2D ball collisions without trigonometry.

[NOVARSEG]

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?

[OldMoses]

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

  [ You are not allowed to view this attachment ]  

[NOVARSEG]

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.  

[NOVARSEG]

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.  

[OldMoses]

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.

[NOVARSEG]

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

[NOVARSEG]

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.  

[NOVARSEG]

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 !!!!!!!!!!!!!!!!!!!!!!!!!

[NOVARSEG]

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

[OldMoses]

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

[bplus]

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.

[johnno56]

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....

[bplus]

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.

[johnno56]

WHAT!?!?  No coffee?  Heresy!!!

[bplus]

WHAT!?!?  No coffee?  Heresy!!!

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