() AS V2, Fvec() AS V2)
216.  
217.     DIM un AS V2
218.     DIM ut AS V2
219.     DIM MAG AS SINGLE
220.  
221.     DIM unDOT0 AS SINGLE 'unit normal vector "dot" pre collision heading ball0
222.     DIM unDOT1 AS SINGLE 'unit normal vector "dot" pre collision heading ball1
223.     DIM utDOT0 AS SINGLE 'unit tangent vector "dot" pre collision heading ball0
224.     DIM utDOT1 AS SINGLE 'unit tangent vector "dot" pre collision heading ball1
225.  
226.     DIM unVec0 AS V2
227.     DIM utVec0 AS V2
228.     DIM unVec1 AS V2
229.     DIM utVec1 AS V2
230.  
231.     'calculate unit normql vector from ball positions
232.     'ball0 = red, ball1 =cyan
233.     un.x = ball1.p.x - ball0.p.x
234.     un.y = ball1.p.y - ball0.p.y
235.     MAG = (un.x ^ 2 + un.y ^ 2) ^ .5
236.     un.x = un.x / MAG
237.     un.y = un.y / MAG
238.  
239.     ut.x = -un.y: ut.y = un.x '     establish unit tangent
240.  
241.     unDOT0 = un.x * ball0.m.x + un.y * ball0.m.y 'unit normal vector DOT ball vector
242.     unDOT1 = un.x * ball1.m.x + un.y * ball1.m.y 'unit normal vector DOT ball vector
243.     utDOT0 = ut.x * ball0.m.x + ut.y * ball0.m.y 'unit tangent vector DOT ball vector
244.     utDOT1 = ut.x * ball1.m.x + ut.y * ball1.m.y 'unit tangent vector DOT ball vector
245.  
246.     'swap "unit normal" scaled ball vectors (pre collision)   according to https://www.vobarian.com/collisions/2dcollisions2.pdf
247.     A = unDOT0
248.     B = unDOT1
249.     unDOT0 = B: unDOT1 = A
250.  
251.     'Convert the scalar normal and tangential velocities into vectors
252.     'according to https://www.vobarian.com/collisions/2dcollisions2.pdf
253.     VecMult2 un, unDOT0, unVec0 '  third parameter is output
254.     VecMult2 ut, utDOT0, utVec0 '  third parameter is output
255.     VecMult2 un, unDOT1, unVec1 '  third parameter is output
256.     VecMult2 ut, utDOT1, utVec1 '  third parameter is output
257.  
258.     VecAdd2 unVec1, utVec1, Fvec(1) 'vector addition to calculate final ball vectors
259.     VecAdd2 unVec0, utVec0, Fvec(0) 'vector addition to calculate final ball vectors
260.  
261.     Nvec(0).x = -unVec0.x 'not necessary code - for display only
262.     Nvec(0).y = -unVec0.y 'not necessary code - for display only
263.  
264.     Nvec(1).x = -unVec1.x 'not necessary code - for display only
265.     Nvec(1).y = -unVec1.y 'not necessary code - for display only
266.  
267.     Tvec(0).x = -utVec0.x 'not necessary code - for display only
268.     Tvec(0).y = -utVec0.y 'not necessary code - for display only
269.  
270.     Tvec(1).x = -utVec1.x 'not necessary code - for display only
271.     Tvec(1).y = -utVec1.y 'not necessary code - for display only
272.  
273. END SUB 'B2BCollision
274.  
275.  
276. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
277.  
278.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
279.  
280. END FUNCTION 'map!
281.  
282.  
283. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
284.     STATIC StartTimer AS _FLOAT
285.     STATIC ButtonDown AS INTEGER
286.     STATIC ClickCount AS INTEGER
287.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
288.     '                          Down longer counts as a HOLD event.
289.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
290.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
291.         SELECT CASE SGN(_MOUSEWHEEL)
292.             CASE 1: MBS = MBS OR 512
293.             CASE -1: MBS = MBS OR 1024
294.         END SELECT
295.     WEND
296.  
297.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
298.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
299.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
300.  
301.     IF StartTimer = 0 THEN
302.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
303.             ButtonDown = 1: StartTimer = TIMER(0.01)
304.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
305.         ELSEIF _MOUSEBUTTON(2) THEN
306.             ButtonDown = 2: StartTimer = TIMER(0.01)
307.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
308.         ELSEIF _MOUSEBUTTON(3) THEN
309.             ButtonDown = 3: StartTimer = TIMER(0.01)
310.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
311.         END IF
312.     ELSE
313.         BD = ButtonDown MOD 3
314.         IF BD = 0 THEN BD = 3
315.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
316.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
317.         ELSE
318.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
319.                 MBS = 0: ButtonDown = 0: StartTimer = 0
320.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
321.             ELSE 'We've now started the hold event
322.                 MBS = MBS OR 32 * 2 ^ ButtonDown
323.             END IF
324.         END IF
325.     END IF
326. END FUNCTION 'MBS%
327.  
328.  
329. FUNCTION PyT (var1 AS V2, var2 AS V2)
330.  
331.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
332.  
333. END FUNCTION 'PyT
334.  
335. FUNCTION bPyT (var1 AS V2, var2 AS V2, var3) 'to calulate ball radius only
336.  
337.     bPyT = _HYPOT((var1.x - var2.x) * var3, (var1.y - var2.y) * var3)
338.  
339. END FUNCTION 'bPyT
340.  
341.  
342.  
343. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
344.  
345.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
346.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
347.  
348. END SUB 'Add_Vector
349.  
350. SUB VecAdd2 (var1 AS V2, var2 AS V2, var3 AS V2)
351.  
352.     var3.x = -var1.x + -var2.x '
353.     var3.y = -var1.y + -var2.y '
354.  
355. END SUB 'Add_Vector
356.  
357.  
358. FUNCTION VecDot (var AS V2, var2 AS V2)
359.  
360.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
361.  
362. END FUNCTION 'VecDot
363.  
364.  
365. SUB VecMult (vec AS V2, multiplier AS SINGLE)
366.  
367.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
368.     vec.y = vec.y * multiplier
369.  
370. END SUB 'Vec_Mult
371.  
372. SUB VecMult2 (var1 AS V2, var2 AS SINGLE, out1 AS V2)
373.  
374.     out1.x = var1.x * var2
375.     out1.y = var1.y * var2
376.  
377. END SUB 'Vec_Mult
378.  
379. SUB VecDIV (vec AS V2, divisor AS SINGLE) 'added by Novarseg
380.  
381.     vec.x = vec.x / divisor
382.     vec.y = vec.y / divisor
383.  
384. END SUB 'VecDIV
385.  
386.  
387. SUB VecNorm (var AS V2)
388.  
389.     m = PyT(origin, var)
390.     IF m = 0 THEN
391.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
392.     ELSE
393.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
394.     END IF
395.  
396. END SUB 'VecNorm
397.  

Title: Re: 2D ball collisions without trigonometry.
Post by: NOVARSEG on June 06, 2021, 10:50:02 pm

Got the math from STxAxTIC's notes working

In the following code there are 2 subs

B2B_Collision   which is based on math from STxAxTIC's notes

B2BCollision   which is based on math from  https://www.vobarian.com/collisions/2dcollisions2.pdf

Both subs produce the same final (exit) vectors

Code: QB64: [Select]

1. $COLOR:32
2. TYPE V2
3.     x AS SINGLE
4.     y AS SINGLE
5. END TYPE
6.  
7. TYPE ball
8.     cn AS STRING * 4 '                                          ball name by color
9.     c AS _UNSIGNED LONG '                                       color
10.     p AS V2 '                                                   ball position
11.     m AS V2 '                                                   heading vector
12.     x AS V2 '                                                   exit vector
13.     s AS INTEGER '                                              magnitude of movement
14. END TYPE
15.  
16. DIM Nvec(1) AS V2 'normal velocity vectors
17. DIM Tvec(1) AS V2 'tangential velocity vectors
18. DIM Fvec(1) AS V2 'Final or exit vectors
19. DIM kh AS LONG
20.  
21. DIM TEXT(1) AS STRING
22. DIM RAD(1) AS SINGLE
23.  
24. DIM c(1) AS STRING
25.  
26. DIM vertex(1, 1) AS V2 '                                        mouse grabbing handles
27. DIM mouse AS V2
28. DIM b(1) AS ball
29.  
30. 'DIM SHARED AS V2 origin
31. DIM SHARED origin AS V2
32. origin.x = 0: origin.y = 0
33. b(0).c = Red: b(0).cn = "red"
34. b(1).c = Cyan: b(1).cn = "cyan"
35.  
36. SCREEN _NEWIMAGE(_DESKTOPWIDTH, _DESKTOPHEIGHT, 32) 'prevents FULLSCREEN distortion
37.  
38. MAG = _DESKTOPHEIGHT / 300 'this 300 is from the grid drawing code.
39.  
40. WINDOW (-_DESKTOPWIDTH / MAG, -_DESKTOPHEIGHT / MAG)-(_DESKTOPWIDTH / MAG, _DESKTOPHEIGHT / MAG)
41.  
42. _FULLSCREEN 'gives a full screen - not a window!
43. 'advantage:  only one position - the screen!
44. 'disadvantage: can't be minimized - or can it?
45.  
46. 'starting state
47. b(0).m.x = 0: b(0).m.y = 100 '    reds approach vector
48. RAD(0) = 2 * _PI / 2
49. b(0).s = PyT(origin, b(0).m)
50.  
51. b(1).m.x = -100: b(1).m.y = 0 '   cyans approach vector
52. RAD(1) = 3 * _PI / 2
53. b(1).s = PyT(origin, b(1).m)
54.  
55. b(0).p.x = 0: b(0).p.y = 0 '     ball position x, y
56. b(1).p.x = -100: b(1).p.y = 100 'ball position x, y
57.  
58. f4 = 0 'initial ball select flag
59. f5 = 0 'inital ball display flag
60.  
61. DO
62.  
63.     CLS
64.     ms = MBS '                                                  process mouse actions dragging endpoints
65.     IF ms AND 64 THEN
66.  
67.         mouse.x = map!(_MOUSEX, 0, 599, -300, 300)
68.         mouse.y = map!(_MOUSEY, 0, 599, 300, -300)
69.  
70.         FOR x = 0 TO 1
71.             FOR y = 0 TO 1
72.                 ds! = PyT(vertex(x, y), mouse)
73.                 IF ds! < ballradius * .5 THEN i = x: j = y
74.             NEXT y
75.         NEXT x
76.         SELECT CASE j '                                         grabbing impact position or start of incoming vector
77.             CASE IS = 0 '                                       impact position- here we use mouse as the new b(#).p
78.                 b(i).p = mouse
79.             CASE IS = 1 '                                       starting point- here we obtain the b(#).m mathematically
80.                 b(i).m = b(i).p: VecAdd b(i).m, mouse, -1
81.         END SELECT
82.     END IF
83.  
84.     IF kh = 18432 THEN b(i).p.y = b(i).p.y + 1
85.     IF kh = 20480 THEN b(i).p.y = b(i).p.y - 1
86.     IF kh = 19200 THEN b(i).p.x = b(i).p.x - 1
87.     IF kh = 19712 THEN b(i).p.x = b(i).p.x + 1
88.  
89.  
90.     'Vector rotation and vector magnitude adjustment using keyboard input
91.  
92.     IF f5 = 0 THEN
93.         f5 = 1
94.         FOR i = 0 TO 1
95.             b(i).s = PyT(origin, b(i).m)
96.             b(i).m.y = b(i).s * COS(RAD(i))
97.             b(i).m.x = b(i).s * SIN(RAD(i))
98.         NEXT i
99.         i = 1
100.     END IF
101.  
102.     IF kh = 122 OR kh = 120 THEN f3 = 1
103.  
104.     IF (kh = -122 OR kh = -120) AND f3 = 1 THEN f1 = 0: f3 = 0
105.  
106.     IF f4 = 0 THEN kh = 98: f4 = 1
107.     IF kh = 98 AND f2 = 0 THEN i = 1: f2 = 1: c(1) = "  SELECTED": c(0) = "           ": GOTO LL1 'cyan
108.     IF kh = 98 AND f2 = 1 THEN i = 0: f2 = 0: c(0) = "  SELECTED": c(1) = "           " 'red
109.     LL1:
110.  
111.     IF kh = 99 THEN 'increase vector magnitude  press c
112.         mult = 1.01
113.         VecMult b(i).m, mult
114.     END IF
115.  
116.     IF kh = 118 THEN 'decrease vector magnitude     press v
117.         div = 1.01
118.         VecDIV b(i).m, div 'added a new sub
119.     END IF
120.  
121.     IF kh = 122 THEN 'rotate vector counter clockwise  'press z
122.         IF RAD(i) > _PI * 2 THEN RAD(i) = 0
123.  
124.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
125.  
126.         IF TIMER - t1 <= 1 THEN RAD(i) = RAD(i) + .005
127.         IF TIMER - t1 > 1 THEN RAD(i) = RAD(i) + .020
128.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) + .05
129.  
130.         b(i).s = PyT(origin, b(i).m)
131.         b(i).m.y = b(i).s * COS(RAD(i))
132.         b(i).m.x = b(i).s * SIN(RAD(i))
133.  
134.     END IF
135.  
136.     IF kh = 120 THEN 'rotate vector clockwise   'press x
137.         IF RAD(i) < 0 THEN RAD(i) = _PI * 2
138.  
139.         IF f1 = 0 THEN t1 = TIMER: f1 = 1
140.  
141.         IF TIMER - t1 <= 1 THEN RAD(i) = RAD(i) - .005
142.         IF TIMER - t1 > 1 THEN RAD(i) = RAD(i) - .020
143.         IF TIMER - t1 > 1.5 THEN RAD(i) = RAD(i) - .05
144.  
145.         b(i).s = PyT(origin, b(i).m)
146.         b(i).m.y = b(i).s * COS(RAD(i))
147.         b(i).m.x = b(i).s * SIN(RAD(i))
148.     END IF
149.  
150.     'START OF COLLISION MATHEMATICS SECTION
151.  
152.     ballradius = PyT(b(0).p, b(1).p) / 2
153.  
154.     FOR bn = 0 TO 1
155.         vertex(bn, 0) = b(bn).p '                               first we establish the mouse handles for ball position
156.         vertex(bn, 1) = b(bn).p: VecAdd vertex(bn, 1), b(bn).m, -1 ' and incoming vector starting point
157.     NEXT bn
158.  
159.     'Now all the previous garbage is distilled into a single SUB call once a collision is determined
160.     B2B_Collision b(0), b(1), Nvec(), Tvec(), Fvec()
161.     'END OF COLLISION MATHEMATICS SECTION
162.  
163.     'graphic representation
164.     FOR grid = -300 TO 300 STEP 20
165.         IF grid MOD 100 = 0 THEN c& = &HFF7F7F7F ELSE c& = &H5F7F7F7F
166.         LINE (grid, 300)-(grid, -300), c& 'Gray  'vertical lines
167.         LINE (-300, grid)-(300, grid), c& ' Gray  'horizontal lines
168.     NEXT grid
169.  
170.  
171.     LINE (b(1).p.x, b(1).p.y)-(b(0).p.x, b(0).p.y), White, , &B0010001000100010 'strike vector
172.  
173.     FOR dr = 0 TO 1
174.  
175.         CIRCLE (b(dr).p.x, b(dr).p.y), ballradius, b(dr).c, , , 1 'AR
176.  
177.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + b(dr).m.x, b(dr).p.y + b(dr).m.y), b(dr).c 'incoming
178.         LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Fvec(dr).x, b(dr).p.y + Fvec(dr).y), b(dr).c, , &B1111000011110000 'exit vector
179.  
180.         ' LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Nvec(dr).x, b(dr).p.y + Nvec(dr).y), b(dr).c, , &B1111000011110000 ' for testing
181.         ' LINE (b(dr).p.x, b(dr).p.y)-(b(dr).p.x + Tvec(dr).x, b(dr).p.y + Tvec(dr).y), b(dr).c, , &B1111000011110000 ' for testing
182.  
183.         b$ = b(dr).cn + " @ (" + _TRIM$(STR$(INT(b(dr).p.x))) + ", " + _TRIM$(STR$(INT(b(dr).p.y))) + ")"
184.         b$ = b$ + "  along <" + _TRIM$(STR$(INT(b(dr).m.x))) + ", " + _TRIM$(STR$(INT(b(dr).m.y))) + ">"
185.         b$ = b$ + "  exits along <" + _TRIM$(STR$(INT(Fvec(dr).x))) + ", " + _TRIM$(STR$(INT(Fvec(dr).y))) + ">" + c(dr)
186.  
187.         _PRINTSTRING (0, 567 + (16 * dr)), b$
188.  
189.         TEXT(dr) = b$ + CHR$(13) + CHR$(10) 'NOVARSEG added this line
190.     NEXT dr
191.  
192.     IF _KEYHIT = ASC("f") THEN 'NOVARSEG added this line
193.         OPEN "BALL STUFF.TXT" FOR BINARY AS #1 'NOVARSEG added this line
194.         PUT #1, , TEXT(0) 'NOVARSEG added this line
195.         PUT #1, , TEXT(1) 'NOVARSEG added this line
196.         CLOSE 'NOVARSEG added this line
197.     END IF 'NOVARSEG added this line
198.  
199.     _DISPLAY
200.  
201.     DO
202.         _LIMIT 500
203.         kh = _KEYHIT
204.         IF kh > 0 OR kh < 0 THEN EXIT DO
205.     LOOP
206.  
207. LOOP UNTIL _KEYDOWN(27)
208.  
209. END
210.  
211.  
212. SUB B2BCollision (ball0 AS ball, ball1 AS ball, Nvec() AS V2, Tvec() AS V2, Fvec() AS V2)
213.  
214.     DIM un AS V2
215.     DIM ut AS V2
216.     DIM MAG AS SINGLE
217.  
218.     DIM unDOT0 AS SINGLE 'unit normal vector "dot" pre collision heading ball0
219.     DIM unDOT1 AS SINGLE 'unit normal vector "dot" pre collision heading ball1
220.     DIM utDOT0 AS SINGLE 'unit tangent vector "dot" pre collision heading ball0
221.     DIM utDOT1 AS SINGLE 'unit tangent vector "dot" pre collision heading ball1
222.  
223.     DIM unVec0 AS V2
224.     DIM utVec0 AS V2
225.     DIM unVec1 AS V2
226.     DIM utVec1 AS V2
227.  
228.     'calculate unit normql vector from ball positions
229.     'ball0 = red, ball1 =cyan
230.     un.x = ball1.p.x - ball0.p.x
231.     un.y = ball1.p.y - ball0.p.y
232.     MAG = (un.x ^ 2 + un.y ^ 2) ^ .5
233.     un.x = un.x / MAG
234.     un.y = un.y / MAG
235.  
236.     ut.x = -un.y: ut.y = un.x '     establish unit tangent
237.  
238.     unDOT0 = un.x * ball0.m.x + un.y * ball0.m.y 'unit normal vector DOT ball vector
239.     unDOT1 = un.x * ball1.m.x + un.y * ball1.m.y 'unit normal vector DOT ball vector
240.     utDOT0 = ut.x * ball0.m.x + ut.y * ball0.m.y 'unit tangent vector DOT ball vector
241.     utDOT1 = ut.x * ball1.m.x + ut.y * ball1.m.y 'unit tangent vector DOT ball vector
242.  
243.     'swap "unit normal" scaled ball vectors (pre collision)   according to https://www.vobarian.com/collisions/2dcollisions2.pdf
244.     A = unDOT0
245.     B = unDOT1
246.     unDOT0 = B: unDOT1 = A
247.  
248.     'Convert the scalar normal and tangential velocities into vectors
249.     'according to https://www.vobarian.com/collisions/2dcollisions2.pdf
250.     VecMult2 un, unDOT0, unVec0 '  third parameter is output
251.     VecMult2 ut, utDOT0, utVec0 '  third parameter is output
252.     VecMult2 un, unDOT1, unVec1 '  third parameter is output
253.     VecMult2 ut, utDOT1, utVec1 '  third parameter is output
254.  
255.     VecAdd2 unVec1, utVec1, Fvec(1) 'vector addition to calculate final ball vectors
256.     VecAdd2 unVec0, utVec0, Fvec(0) 'vector addition to calculate final ball vectors
257.  
258.     'Nvec(0).x = -unVec0.x 'not necessary code - for testing only
259.     'Nvec(0).y = -unVec0.y 'not necessary code - for testing only
260.  
261.     'Nvec(1).x = -unVec1.x 'not necessary code - for testing only
262.     'Nvec(1).y = -unVec1.y 'not necessary code - for testing only
263.  
264.     'Tvec(0).x = -utVec0.x 'not necessary code - for testing only
265.     'Tvec(0).y = -utVec0.y 'not necessary code - for testing only
266.  
267.     'Tvec(1).x = -utVec1.x 'not necessary code - for testing only
268.     'Tvec(1).y = -utVec1.y 'not necessary code - for testing only
269.  
270. END SUB 'B2BCollision
271. '************
272. SUB B2B_Collision (ball0 AS ball, ball1 AS ball, Nvec() AS V2, Tvec() AS V2, Fvec() AS V2)
273.  
274.     DIM un AS V2
275.     DIM ut AS V2
276.     DIM MAG AS SINGLE
277.  
278.     DIM unDOT0 AS SINGLE 'unit normal vector "dot" pre collision heading ball0
279.     DIM unDOT1 AS SINGLE 'unit normal vector "dot" pre collision heading ball1
280.     DIM utDOT0 AS SINGLE 'unit tangent vector "dot" pre collision heading ball0
281.     DIM utDOT1 AS SINGLE 'unit tangent vector "dot" pre collision heading ball1
282.  
283.     DIM unVec0 AS V2
284.     DIM utVec0 AS V2
285.     DIM unVec1 AS V2
286.     DIM utVec1 AS V2
287.  
288.     'calculate unit normql vector from ball positions
289.     'ball0 = red, ball1 =cyan
290.     un.x = ball1.p.x - ball0.p.x
291.     un.y = ball1.p.y - ball0.p.y
292.     MAG = (un.x ^ 2 + un.y ^ 2) ^ .5
293.     un.x = un.x / MAG
294.     un.y = un.y / MAG
295.  
296.     'ut.x = -un.y: ut.y = un.x '     establish unit tangent
297.  
298.     unDOT0 = un.x * ball0.m.x + un.y * ball0.m.y 'unit normal vector DOT ball vector
299.     unDOT1 = un.x * ball1.m.x + un.y * ball1.m.y 'unit normal vector DOT ball vector
300.     ' utDOT0 = ut.x * ball0.m.x + ut.y * ball0.m.y 'unit tangent vector DOT ball vector
301.     ' utDOT1 = ut.x * ball1.m.x + ut.y * ball1.m.y 'unit tangent vector DOT ball vector
302.  
303.     ' 'swap "unit normal" scaled ball vectors (pre collision)   according to https://www.vobarian.com/collisions/2dcollisions2.pdf
304.     ' A = unDOT0
305.     ' B = unDOT1
306.     ' unDOT0 = B: unDOT1 = A
307.  
308.     'Convert the scalar normal and tangential velocities into vectors
309.     'according to https://www.vobarian.com/collisions/2dcollisions2.pdf
310.  
311.     VecMult2 un, unDOT1 - unDOT0, unVec0 '  third parameter is output
312.  
313.     'VecMult2 ut, utDOT0, utVec0 '  third parameter is output
314.  
315.     VecMult2 un, unDOT0 - unDOT1, unVec1 '  third parameter is output
316.  
317.     'VecMult2 ut, utDOT1, utVec1 '  third parameter is output
318.  
319.     VecAdd2 unVec1, ball1.m, Fvec(1) 'vector addition to calculate final ball vectors
320.     VecAdd2 unVec0, ball0.m, Fvec(0) 'vector addition to calculate final ball vectors
321.  
322. END SUB 'B2B_Collision
323.  
324.  
325.  
326. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
327.  
328.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
329.  
330. END FUNCTION 'map!
331.  
332.  
333. FUNCTION MBS% 'Mouse Button Status  Author: Steve McNeill
334.     STATIC StartTimer AS _FLOAT
335.     STATIC ButtonDown AS INTEGER
336.     STATIC ClickCount AS INTEGER
337.     CONST ClickLimit## = 0.2 'Less than 1/4th of a second to down, up a key to count as a CLICK.
338.     '                          Down longer counts as a HOLD event.
339.     SHARED Mouse_StartX, Mouse_StartY, Mouse_EndX, Mouse_EndY
340.     WHILE _MOUSEINPUT 'Remark out this block, if mouse main input/clear is going to be handled manually in main program.
341.         SELECT CASE SGN(_MOUSEWHEEL)
342.             CASE 1: MBS = MBS OR 512
343.             CASE -1: MBS = MBS OR 1024
344.         END SELECT
345.     WEND
346.  
347.     IF _MOUSEBUTTON(1) THEN MBS = MBS OR 1
348.     IF _MOUSEBUTTON(2) THEN MBS = MBS OR 2
349.     IF _MOUSEBUTTON(3) THEN MBS = MBS OR 4
350.  
351.     IF StartTimer = 0 THEN
352.         IF _MOUSEBUTTON(1) THEN 'If a button is pressed, start the timer to see what it does (click or hold)
353.             ButtonDown = 1: StartTimer = TIMER(0.01)
354.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
355.         ELSEIF _MOUSEBUTTON(2) THEN
356.             ButtonDown = 2: StartTimer = TIMER(0.01)
357.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
358.         ELSEIF _MOUSEBUTTON(3) THEN
359.             ButtonDown = 3: StartTimer = TIMER(0.01)
360.             Mouse_StartX = _MOUSEX: Mouse_StartY = _MOUSEY
361.         END IF
362.     ELSE
363.         BD = ButtonDown MOD 3
364.         IF BD = 0 THEN BD = 3
365.         IF TIMER(0.01) - StartTimer <= ClickLimit THEN 'Button was down, then up, within time limit.  It's a click
366.             IF _MOUSEBUTTON(BD) = 0 THEN MBS = 4 * 2 ^ ButtonDown: ButtonDown = 0: StartTimer = 0
367.         ELSE
368.             IF _MOUSEBUTTON(BD) = 0 THEN 'hold event has now ended
369.                 MBS = 0: ButtonDown = 0: StartTimer = 0
370.                 Mouse_EndX = _MOUSEX: Mouse_EndY = _MOUSEY
371.             ELSE 'We've now started the hold event
372.                 MBS = MBS OR 32 * 2 ^ ButtonDown
373.             END IF
374.         END IF
375.     END IF
376. END FUNCTION 'MBS%
377.  
378.  
379. FUNCTION PyT (var1 AS V2, var2 AS V2)
380.  
381.     PyT = _HYPOT(var1.x - var2.x, var1.y - var2.y)
382.  
383. END FUNCTION 'PyT
384.  
385.  
386. SUB VecAdd (var AS V2, var2 AS V2, var3 AS SINGLE)
387.  
388.     var.x = -(var.x + (var2.x * var3)) '                           add vector (or a scalar multiple of) var2 to var)
389.     var.y = var.y + (var2.y * var3) '                           use var3 = -1 to subtract var2 from var
390.  
391. END SUB 'Add_Vector
392.  
393. SUB VecAdd2 (var1 AS V2, var2 AS V2, var3 AS V2)
394.  
395.     var3.x = -var1.x + -var2.x '
396.     var3.y = -var1.y + -var2.y '
397.  
398. END SUB 'Add_Vector
399.  
400.  
401. FUNCTION VecDot (var AS V2, var2 AS V2)
402.  
403.     VecDot = var.x * var2.x + var.y * var2.y '                  get dot product of var & var2
404.  
405. END FUNCTION 'VecDot
406.  
407.  
408. SUB VecMult (vec AS V2, multiplier AS SINGLE)
409.  
410.     vec.x = vec.x * multiplier '                                multiply vector by scalar value
411.     vec.y = vec.y * multiplier
412.  
413. END SUB 'Vec_Mult
414.  
415. SUB VecMult2 (var1 AS V2, var2 AS SINGLE, out1 AS V2)
416.  
417.     out1.x = var1.x * var2
418.     out1.y = var1.y * var2
419.  
420. END SUB 'Vec_Mult
421.  
422. SUB VecDIV (vec AS V2, divisor AS SINGLE)
423.  
424.     vec.x = vec.x / divisor
425.     vec.y = vec.y / divisor
426.  
427. END SUB 'VecDIV
428.  
429.  
430. SUB VecNorm (var AS V2)
431.  
432.     m = PyT(origin, var)
433.     IF m = 0 THEN
434.         var.x = 0: var.y = 0 '                                  vector with magnitude 0 is a zero vector
435.     ELSE
436.         var.x = var.x / m: var.y = var.y / m '                  convert var to unit vector
437.     END IF
438.  
439. END SUB 'VecNorm
440.  

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