2 Ball Collision with an itsy-bitsy-teeny-tiny little bit of trig

[bplus]

Code: QB64: [Select]

1. '  Collision Study Mouse and Ball.bas for QB64 fork (B+=MGA) 2017-08-23
2. 'updated from: Collision study mouse and ball.bas for QB64 fork (B+=MGA) trans 2017-08-20
3. 'translated from "collision mouse study.bas"  SmallBASIC version 2017-01-10
4. 'which was modify the yab version from six posts to one mouse
5.  
6. Const xmax = 800
7. Const ymax = 600
8. Screen _NewImage(xmax, ymax, 32)
9. _Title "Collision Study: Mouse versus Ball - bplus"
10.  
11. Const RADIUS = 30 ' radius for both ball and angle
12. Const SPEED = 5
13. ba = _Pi(1 / 6) 'ball angle in radians
14. bx = xmax / 2 'ball x
15. by = ymax / 2 'ball y
16.  
17.  
18. While 1
19.     Cls , _RGB(30, 70, 48)
20.     If _KeyHit = 27 Then End 'pressed escape goodbye!
21.  
22.     'paddle px, py location
23.     While _MouseInput: Wend  ' <<<<<<<<<< this code so old I had to fix this
24.     px = _MouseX: py = _MouseY
25.  
26.     pbDistance = Sqr((px - bx) ^ 2 + (py - by) ^ 2)
27.     'LOCATE 1, 1: PRINT px, py, pbDistance  'debug
28.  
29.     'show paddle
30.     For i = RADIUS To 0 Step -1
31.         Color _RGB(255 - i * 5, 0, 0)
32.         CircleFill px, py, i
33.     Next
34.  
35.     'update ball hit paddle
36.     If Sqr((px - bx) ^ 2 + (py - by) ^ 2) < RADIUS * 2 Then ba = _Atan2(by - py, bx - px)
37.  
38.     'handle ball hit border
39.     If bx < 0 + RADIUS Then ba = _Pi(1) - ba: bx = RADIUS
40.     If bx > xmax - RADIUS Then ba = _Pi(1) - ba: bx = xmax - RADIUS
41.     If by < 0 + RADIUS Then ba = -ba: by = RADIUS
42.     If by > ymax - RADIUS Then ba = -ba: by = ymax - RADIUS
43.  
44.     'ball angle adjustments to keep between 0 and 2*pi
45.     If ba > 2 * _Pi(1) Then ba = ba - _Pi(2)
46.     If ba < 0 Then ba = ba + _Pi(2)
47.  
48.     'OK the ball is here
49.     bx = bx + Cos(ba) * SPEED
50.     by = by + Sin(ba) * SPEED
51.  
52.     'show ball
53.     For i = RADIUS To 0 Step -1
54.         Color _RGB(255 - i * 6, 255 - i * 6, 255 - i * 6)
55.         CircleFill bx, by, i
56.     Next
57.  
58.     'update screen and keep loops under 61 per second
59.     _Display
60.     _Limit 60
61. Wend
62.  
63. 'Steve McNeil's  copied from his forum
64. Sub CircleFill (CX As Long, CY As Long, R As Long)
65.     Dim subRADIUS As Long, RadiusError As Long
66.     Dim X As Long, Y As Long
67.  
68.     subRADIUS = Abs(R)
69.     RadiusError = -subRADIUS
70.     X = subRADIUS
71.     Y = 0
72.  
73.     If subRADIUS = 0 Then PSet (CX, CY): Exit Sub
74.  
75.     ' Draw the middle span here so we don't draw it twice in the main loop,
76.     ' which would be a problem with blending turned on.
77.     Line (CX - X, CY)-(CX + X, CY), , BF
78.  
79.     While X > Y
80.         RadiusError = RadiusError + Y * 2 + 1
81.         If RadiusError >= 0 Then
82.             If X <> Y + 1 Then
83.                 Line (CX - Y, CY - X)-(CX + Y, CY - X), , BF
84.                 Line (CX - Y, CY + X)-(CX + Y, CY + X), , BF
85.             End If
86.             X = X - 1
87.             RadiusError = RadiusError - X * 2
88.         End If
89.         Y = Y + 1
90.         Line (CX - X, CY - Y)-(CX + X, CY - Y), , BF
91.         Line (CX - X, CY + Y)-(CX + X, CY + Y), , BF
92.     Wend
93. End Sub
94.  
95.  
96.  

[johnno56]

I can prove that you are clairvoyant.... Can you guess my next question? lol

[SMcNeill]

I can prove that you are clairvoyant.... Can you guess my next question? lol

Does it come in Blue?

[Abacus]

Very cool!

[justsomeguy]

Edit: http://kishimotostudios.com/articles/circle_collision/ has a very nice explanation on how it works

Very Nice!

May propose a small optimization? If you are looking for circle to circle collisions, there is a faster way and it does not involve square roots which are normally slower.

I borrowed this from my physics engine and it may be useful to you. I'm not sure about the mathamatics behind it but it works great.

Code: QB64: [Select]

1. FUNCTION circleCircleCollision (cx1 AS SINGLE, cy1 AS SINGLE, radius1 AS SINGLE, cx2 AS SINGLE, cy2 AS SINGLE, radius2 AS SINGLE)
2.     DIM AS SINGLE dx, dy, vlq, radius
3.     dx = cx1 - cx2
4.     dy = cy1 - cy2
5.     vlq = dx * dx + dy * dy
6.     radius = radius1 + radius2
7.     circleCircleCollision = (vlq >= radius * radius)
8. END FUNCTION

I even made a little demo so that you can verify that it works.

Code: QB64: [Select]

1. DIM h$(1): h$(0) = "Hit": h$(1) = "No Hit"
2. DIM hs$
3. _TITLE "Circle Collison Example"
4. SCREEN _NEWIMAGE(800, 600, 32)
5.  
6. DIM AS SINGLE cx1, cy1, rad1, cx2, cy2, rad2
7. cx1 = _WIDTH / 2
8. cy1 = _HEIGHT / 2
9. rad1 = 100
10. rad2 = 50
11.  
12. DO
13.     CLS
14.     DO WHILE _MOUSEINPUT
15.         cx2 = _MOUSEX
16.         cy2 = _MOUSEY
17.         rad2 = rad2 + _MOUSEWHEEL
18.     LOOP
19.  
20.     CIRCLE (cx1, cy1), rad1
21.     CIRCLE (cx2, cy2), rad2
22.  
23.     hit = circleCircleCollision(cx1, cy1, rad1, cx2, cy2, rad2)
24.     hs$ = h$(ABS(hit))
25.     _PRINTSTRING (_WIDTH / 2 - (_PRINTWIDTH(hs$)) / 2, _HEIGHT * .75), hs$
26.  
27.     _DISPLAY
28.     _LIMIT 60
29. LOOP UNTIL _KEYHIT = 27
30. SYSTEM
31.  
32. FUNCTION circleCircleCollision (cx1 AS SINGLE, cy1 AS SINGLE, radius1 AS SINGLE, cx2 AS SINGLE, cy2 AS SINGLE, radius2 AS SINGLE)
33.     DIM AS SINGLE dx, dy, vlq, radius
34.     dx = cx1 - cx2
35.     dy = cy1 - cy2
36.     vlq = dx * dx + dy * dy
37.     radius = radius1 + radius2
38.     circleCircleCollision = (vlq >= radius * radius)
39. END FUNCTION

 

[bplus]

Thanks guys,

@johnno56 coffee is ready now :)

@justsomeguy  yes I like loosing the SQR for distance calc, not really needed and I think x*x is better than x^2 as well. This gives me idea for further optimizing, I will experiment a little, thanks again.

PS this isn't really 2 ball collision, I realized after posting, but very handy for a game with a ball and paddle! I went on to Air Hockey after this study and a variation of Break-out with roundish paddle gives one more control of the angle of ball return.

[bplus]

At the moment of collision when the 2 balls are kissing each other, you need the angle the one ball is to the other.

Using  ballRadianAngleBall2ToBall1 = _ATan2(ball2Y - ball1Y, ball2X - ball1X)
and    ballRadianAngleBall1ToBall2 = _ATan2(ball1Y - ball2Y, ball1X - ball2X)

The QB64 functions convert Degree To Radian units:  _D2R(degreeAngle)
           and complementary Radian To Degree units:  _R2D(RadianAngle)

Here is a demo to show ball angles to each other at moment of collision:

Code: QB64: [Select]

1. _Title "Angle of Ball to each other at moment of collision, press any to move outer ball around inner" 'B+ 2021-05-10
2. ' 2021-05-10  fixed arrow so points from base x,y To angle
3.  
4. Screen _NewImage(800, 600, 32)
5. _Delay .25
6. _ScreenMove _Middle
7. Dim As Double a
8. x1 = 400: y1 = 300 'at middle of screen
9. '
10. ' now take a known ball angle 45 degree ( so we can check it with the trig calc ) to that point South East
11. ' lets say add 100 to x1, y1 for x2, y2
12. x2 = 500: y2 = 400
13.  
14. ' now at what = radius will make the 2 balls kiss ( ie like at moment of collision so I can show trig comes up with 45 degrees)
15. distanceBetweenCenters = Sqr((x1 - x2) ^ 2 + (y1 - y2) ^ 2)
16. radiusForBothBalls = distanceBetweenCenters / 2
17. 'now we can draw the balls
18. Circle (x1, y1), radiusForBothBalls
19. Circle (x2, y2), radiusForBothBalls
20.  
21. angleDegreesB2toB1 = _R2D(_Atan2(y2 - y1, x2 - x1))
22. Print "angleDegreesB2toB1 "; angleDegreesB2toB1
23. ArrowTo x1, y1, _D2R(angleDegreesB2toB1), 60, &HFFFFFF00
24.  
25.  
26. angleDegreesB1toB2 = _R2D(_Atan2(y1 - y2, x1 - x2))
27. Print "angleDegreesB1toB2 "; angleDegreesB1toB2
28. ArrowTo x2, y2, _D2R(angleDegreesB1toB2), 60, &HFFFFFF00
29.  
30. 'OK now lets go around the clock
31. a = _Pi(.25) ' 45 degrees
32. radius = Sqr((400 - 500) ^ 2 + (300 - 400) ^ 2) ' move outer circle around inner every 5 degree
33. Do
34.     Cls
35.     Print "Angle of outer ball to center of screen ="; Int(10000 * _R2D(a)) / 10000 mod 360  ' edit: to keep number in ball park
36.     x2 = 400 + radius * Cos(a)
37.     y2 = 300 + radius * Sin(a)
38.     Circle (x1, y1), radiusForBothBalls
39.     Circle (x2, y2), radiusForBothBalls
40.  
41.     angleDegreesB2toB1 = Int(10000 * _R2D(_Atan2(y2 - y1, x2 - x1))) / 10000
42.     Print "angleDegreesB2toB1 "; angleDegreesB2toB1
43.     ArrowTo x1, y1, _D2R(angleDegreesB2toB1), 60, &HFFFFFF00
44.  
45.     angleDegreesB1toB2 = Int(10000 * _R2D(_Atan2(y1 - y2, x1 - x2))) / 10000
46.     Print "angleDegreesB1toB2 "; angleDegreesB1toB2
47.     ArrowTo x2, y2, _D2R(angleDegreesB1toB2), 60, &HFFFFFF00
48.     Sleep
49.     a = a + _Pi(5 / 180)
50. Loop
51.  
52. Sub ArrowTo (BaseX As Long, BaseY As Long, rAngle As Double, lngth As Long, colr As _Unsigned Long)
53.     Dim As Long x1, y1, x2, y2, x3, y3
54.     x1 = BaseX + lngth * Cos(rAngle)
55.     y1 = BaseY + lngth * Sin(rAngle)
56.     x2 = BaseX + .8 * lngth * Cos(rAngle - _Pi(.05))
57.     y2 = BaseY + .8 * lngth * Sin(rAngle - _Pi(.05))
58.     x3 = BaseX + .8 * lngth * Cos(rAngle + _Pi(.05))
59.     y3 = BaseY + .8 * lngth * Sin(rAngle + _Pi(.05))
60.     Line (BaseX, BaseY)-(x1, y1), colr
61.     Line (x1, y1)-(x2, y2), colr
62.     Line (x1, y1)-(x3, y3), colr
63. End Sub
64.  

PS all that extra calc for Degree Angle was attempt to print nice numbers without a bunch of decimal junk, just using INT(DegreeAngle) was often 1 off of nice (advancing around circle 5 degrees at so 45, 50, 55,... was what was supposed to be showing).

You can use this method when ever you need to know the angle one point is to another.