2D Physics Engine

[justsomeguy]

Hello

I've ported a simple 2D physics engine from JAVA/C++ to QB. I was thinking about using it for a larger project I have in mind, but I thought others might find some use in it or just use it to mess around.

It's a bit slow and it only handles convex polygons and circles. In future iterations I hope to add more features and optimzations.

The orginal code was written by Randy Gaul, and he has nothing to do with this project. His website is http://RandyGaul.net and it has a lot programming resources and articles.

Code: QB64: [Select]

1. Option _Explicit
2. '/*
3. '    Copyright (c) 2013 Randy Gaul http://RandyGaul.net
4.  
5. '    This software is provided 'as-is', without any express or implied
6. '    warranty. In no event will the authors be held liable for any damages
7. '    arising from the use of this software.
8.  
9. '    Permission is granted to anyone to use this software for any purpose,
10. '    including commercial applications, and to alter it and redistribute it
11. '    freely, subject to the following restrictions:
12. '      1. The origin of this software must not be misrepresented; you must not
13. '         claim that you wrote the original software. If you use this software
14. '         in a product, an acknowledgment in the product documentation would be
15. '         appreciated but is not required.
16. '      2. Altered source versions must be plainly marked as such, and must not be
17. '         misrepresented as being the original software.
18. '      3. This notice may not be removed or altered from any source distribution.
19.  
20. '    Port to Java by Philip Diffenderfer http://magnos.org
21. '    Port to QB64 by justsomeguy
22. '*/
23. '
24.  
25. '**********************************************************************************************
26. '   Setup Types and Variables
27. '**********************************************************************************************
28. Type tVECTOR2d
29.     x As _Float
30.     y As _Float
31. End Type
32.  
33. Type tLINE2d ' Not used
34.     a As tVECTOR2d
35.     b As tVECTOR2d
36. End Type
37.  
38. Type tFACE2d ' Not used
39.     f0 As tVECTOR2d
40.     f1 As tVECTOR2d
41. End Type
42.  
43. Type tTRIANGLE ' Not used
44.     a As tVECTOR2d
45.     b As tVECTOR2d
46.     c As tVECTOR2d
47. End Type
48.  
49. Type tMATRIX2d
50.     m00 As _Float
51.     m01 As _Float
52.     m10 As _Float
53.     m11 As _Float
54. End Type
55.  
56. Type tSHAPE
57.     ty As Integer ' cSHAPE_CIRCLE = 1, cSHAPE_POLYGON = 2
58.     radius As _Float ' Only necessary for circle shapes
59.     u As tMATRIX2d ' Only neceassary for polygons
60. End Type
61.  
62. Type tPOLY 'list of vertices for all objects in simulation
63.     vert As tVECTOR2d
64.     norm As tVECTOR2d
65. End Type
66.  
67. Type tPOLYATTRIB 'keep track of polys in monlithic list of vertices
68.     start As Integer ' starting vertex of the polygon
69.     count As Integer ' number of vertices in polygon
70. End Type
71.  
72. Type tBODY
73.     position As tVECTOR2d
74.     velocity As tVECTOR2d
75.     force As tVECTOR2d
76.     angularVelocity As _Float
77.     torque As _Float
78.     orient As _Float
79.     mass As _Float
80.     invMass As _Float
81.     inertia As _Float
82.     invInertia As _Float
83.     staticFriction As _Float
84.     dynamicFriction As _Float
85.     restitution As _Float
86.     shape As tSHAPE
87.     c As Long ' color
88.     visible As Integer 'Hide a body ;)
89. End Type
90.  
91. Type tMANIFOLD
92.     A As Integer
93.     B As Integer
94.     penetration As _Float
95.     normal As tVECTOR2d
96.     contactCount As Integer
97.     e As _Float
98.     df As _Float
99.     sf As _Float
100. End Type
101.  
102. Const cSHAPE_CIRCLE = 1
103. Const cSHAPE_POLYGON = 2
104. Const cPRECISION = 100
105. Const cMAXNUMOFTRIANGLES = 100
106. Const cMAXNUMBEROFOBJECTS = 1000 ' Max number of objects at one time
107. Const cMAXNUMBEROFPOLYGONS = 10000 ' Max number of total vertices included in all objects
108. Const cPI = 3.14159
109. Const cEPSILON = 0.0001
110. Const cEPSILON_SQ = cEPSILON * cEPSILON
111. Const cBIAS_RELATIVE = 0.95
112. Const cBIAS_ABSOLUTE = 0.01
113. Const cDT = 1.0 / 60.0
114. Const cITERATIONS = 10
115. Const cPENETRATION_ALLOWANCE = 0.05
116. Const cPENETRATION_CORRECTION = 0.4 ' misspelled in original code
117.  
118. Dim Shared sGRAVITY As tVECTOR2d: Call vectorSet(sGRAVITY, 0.0, 100.0)
119. Dim Shared sRESTING As _Float: Dim o As tVECTOR2d: Call vectorMultiplyScalarND(o, sGRAVITY, cDT): sRESTING = vectorLengthSq(o) + cEPSILON
120. Dim Shared sNUMBEROFBODIES As Integer: sNUMBEROFBODIES = 80 ' 0 is included - Don't go under 10 for the current scene
121.  
122. Dim poly(cMAXNUMBEROFPOLYGONS) As tPOLY
123. Dim polyattributes(cMAXNUMBEROFPOLYGONS) As tPOLYATTRIB
124. Dim body(cMAXNUMBEROFOBJECTS) As tBODY
125.  
126.  
127. Const cSCENE_USER = 0
128. Const cSCENE_FLOOR = 1
129. Const cSCENE_SPINNEROFDEATH = 2
130. Const cSCENE_RIGHTRAMP = 3
131. Const cSCENE_LEFTRAMP = 4
132. Const cSCENE_DOZEROFDOOM = 5
133. Const cSCENE_ELEVATOROFTERROR = 6
134. Const cSCENE_RIGHTWALL = 7
135. Const cSCENE_ELEVATORKICKER = 8
136.  
137.  
138. '**********************************************************************************************
139. _Title "phyNGN"
140. Screen _NewImage(1024, 768, 32)
141. Randomize Timer
142. Call buildSimpleScene(poly(), polyattributes(), body())
143. '**********************************************************************************************
144. Do
145.     Cls , _RGB32(28, 28, 22)
146.     Call animateScene(body())
147.     Call renderBodies(poly(), polyattributes(), body())
148.     Call impulseStep(poly(), polyattributes(), body(), cDT, cITERATIONS)
149.     _Display
150.     _Limit 240
151. Loop Until _KeyHit = 27
152. System
153. '**********************************************************************************************
154. '   End of Main loop
155. '**********************************************************************************************
156.  
157. '**********************************************************************************************
158. '   Scene Creation and Handling Ahead
159. '**********************************************************************************************
160.  
161. Sub animateScene (body() As tBODY)
162.     If _MouseInput Then ' Terrible use interaction
163.         Call vectorSet(body(cSCENE_USER).velocity, _MouseMovementX * 100, _MouseMovementY * 100)
164.     End If
165.  
166.     body(cSCENE_SPINNEROFDEATH).orient = body(cSCENE_SPINNEROFDEATH).orient + (cPI / 90): If body(cSCENE_SPINNEROFDEATH).orient > 2 * cPI Then body(cSCENE_SPINNEROFDEATH).orient = 0
167.     Call matrixSetRadians(body(cSCENE_SPINNEROFDEATH).shape.u, body(cSCENE_SPINNEROFDEATH).orient)
168.     body(cSCENE_DOZEROFDOOM).position.x = body(cSCENE_DOZEROFDOOM).position.x - 1
169.     If body(cSCENE_DOZEROFDOOM).position.x < 120 Then body(cSCENE_DOZEROFDOOM).position.x = _Width
170.  
171.     body(cSCENE_ELEVATOROFTERROR).position.y = body(cSCENE_ELEVATOROFTERROR).position.y - 1
172.     If body(cSCENE_ELEVATOROFTERROR).position.y < 50 Then body(cSCENE_ELEVATOROFTERROR).position.y = _Height - 25
173. End Sub
174.  
175. Sub buildSimpleScene (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY)
176.     Dim i, ty As Integer
177.  
178.     Call createBoxBodies(p(), pa(), body(), cSCENE_USER, 10, 10)
179.     Call vectorSet(body(cSCENE_USER).position, (_Width / 2), (_Height / 2))
180.     Call vectorSet(body(cSCENE_USER).velocity, 0.0, 0.0)
181.  
182.     Call createBoxBodies(p(), pa(), body(), cSCENE_FLOOR, 1000, 5)
183.     Call vectorSet(body(cSCENE_FLOOR).position, (_Width / 2), (_Height - 20))
184.     Call bodySetStatic(body(cSCENE_FLOOR))
185.  
186.     Call createBoxBodies(p(), pa(), body(), cSCENE_SPINNEROFDEATH, 75, 5)
187.     Call vectorSet(body(cSCENE_SPINNEROFDEATH).position, (_Width / 2), (_Height - 100))
188.     Call bodySetStatic(body(cSCENE_SPINNEROFDEATH))
189.  
190.     Call createBoxBodies(p(), pa(), body(), cSCENE_RIGHTRAMP, 350, 5)
191.     Call vectorSet(body(cSCENE_RIGHTRAMP).position, (_Width * .75) + 35, (_Height / 2) + 105)
192.     body(cSCENE_RIGHTRAMP).orient = (cPI * .75)
193.     Call matrixSetRadians(body(cSCENE_RIGHTRAMP).shape.u, body(cSCENE_RIGHTRAMP).orient)
194.     Call bodySetStatic(body(cSCENE_RIGHTRAMP))
195.  
196.     Call createBoxBodies(p(), pa(), body(), cSCENE_LEFTRAMP, 225, 5)
197.     Call vectorSet(body(cSCENE_LEFTRAMP).position, (_Width * .25) + 55, (_Height / 2))
198.     body(cSCENE_LEFTRAMP).orient = (cPI * .1)
199.     Call matrixSetRadians(body(cSCENE_LEFTRAMP).shape.u, body(cSCENE_LEFTRAMP).orient)
200.     Call bodySetStatic(body(cSCENE_LEFTRAMP))
201.  
202.     Call createBoxBodies(p(), pa(), body(), cSCENE_DOZEROFDOOM, 5, 50)
203.     Call vectorSet(body(cSCENE_DOZEROFDOOM).position, 0, _Height - 75)
204.     Call bodySetStatic(body(cSCENE_DOZEROFDOOM))
205.  
206.     Call createBoxBodies(p(), pa(), body(), cSCENE_ELEVATOROFTERROR, 50, 5)
207.     Call vectorSet(body(cSCENE_ELEVATOROFTERROR).position, 55, _Height - 25)
208.     body(cSCENE_ELEVATOROFTERROR).orient = (cPI * .98)
209.     Call matrixSetRadians(body(cSCENE_ELEVATOROFTERROR).shape.u, body(cSCENE_ELEVATOROFTERROR).orient)
210.     Call bodySetStatic(body(cSCENE_ELEVATOROFTERROR))
211.  
212.     Call createBoxBodies(p(), pa(), body(), cSCENE_RIGHTWALL, 5, 375)
213.     Call vectorSet(body(cSCENE_RIGHTWALL).position, 5, _Height / 2 - 20)
214.     Call bodySetStatic(body(cSCENE_RIGHTWALL))
215.  
216.     Call createBoxBodies(p(), pa(), body(), cSCENE_ELEVATORKICKER, 100, 5)
217.     Call vectorSet(body(cSCENE_ELEVATORKICKER).position, 55, 120)
218.     body(cSCENE_ELEVATORKICKER).orient = (cPI * .70)
219.     Call matrixSetRadians(body(cSCENE_ELEVATORKICKER).shape.u, body(cSCENE_ELEVATORKICKER).orient)
220.     Call bodySetStatic(body(cSCENE_ELEVATORKICKER))
221.  
222.     For i = 9 To sNUMBEROFBODIES
223.         If Rnd > .25 Then ' Circles are must faster than polygons
224.             ty = cSHAPE_CIRCLE
225.         Else
226.             ty = cSHAPE_POLYGON
227.         End If
228.         Call createBodies(p(), pa(), body(), i, ty)
229.         Call vectorSet(body(i).position, (Rnd * _Width / 2) + (_Width / 4), ((Rnd * _Height / 2) + (_Height / 4)) - 200)
230.         Call vectorSet(body(i).velocity, Rnd * 100 - 50, Rnd * 100 - 50)
231.     Next
232.  
233. End Sub
234.  
235. Sub createCircleBody (pa() As tPOLYATTRIB, body() As tBODY, index As Integer, radius As _Float)
236.     Dim shape As tSHAPE
237.     Call shapeCreate(shape, cSHAPE_CIRCLE, radius)
238.     Call bodyCreate(body(), index, shape)
239.     Call circleInitialize(body(), index)
240.     ' Even though circles do not have Polygons, they still must be included in the Vertices
241.     If index = 0 Then
242.         pa(index).start = 0
243.     Else
244.         pa(index).start = pa(index - 1).start + pa(index - 1).count + 1
245.     End If
246.     pa(index).count = 1
247.     body(index).c = _RGB32(255, 255, 255)
248. End Sub
249.  
250. Sub createBoxBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, index As Integer, xs As _Float, ys As _Float)
251.     Dim shape As tSHAPE
252.     Call shapeCreate(shape, cSHAPE_POLYGON, 0)
253.     Call bodyCreate(body(), index, shape)
254.     Call boxCreate(p(), pa(), index, xs, ys)
255.     Call polygonInitialize(body(), p(), pa(), index)
256.     body(index).c = _RGB32(255, 255, 255)
257. End Sub
258.  
259. Sub createBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, index As Integer, ty As Integer)
260.     If ty = cSHAPE_CIRCLE Then
261.         Call createCircleBody(pa(), body(), index, 10 + Rnd * 20)
262.     Else
263.         If ty = cSHAPE_POLYGON Then
264.             Call createBoxBodies(p(), pa(), body(), index, 5 + Rnd * 10, 5 + Rnd * 10)
265.         End If
266.     End If
267.     body(index).c = _RGB32(55 + Rnd * 200, 55 + Rnd * 200, 55 + Rnd * 200)
268. End Sub
269.  
270. '**********************************************************************************************
271. '   Physics and Collision Stuff Ahead
272. '**********************************************************************************************
273.  
274. Sub impulseIntegrateForces (b As tBODY, dt As _Float)
275.     If b.invMass = 0.0 Then Exit Sub
276.     Dim dts As _Float
277.     dts = dt * .5
278.     Call vectorAddVectorScalar(b.velocity, b.force, b.invMass * dts)
279.     Call vectorAddVectorScalar(b.velocity, sGRAVITY, dts)
280.     b.angularVelocity = b.angularVelocity + (b.torque * b.invInertia * dts)
281. End Sub
282.  
283. Sub impulseIntegrateVelocity (body As tBODY, dt As _Float)
284.     If body.invMass = 0.0 Then Exit Sub
285.     Call vectorAddVectorScalar(body.position, body.velocity, dt)
286.     body.orient = body.orient + (body.angularVelocity * dt)
287.     Call matrixSetRadians(body.shape.u, body.orient)
288.     Call impulseIntegrateForces(body, dt)
289. End Sub
290.  
291. Sub impulseStep (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, dt As _Float, iterations As Integer)
292.     Dim A As tBODY
293.     Dim B As tBODY
294.     Dim c(cMAXNUMBEROFOBJECTS) As tVECTOR2d
295.     Dim m As tMANIFOLD
296.     Dim manifolds(sNUMBEROFBODIES * sNUMBEROFBODIES) As tMANIFOLD
297.     Dim collisions(sNUMBEROFBODIES * sNUMBEROFBODIES, cMAXNUMBEROFOBJECTS) As tVECTOR2d
298.     Dim manifoldCount As Integer: manifoldCount = 0
299.     '    // Generate new collision info
300.     Dim i, j, k As Integer
301.     ' TODO: Implement hidden object logic
302.     For i = 0 To sNUMBEROFBODIES ' number of bodies
303.         A = body(i)
304.         For j = i + 1 To sNUMBEROFBODIES
305.             B = body(j)
306.             If A.invMass = 0.0 And B.invMass = 0.0 Then _Continue
307.             'Mainfold solve - handle collisions
308.             If A.shape.ty = cSHAPE_CIRCLE And B.shape.ty = cSHAPE_CIRCLE Then
309.                 Call collisionCCHandle(m, c(), A, B)
310.             Else
311.                 If A.shape.ty = cSHAPE_POLYGON And B.shape.ty = cSHAPE_POLYGON Then
312.                     Call collisionPPHandle(p(), pa(), body(), m, c(), i, j)
313.                 Else
314.                     If A.shape.ty = cSHAPE_CIRCLE And B.shape.ty = cSHAPE_POLYGON Then
315.                         Call collisionCPHandle(p(), pa(), body(), m, c(), i, j)
316.                     Else
317.                         If B.shape.ty = cSHAPE_CIRCLE And A.shape.ty = cSHAPE_POLYGON Then
318.                             Call collisionPCHandle(p(), pa(), body(), m, c(), i, j)
319.                         End If
320.                     End If
321.                 End If
322.             End If
323.             If m.contactCount > 0 Then
324.                 m.A = i 'identify the index of objects
325.                 m.B = j
326.                 manifolds(manifoldCount) = m
327.                 For k = 0 To m.contactCount
328.                     collisions(manifoldCount, k) = c(k)
329.                 Next
330.                 manifoldCount = manifoldCount + 1
331.             End If
332.         Next
333.     Next
334.     '   // Integrate forces
335.     For i = 0 To sNUMBEROFBODIES
336.         Call impulseIntegrateForces(body(i), dt)
337.     Next
338.     '   // Initialize collision
339.     For i = 0 To manifoldCount - 1
340.         ' this is the stupidest thing ever since QB will not let you split arrays
341.         For k = 0 To manifolds(i).contactCount - 1
342.             c(k) = collisions(i, k)
343.         Next
344.         Call manifoldInit(manifolds(i), body(), c())
345.     Next
346.     '// Solve collisions
347.     For j = 0 To iterations - 1
348.         For i = 0 To manifoldCount - 1
349.             For k = 0 To manifolds(i).contactCount - 1
350.                 c(k) = collisions(i, k)
351.             Next
352.             Call manifoldApplyImpulse(manifolds(i), body(), c())
353.         Next i
354.     Next j
355.     '// Integrate velocities
356.     For i = 0 To sNUMBEROFBODIES
357.         Call impulseIntegrateVelocity(body(i), dt)
358.     Next
359.     '// Correct positions
360.     For i = 0 To manifoldCount - 1
361.         Call manifoldPositionalCorrection(manifolds(i), body())
362.     Next
363.     '// Clear all forces
364.     For i = 0 To sNUMBEROFBODIES
365.         Call vectorSet(body(i).force, 0, 0)
366.         body(i).torque = 0
367.     Next
368. End Sub
369.  
370. Sub bodyApplyImpulse (body As tBODY, impulse As tVECTOR2d, contactVector As tVECTOR2d)
371.     Call vectorAddVectorScalar(body.velocity, impulse, body.invMass)
372.     body.angularVelocity = body.angularVelocity + body.invInertia * vectorCross(contactVector, impulse)
373. End Sub
374.  
375. Sub bodySetStatic (body As tBODY)
376.     body.inertia = 0.0
377.     body.invInertia = 0.0
378.     body.mass = 0.0
379.     body.invMass = 0.0
380. End Sub
381.  
382. Sub manifoldInit (m As tMANIFOLD, body() As tBODY, contacts() As tVECTOR2d)
383.     Dim ra As tVECTOR2d
384.     Dim rb As tVECTOR2d
385.     Dim rv As tVECTOR2d
386.     Dim tv1 As tVECTOR2d
387.     Dim tv2 As tVECTOR2d
388.     m.e = scalarMin(body(m.A).restitution, body(m.B).restitution)
389.     m.sf = Sqr(body(m.A).staticFriction * body(m.A).staticFriction)
390.     m.df = Sqr(body(m.A).dynamicFriction * body(m.A).dynamicFriction)
391.     Dim i As Integer
392.     For i = 0 To m.contactCount - 1
393.         Call vectorSubVectorND(contacts(i), body(m.A).position, ra)
394.         Call vectorSubVectorND(contacts(i), body(m.B).position, rb)
395.  
396.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
397.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
398.         Call vectorAddVector(tv1, body(m.B).velocity)
399.         Call vectorSubVectorND(tv2, body(m.A).velocity, tv2)
400.         Call vectorSubVectorND(rv, tv1, tv2)
401.  
402.         If vectorLengthSq(rv) < sRESTING Then
403.             m.e = 0.0
404.         End If
405.     Next
406. End Sub
407.  
408. Sub manifoldApplyImpulse (m As tMANIFOLD, body() As tBODY, contacts() As tVECTOR2d)
409.     Dim ra As tVECTOR2d
410.     Dim rb As tVECTOR2d
411.     Dim rv As tVECTOR2d
412.     Dim tv1 As tVECTOR2d
413.     Dim tv2 As tVECTOR2d
414.     Dim contactVel As _Float
415.  
416.     Dim raCrossN As _Float
417.     Dim rbCrossN As _Float
418.     Dim invMassSum As _Float
419.     Dim i As Integer
420.     Dim j As _Float
421.     Dim impulse As tVECTOR2d
422.  
423.     Dim t As tVECTOR2d
424.     Dim jt As _Float
425.     Dim tangentImpulse As tVECTOR2d
426.  
427.     If impulseEqual(body(m.A).invMass + body(m.B).invMass, 0.0) Then
428.         Call manifoldInfiniteMassCorrection(body(m.A), body(m.B))
429.         Exit Sub
430.     End If
431.  
432.     For i = 0 To m.contactCount - 1
433.         '// Calculate radii from COM to contact
434.         '// Vec2 ra = contacts[i] - A->position;
435.         '// Vec2 rb = contacts[i] - B->position;
436.         Call vectorSubVectorND(ra, contacts(i), body(m.A).position)
437.         Call vectorSubVectorND(rb, contacts(i), body(m.B).position)
438.  
439.         '// Relative velocity
440.         '// Vec2 rv = B->velocity + Cross( B->angularVelocity, rb ) - A->velocity - Cross( A->angularVelocity, ra );
441.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
442.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
443.         Call vectorAddVectorND(rv, tv1, body(m.B).velocity)
444.         Call vectorSubVector(rv, body(m.A).velocity)
445.         Call vectorSubVector(rv, tv2)
446.  
447.         '// Relative velocity along the normal
448.         '// real contactVel = Dot( rv, normal );
449.         contactVel = vectorDot(rv, m.normal)
450.  
451.  
452.         '// Do not resolve if velocities are separating
453.         If contactVel > 0 Then Exit Sub
454.  
455.         '// real raCrossN = Cross( ra, normal );
456.         '// real rbCrossN = Cross( rb, normal );
457.         '// real invMassSum = A->im + B->im + Sqr( raCrossN ) * A->iI + Sqr( rbCrossN ) * B->iI;
458.         raCrossN = vectorCross(ra, m.normal)
459.         rbCrossN = vectorCross(rb, m.normal)
460.         invMassSum = body(m.A).invMass + body(m.B).invMass + (raCrossN * raCrossN) * body(m.A).invInertia + (rbCrossN * rbCrossN) * body(m.B).invInertia
461.  
462.  
463.         '// Calculate impulse scalar
464.         j = -(1.0 + m.e) * contactVel
465.         j = j / invMassSum
466.         j = j / m.contactCount
467.  
468.         '// Apply impulse
469.         Call vectorMultiplyScalarND(impulse, m.normal, j)
470.  
471.         Call vectorNegND(tv1, impulse)
472.         Call bodyApplyImpulse(body(m.A), tv1, ra)
473.         Call bodyApplyImpulse(body(m.B), impulse, rb)
474.  
475.         '// Friction impulse
476.         '// rv = B->velocity + Cross( B->angularVelocity, rb ) - A->velocity - Cross( A->angularVelocity, ra );
477.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
478.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
479.         Call vectorAddVectorND(rv, tv1, body(m.B).velocity)
480.         Call vectorSubVector(rv, body(m.A).velocity)
481.         Call vectorSubVector(rv, tv2)
482.  
483.         '// Vec2 t = rv - (normal * Dot( rv, normal ));
484.         '// t.Normalize( );
485.         Call vectorMultiplyScalarND(t, m.normal, vectorDot(rv, m.normal))
486.         Call vectorSubVectorND(t, rv, t)
487.         Call vectorNormalize(t)
488.  
489.         '// j tangent magnitude
490.         jt = -vectorDot(rv, t)
491.         jt = jt / invMassSum
492.         jt = jt / m.contactCount
493.  
494.         '// Don't apply tiny friction impulses
495.         If impulseEqual(jt, 0.0) Then Exit Sub
496.  
497.         '// Coulumb's law
498.         If Abs(jt) < j * m.sf Then
499.             Call vectorMultiplyScalarND(tangentImpulse, t, jt)
500.         Else
501.             Call vectorMultiplyScalarND(tangentImpulse, t, -j * m.df)
502.         End If
503.  
504.         '// Apply friction impulse
505.         '// A->ApplyImpulse( -tangentImpulse, ra );
506.         '// B->ApplyImpulse( tangentImpulse, rb );
507.         Call vectorNegND(tv1, tangentImpulse)
508.         Call bodyApplyImpulse(body(m.A), tv1, ra)
509.         Call bodyApplyImpulse(body(m.B), tangentImpulse, rb)
510.     Next i
511. End Sub
512.  
513. Sub manifoldPositionalCorrection (m As tMANIFOLD, body() As tBODY)
514.     Dim correction As _Float
515.     correction = scalarMax(m.penetration - cPENETRATION_ALLOWANCE, 0.0) / (body(m.A).invMass + body(m.B).invMass) * cPENETRATION_CORRECTION
516.     Call vectorAddVectorScalar(body(m.A).position, m.normal, -body(m.A).invMass * correction)
517.     Call vectorAddVectorScalar(body(m.B).position, m.normal, body(m.B).invMass * correction)
518. End Sub
519.  
520. Sub manifoldInfiniteMassCorrection (A As tBODY, B As tBODY)
521.     Call vectorSet(A.velocity, 0, 0)
522.     Call vectorSet(B.velocity, 0, 0)
523. End Sub
524.  
525. '**********************************************************************************************
526. '   Collision Stuff Ahead
527. '**********************************************************************************************
528.  
529. Sub collisionCCHandle (m As tMANIFOLD, contacts() As tVECTOR2d, A As tBODY, B As tBODY)
530.     Dim normal As tVECTOR2d
531.     Dim dist_sqr As _Float
532.     Dim radius As _Float
533.  
534.     Call vectorSubVectorND(normal, B.position, A.position)
535.     dist_sqr = vectorLengthSq(normal)
536.     radius = A.shape.radius + B.shape.radius
537.  
538.     If (dist_sqr >= radius * radius) Then
539.         m.contactCount = 0
540.     Else
541.         Dim distance As _Float
542.         distance = Sqr(dist_sqr)
543.         m.contactCount = 1
544.  
545.         If distance = 0 Then
546.             m.penetration = A.shape.radius
547.             Call vectorSet(m.normal, 1.0, 0.0)
548.             Call vectorSetVector(contacts(0), A.position)
549.         Else
550.             m.penetration = radius - distance
551.             Call vectorDivideScalarND(m.normal, normal, distance)
552.  
553.             Call vectorMultiplyScalarND(contacts(0), m.normal, A.shape.radius)
554.             Call vectorAddVector(contacts(0), A.position)
555.         End If
556.     End If
557. End Sub
558.  
559. Sub collisionPCHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
560.     Call collisionCPHandle(p(), pa(), body(), m, contacts(), B, A)
561.     If m.contactCount > 0 Then
562.         Call vectorNeg(m.normal)
563.     End If
564. End Sub
565.  
566. Sub collisionCPHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
567.     'A is the Circle
568.     'B is the POLY
569.     m.contactCount = 0
570.     Dim center As tVECTOR2d
571.     Dim tm As tMATRIX2d
572.     Dim tv As tVECTOR2d
573.     Dim ARadius As _Float: ARadius = body(A).shape.radius
574.  
575.  
576.     Call vectorSubVectorND(center, body(A).position, body(B).position)
577.     Call matrixTranspose(body(B).shape.u, tm)
578.     Call matrixMultiplyVector(tm, center, center)
579.  
580.     Dim separation As _Float: separation = -9999999
581.     Dim faceNormal As Integer: faceNormal = 0
582.     Dim i As Integer
583.     Dim s As _Float
584.     For i = 0 To pa(B).count
585.         Call vectorSubVectorND(tv, center, p(pa(B).start + i).vert)
586.         s = vectorDot(p(pa(B).start + i).norm, tv)
587.         If s > ARadius Then Exit Sub
588.         If s > separation Then
589.             separation = s
590.             faceNormal = i
591.         End If
592.     Next
593.     Dim v1 As tVECTOR2d
594.     v1 = p(pa(B).start + faceNormal).vert
595.     Dim i2 As Integer
596.     i2 = pa(B).start + arrayNextIndex(faceNormal, pa(B).count)
597.     Dim v2 As tVECTOR2d
598.     v2 = p(i2).vert
599.  
600.     If separation < cEPSILON Then
601.         m.contactCount = 1
602.         Call matrixMultiplyVector(body(B).shape.u, p(pa(B).start + faceNormal).norm, m.normal)
603.         Call vectorNeg(m.normal)
604.         Call vectorMultiplyScalarND(contacts(0), m.normal, ARadius)
605.         Call vectorAddVector(contacts(0), body(A).position)
606.         m.penetration = ARadius
607.         Exit Sub
608.     End If
609.  
610.     Dim dot1 As _Float
611.     Dim dot2 As _Float
612.  
613.     Dim tv1 As tVECTOR2d
614.     Dim tv2 As tVECTOR2d
615.     Dim n As tVECTOR2d
616.     Call vectorSubVectorND(tv1, center, v1)
617.     Call vectorSubVectorND(tv2, v2, v1)
618.     dot1 = vectorDot(tv1, tv2)
619.     Call vectorSubVectorND(tv1, center, v2)
620.     Call vectorSubVectorND(tv2, v1, v2)
621.     dot2 = vectorDot(tv1, tv2)
622.     m.penetration = ARadius - separation
623.     If dot1 <= 0.0 Then
624.         If vectorSqDist(center, v1) > ARadius * ARadius Then Exit Sub
625.         m.contactCount = 1
626.         Call vectorSubVectorND(n, v1, center)
627.         Call matrixMultiplyVector(body(B).shape.u, n, n)
628.         Call vectorNormalize(n)
629.         m.normal = n
630.         Call matrixMultiplyVector(body(B).shape.u, v1, v1)
631.         Call vectorAddVectorND(v1, v1, body(B).position)
632.         contacts(0) = v1
633.     Else
634.         If dot2 <= 0.0 Then
635.             If vectorSqDist(center, v2) > ARadius * ARadius Then Exit Sub
636.             m.contactCount = 1
637.             Call vectorSubVectorND(n, v2, center)
638.             Call matrixMultiplyVector(body(B).shape.u, v2, v2)
639.             Call vectorAddVectorND(v2, v2, body(B).position)
640.             contacts(0) = v2
641.             Call matrixMultiplyVector(body(B).shape.u, n, n)
642.             Call vectorNormalize(n)
643.             m.normal = n
644.         Else
645.             n = p(pa(B).start + faceNormal).norm
646.             Call vectorSubVectorND(tv1, center, v1)
647.             If vectorDot(tv1, n) > ARadius Then Exit Sub
648.             m.contactCount = 1
649.             Call matrixMultiplyVector(body(B).shape.u, n, n)
650.             Call vectorNeg(n)
651.             m.normal = n
652.             Call vectorMultiplyScalarND(contacts(0), m.normal, ARadius)
653.             Call vectorAddVector(contacts(0), body(A).position)
654.  
655.         End If
656.     End If
657. End Sub
658.  
659. Function collisionPPClip (n As tVECTOR2d, c As _Float, face() As tVECTOR2d)
660.     Dim sp As Integer: sp = 0
661.     Dim o(cMAXNUMBEROFPOLYGONS) As tVECTOR2d
662.  
663.     o(0) = face(0)
664.     o(1) = face(1)
665.  
666.     Dim d1 As _Float: d1 = vectorDot(n, face(0)) - c
667.     Dim d2 As _Float: d2 = vectorDot(n, face(1)) - c
668.  
669.     If d1 <= 0.0 Then
670.         o(sp) = face(0)
671.         sp = sp + 1
672.     End If
673.  
674.     If d2 <= 0.0 Then
675.         o(sp) = face(1)
676.         sp = sp + 1
677.     End If
678.  
679.     If d1 * d2 < 0.0 Then
680.         Dim alpha As _Float: alpha = d1 / (d1 - d2)
681.         Dim tempv As tVECTOR2d
682.         'out[sp] = face[0] + alpha * (face[1] - face[0]);
683.         Call vectorSubVectorND(tempv, face(1), face(0))
684.         Call vectorMultiplyScalar(tempv, alpha)
685.         Call vectorAddVectorND(o(sp), tempv, face(0))
686.         sp = sp + 1
687.     End If
688.     face(0) = o(0)
689.     face(1) = o(1)
690.     collisionPPClip = sp
691. End Function
692.  
693. Sub collisionPPFindIncidentFace (p() As tPOLY, pa() As tPOLYATTRIB, b() As tBODY, v() As tVECTOR2d, RefPoly As Integer, IncPoly As Integer, referenceIndex As Integer)
694.     Dim referenceNormal As tVECTOR2d
695.     Dim uRef As tMATRIX2d: uRef = b(RefPoly).shape.u
696.     Dim uInc As tMATRIX2d: uInc = b(IncPoly).shape.u
697.     Dim uTemp As tMATRIX2d
698.     Dim i As Integer
699.     referenceNormal = p(pa(RefPoly).start + referenceIndex).norm
700.  
701.     '        // Calculate normal in incident's frame of reference
702.     '        // referenceNormal = RefPoly->u * referenceNormal; // To world space
703.     Call matrixMultiplyVector(uRef, referenceNormal, referenceNormal)
704.     '        // referenceNormal = IncPoly->u.Transpose( ) * referenceNormal; // To incident's model space
705.     Call matrixTranspose(uInc, uTemp)
706.     Call matrixMultiplyVector(uTemp, referenceNormal, referenceNormal)
707.  
708.     Dim incidentFace As Integer: incidentFace = 0
709.     Dim minDot As _Float: minDot = 9999999
710.     Dim dot As _Float
711.     For i = 0 To pa(IncPoly).count
712.         dot = vectorDot(referenceNormal, p(pa(IncPoly).start + i).norm)
713.         If (dot < minDot) Then
714.             minDot = dot
715.             incidentFace = i
716.         End If
717.     Next
718.  
719.     '// Assign face vertices for incidentFace
720.     '// v[0] = IncPoly->u * IncPoly->m_vertices[incidentFace] + IncPoly->body->position;
721.     Call matrixMultiplyVector(uInc, p(pa(IncPoly).start + incidentFace).vert, v(0))
722.     Call vectorAddVector(v(0), b(IncPoly).position)
723.  
724.     '// incidentFace = incidentFace + 1 >= (int32)IncPoly->m_vertexCount ? 0 : incidentFace + 1;
725.     incidentFace = arrayNextIndex(incidentFace, pa(IncPoly).count)
726.  
727.     '// v[1] = IncPoly->u * IncPoly->m_vertices[incidentFace] +  IncPoly->body->position;
728.     Call matrixMultiplyVector(uInc, p(pa(IncPoly).start + incidentFace).vert, v(1))
729.     Call vectorAddVector(v(1), b(IncPoly).position)
730. End Sub
731.  
732. Sub collisionPPHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
733.     m.contactCount = 0
734.  
735.     Dim faceA(100) As Integer
736.  
737.     Dim penetrationA As _Float
738.     penetrationA = collisionPPFindAxisLeastPenetration(p(), pa(), body(), faceA(), A, B)
739.     If penetrationA >= 0.0 Then Exit Sub
740.  
741.     Dim faceB(100) As Integer
742.  
743.     Dim penetrationB As _Float
744.     penetrationB = collisionPPFindAxisLeastPenetration(p(), pa(), body(), faceB(), B, A)
745.     If penetrationB >= 0.0 Then Exit Sub
746.  
747.  
748.     Dim referenceIndex As Integer
749.     Dim flip As Integer
750.  
751.     Dim RefPoly As Integer
752.     Dim IncPoly As Integer
753.  
754.     If impulseGT(penetrationA, penetrationB) Then
755.         RefPoly = A
756.         IncPoly = B
757.         referenceIndex = faceA(0)
758.         flip = 0
759.     Else
760.         RefPoly = B
761.         IncPoly = A
762.         referenceIndex = faceB(0)
763.         flip = 1
764.     End If
765.  
766.     Dim incidentFace(2) As tVECTOR2d
767.  
768.     Call collisionPPFindIncidentFace(p(), pa(), body(), incidentFace(), RefPoly, IncPoly, referenceIndex)
769.     Dim v1 As tVECTOR2d
770.     Dim v2 As tVECTOR2d
771.     Dim v1t As tVECTOR2d
772.     Dim v2t As tVECTOR2d
773.  
774.  
775.     v1 = p(pa(RefPoly).start + referenceIndex).vert
776.     referenceIndex = arrayNextIndex(referenceIndex, pa(RefPoly).count)
777.     v2 = p(pa(RefPoly).start + referenceIndex).vert
778.     '// Transform vertices to world space
779.     '// v1 = RefPoly->u * v1 + RefPoly->body->position;
780.     '// v2 = RefPoly->u * v2 + RefPoly->body->position;
781.     Call matrixMultiplyVector(body(RefPoly).shape.u, v1, v1t)
782.     Call vectorAddVectorND(v1, v1t, body(RefPoly).position)
783.     Call matrixMultiplyVector(body(RefPoly).shape.u, v2, v2t)
784.     Call vectorAddVectorND(v2, v2t, body(RefPoly).position)
785.     ' Circle (v1.x, v1.y), 5, _RGB32(255, 255, 0)
786.     'Circle (v2.x, v2.y), 5, _RGB32(255, 255, 0)
787.  
788.     '// Calculate reference face side normal in world space
789.     '// Vec2 sidePlaneNormal = (v2 - v1);
790.     '// sidePlaneNormal.Normalize( );
791.     Dim sidePlaneNormal As tVECTOR2d
792.     Call vectorSubVectorND(sidePlaneNormal, v2, v1)
793.     Call vectorNormalize(sidePlaneNormal)
794.  
795.     '// Orthogonalize
796.     '// Vec2 refFaceNormal( sidePlaneNormal.y, -sidePlaneNormal.x );
797.     Dim refFaceNormal As tVECTOR2d
798.     Call vectorSet(refFaceNormal, sidePlaneNormal.y, -sidePlaneNormal.x)
799.  
800.     '// ax + by = c
801.     '// c is distance from origin
802.     '// real refC = Dot( refFaceNormal, v1 );
803.     '// real negSide = -Dot( sidePlaneNormal, v1 );
804.     '// real posSide = Dot( sidePlaneNormal, v2 );
805.     Dim refC As _Float: refC = vectorDot(refFaceNormal, v1)
806.     Dim negSide As _Float: negSide = -vectorDot(sidePlaneNormal, v1)
807.     Dim posSide As _Float: posSide = vectorDot(sidePlaneNormal, v2)
808.  
809.  
810.     '// Clip incident face to reference face side planes
811.     '// if(Clip( -sidePlaneNormal, negSide, incidentFace ) < 2)
812.     Dim negSidePlaneNormal As tVECTOR2d
813.     Call vectorNegND(negSidePlaneNormal, sidePlaneNormal)
814.  
815.  
816.     If collisionPPClip(negSidePlaneNormal, negSide, incidentFace()) < 2 Then Exit Sub
817.  
818.     If collisionPPClip(sidePlaneNormal, posSide, incidentFace()) < 2 Then Exit Sub
819.  
820.     Call vectorSet(m.normal, refFaceNormal.x, refFaceNormal.y)
821.     If flip Then Call vectorNeg(m.normal)
822.  
823.     '// Keep points behind reference face
824.     Dim cp As Integer: cp = 0 '// clipped points behind reference face
825.     Dim separation As _Float
826.     separation = vectorDot(refFaceNormal, incidentFace(0)) - refC
827.     If separation <= 0.0 Then
828.         contacts(cp) = incidentFace(0)
829.         m.penetration = -separation
830.         cp = cp + 1
831.     Else
832.         m.penetration = 0
833.     End If
834.  
835.     separation = vectorDot(refFaceNormal, incidentFace(1)) - refC
836.     If separation <= 0.0 Then
837.         contacts(cp) = incidentFace(1)
838.         m.penetration = m.penetration + -separation
839.         cp = cp + 1
840.         m.penetration = m.penetration / cp
841.     End If
842.     m.contactCount = cp
843. End Sub
844.  
845. Function collisionPPFindAxisLeastPenetration (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, faceIndex() As Integer, A As Integer, B As Integer)
846.     Dim bestDistance As _Float: bestDistance = -9999999
847.     Dim bestIndex As Integer: bestIndex = 0
848.  
849.     Dim n As tVECTOR2d
850.     Dim nw As tVECTOR2d
851.     Dim buT As tMATRIX2d
852.     Dim s As tVECTOR2d
853.     Dim nn As tVECTOR2d
854.     Dim v As tVECTOR2d
855.     Dim tv As tVECTOR2d
856.     Dim d As _Float
857.     Dim i, k As Integer
858.  
859.     For i = 0 To pa(A).count
860.         k = pa(A).start + i
861.  
862.         '// Retrieve a face normal from A
863.         '// Vec2 n = A->m_normals[i];
864.         '// Vec2 nw = A->u * n;
865.         n = p(k).norm
866.         Call matrixMultiplyVector(body(A).shape.u, n, nw)
867.  
868.  
869.         '// Transform face normal into B's model space
870.         '// Mat2 buT = B->u.Transpose( );
871.         '// n = buT * nw;
872.         Call matrixTranspose(body(B).shape.u, buT)
873.         Call matrixMultiplyVector(buT, nw, n)
874.  
875.         '// Retrieve support point from B along -n
876.         '// Vec2 s = B->GetSupport( -n );
877.         Call vectorNegND(nn, n)
878.         Call vectorGetSupport(p(), pa(), B, nn, s)
879.  
880.         '// Retrieve vertex on face from A, transform into
881.         '// B's model space
882.         '// Vec2 v = A->m_vertices[i];
883.         '// v = A->u * v + A->body->position;
884.         '// v -= B->body->position;
885.         '// v = buT * v;
886.  
887.         v = p(k).vert
888.         Call matrixMultiplyVector(body(A).shape.u, v, tv)
889.         Call vectorAddVectorND(v, tv, body(A).position)
890.  
891.         Call vectorSubVector(v, body(B).position)
892.         Call matrixMultiplyVector(buT, v, tv)
893.  
894.         Call vectorSubVector(s, tv)
895.         d = vectorDot(n, s)
896.  
897.         If d > bestDistance Then
898.             bestDistance = d
899.             bestIndex = i
900.         End If
901.  
902.     Next i
903.  
904.     faceIndex(0) = bestIndex
905.  
906.     collisionPPFindAxisLeastPenetration = bestDistance
907. End Function
908.  
909. '**********************************************************************************************
910. '   Shape Creation Ahead
911. '**********************************************************************************************
912.  
913. Sub shapeCreate (sh As tSHAPE, ty As Integer, radius As _Float)
914.     Dim u As tMATRIX2d
915.     Call matrixSetScalar(u, 1, 0, 0, 1)
916.     sh.ty = ty
917.     sh.radius = radius
918.     sh.u = u
919. End Sub
920.  
921. Sub bodyCreate (body() As tBODY, index As Integer, shape As tSHAPE)
922.     Call vectorSet(body(index).position, 0, 0)
923.     Call vectorSet(body(index).velocity, 0, 0)
924.     body(index).angularVelocity = 0.0
925.     body(index).torque = 0.0
926.     body(index).orient = impulseRandom_float(-cPI, cPI)
927.  
928.     Call vectorSet(body(index).force, 0, 0)
929.     body(index).staticFriction = 0.5
930.     body(index).dynamicFriction = 0.3
931.     body(index).restitution = 0.2
932.     body(index).shape = shape
933. End Sub
934.  
935. Sub boxCreate (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, sizex As _Float, sizey As _Float)
936.     Dim vertlength As Integer: vertlength = 3
937.     Dim verts(vertlength) As tVECTOR2d
938.  
939.     Call vectorSet(verts(0), -sizex, -sizey)
940.     Call vectorSet(verts(1), sizex, -sizey)
941.     Call vectorSet(verts(2), sizex, sizey)
942.     Call vectorSet(verts(3), -sizex, sizey)
943.  
944.     Call vertexSet(p(), pa(), index, verts(), vertlength)
945. End Sub
946.  
947. Sub vShapeCreate (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, sizex As _Float, sizey As _Float)
948.     Dim vertlength As Integer: vertlength = 7
949.     Dim verts(vertlength) As tVECTOR2d
950.  
951.     Call vectorSet(verts(0), -sizex, -sizey)
952.     Call vectorSet(verts(1), sizex, -sizey)
953.     Call vectorSet(verts(2), sizex, sizey)
954.     Call vectorSet(verts(3), -sizex, sizey)
955.     Call vectorSet(verts(4), -sizex, sizey / 2)
956.     Call vectorSet(verts(5), sizex / 2, sizey / 2)
957.     Call vectorSet(verts(6), sizex / 2, -sizey / 2)
958.     Call vectorSet(verts(7), -sizex, sizey / 2)
959.  
960.     Call vertexSet(p(), pa(), index, verts(), vertlength)
961. End Sub
962.  
963. Sub vertexSet (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, verts() As tVECTOR2d, vertLength As Integer)
964.     Dim rightMost As Integer: rightMost = 0
965.     Dim highestXCoord As _Float: highestXCoord = verts(0).x
966.     Dim i As Integer
967.     Dim x As _Float
968.     For i = 1 To vertLength
969.         x = verts(i).x
970.         If x > highestXCoord Then
971.             highestXCoord = x
972.             rightMost = i
973.         Else
974.             If x = highestXCoord Then
975.                 If verts(i).y < verts(rightMost).y Then
976.                     rightMost = i
977.                 End If
978.             End If
979.         End If
980.     Next
981.     Dim hull(cMAXNUMBEROFPOLYGONS) As Integer
982.     Dim outCount As Integer: outCount = 0
983.     Dim indexHull As Integer: indexHull = rightMost
984.     Dim nextHullIndex As Integer
985.     Dim e1 As tVECTOR2d
986.     Dim e2 As tVECTOR2d
987.     Dim c As _Float
988.     Do
989.         hull(outCount) = indexHull
990.         nextHullIndex = 0
991.         For i = 1 To vertLength
992.             If nextHullIndex = indexHull Then
993.                 nextHullIndex = i
994.                 _Continue
995.             End If
996.             Call vectorSubVectorND(e1, verts(nextHullIndex), verts(hull(outCount)))
997.             Call vectorSubVectorND(e2, verts(i), verts(hull(outCount)))
998.             c = vectorCross(e1, e2)
999.             If c < 0.0 Then nextHullIndex = i
1000.             If c = 0.0 And (vectorLengthSq(e2) > vectorLengthSq(e1)) Then
1001.                 nextHullIndex = i
1002.             End If
1003.         Next
1004.         outCount = outCount + 1
1005.         indexHull = nextHullIndex
1006.         If nextHullIndex = rightMost Then
1007.             pa(index).count = outCount - 1
1008.             Exit Do
1009.         End If
1010.     Loop
1011.  
1012.     If index = 0 Then
1013.         pa(index).start = 0
1014.     Else
1015.         pa(index).start = pa(index - 1).start + pa(index - 1).count + 1
1016.     End If
1017.  
1018.     For i = 0 To vertLength
1019.         p(pa(index).start + i).vert = verts(hull(i))
1020.     Next
1021.     Dim face As tVECTOR2d
1022.     For i = 0 To vertLength
1023.         Call vectorSubVectorND(face, p(pa(index).start + arrayNextIndex(i, pa(index).count)).vert, p(pa(index).start + i).vert)
1024.         Call vectorSet(p(pa(index).start + i).norm, face.y, -face.x)
1025.         Call vectorNormalize(p(pa(index).start + i).norm)
1026.     Next
1027. End Sub
1028.  
1029. Function arrayNextIndex (i As Integer, count As Integer)
1030.     arrayNextIndex = ((i + 1) Mod (count + 1))
1031. End Function
1032.  
1033. Sub renderBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY)
1034.     Dim i As Integer
1035.     For i = 0 To sNUMBEROFBODIES
1036.         'TODO: Put hidden object logic
1037.         If body(i).shape.ty = cSHAPE_CIRCLE Then
1038.             Call renderCircle(body(), i)
1039.         Else If body(i).shape.ty = cSHAPE_POLYGON Then
1040.                 Call renderPoly(p(), pa(), body(), i)
1041.             End If
1042.         End If
1043.     Next
1044. End Sub
1045.  
1046. Sub renderPoly (p() As tPOLY, pa() As tPOLYATTRIB, b() As tBODY, index As Integer)
1047.     Dim a As tVECTOR2d ' dummy vertices
1048.     Dim b As tVECTOR2d
1049.  
1050.     Dim i, element, element_next As Integer
1051.     For i = 0 To pa(index).count
1052.         element = pa(index).start + i
1053.         element_next = pa(index).start + arrayNextIndex(i, pa(index).count) ' wrap around back to first element
1054.         a = p(element).vert
1055.         b = p(element_next).vert
1056.  
1057.         Call matrixMultiplyVector(b(index).shape.u, a, a)
1058.         Call matrixMultiplyVector(b(index).shape.u, b, b)
1059.         Call vectorAddVector(a, b(index).position)
1060.         Call vectorAddVector(b, b(index).position)
1061.  
1062.         Line (a.x, a.y)-(b.x, b.y), b(index).c
1063.     Next
1064.     If b(index).position.x < 0 Then b(index).position.x = _Width
1065.     If b(index).position.x > _Width Then b(index).position.x = 0
1066.     ' If b(index).position.y < 0 Then b(index).position.y = _Height
1067.     If b(index).position.y > _Height Then b(index).position.y = 0
1068. End Sub
1069.  
1070. Sub renderCircle (b() As tBODY, index As Integer)
1071.     Circle (b(index).position.x, b(index).position.y), b(index).shape.radius, b(index).c
1072.     Line (b(index).position.x, b(index).position.y)-(b(index).position.x + Cos(b(index).orient) * b(index).shape.radius, b(index).position.y + Sin(b(index).orient) * b(index).shape.radius), b(index).c
1073.     If b(index).position.x < 0 Then b(index).position.x = _Width
1074.     If b(index).position.x > _Width Then b(index).position.x = 0
1075.     ' If b(index).position.y < 0 Then b(index).position.y = _Height
1076.     If b(index).position.y > _Height Then b(index).position.y = 0
1077. End Sub
1078.  
1079. Sub polygonSetOrient (b As tBODY, radians As _Float)
1080.     Call matrixSetRadians(b.shape.u, radians)
1081. End Sub
1082.  
1083. '**********************************************************************************************
1084. '   Object initialization Ahead
1085. '**********************************************************************************************
1086.  
1087. Sub circleInitialize (b() As tBODY, index As Integer)
1088.     Call circleComputeMass(b(), index, 1.0)
1089. End Sub
1090.  
1091. Sub circleComputeMass (b() As tBODY, index As Integer, density As _Float)
1092.     b(index).mass = cPI * b(index).shape.radius * b(index).shape.radius * density
1093.     If b(index).mass <> 0 Then
1094.         b(index).invMass = 1.0 / b(index).mass
1095.     Else
1096.         b(index).invMass = 0.0
1097.     End If
1098.  
1099.     b(index).inertia = b(index).mass * b(index).shape.radius * b(index).shape.radius
1100.  
1101.     If b(index).inertia <> 0 Then
1102.         b(index).invInertia = 1.0 / b(index).inertia
1103.     Else
1104.         b(index).invInertia = 0.0
1105.     End If
1106. End Sub
1107.  
1108. Sub polygonInitialize (body() As tBODY, p() As tPOLY, pa() As tPOLYATTRIB, index As Integer)
1109.     Call polygonComputeMass(body(), p(), pa(), index, 1.0)
1110. End Sub
1111.  
1112. Sub polygonComputeMass (b() As tBODY, p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, density As _Float)
1113.     Dim c As tVECTOR2d ' centroid
1114.     Dim p1 As tVECTOR2d
1115.     Dim p2 As tVECTOR2d
1116.     Dim area As _Float
1117.     Dim I As _Float
1118.     Dim k_inv3 As _Float
1119.     Dim D As _Float
1120.     Dim triangleArea As _Float
1121.     Dim weight As _Float
1122.     Dim intx2 As _Float
1123.     Dim inty2 As _Float
1124.     Dim ii As Integer
1125.  
1126.     k_inv3 = 1.0 / 3.0
1127.  
1128.     For ii = 0 To pa(index).count
1129.         p1 = p(pa(index).start + ii).vert
1130.         p2 = p(pa(index).start + arrayNextIndex(ii, pa(index).count)).vert
1131.         D = vectorCross(p1, p2)
1132.         triangleArea = .5 * D
1133.         area = area + triangleArea
1134.         weight = triangleArea * k_inv3
1135.         Call vectorAddVectorScalar(c, p1, weight)
1136.         Call vectorAddVectorScalar(c, p2, weight)
1137.         intx2 = p1.x * p1.x + p2.x * p1.x + p2.x * p2.x
1138.         inty2 = p1.y * p1.y + p2.y * p1.y + p2.y * p2.y
1139.         I = I + (0.25 * k_inv3 * D) * (intx2 + inty2)
1140.     Next ii
1141.  
1142.     Call vectorMultiplyScalar(c, 1.0 / area)
1143.  
1144.     For ii = 0 To pa(index).count
1145.         Call vectorSubVector(p(pa(index).start + ii).vert, c)
1146.     Next
1147.  
1148.     b(index).mass = density * area
1149.     If b(index).mass <> 0.0 Then
1150.         b(index).invMass = 1.0 / b(index).mass
1151.     Else
1152.         b(index).invMass = 0.0
1153.     End If
1154.  
1155.     b(index).inertia = I * density
1156.     If b(index).inertia <> 0 Then
1157.         b(index).invInertia = 1.0 / b(index).inertia
1158.     Else
1159.         b(index).invInertia = 0.0
1160.     End If
1161. End Sub
1162.  
1163. '**********************************************************************************************
1164. '   Vector Math Ahead
1165. '**********************************************************************************************
1166.  
1167. Sub vectorSet (v As tVECTOR2d, x As _Float, y As _Float)
1168.     v.x = x
1169.     v.y = y
1170. End Sub
1171.  
1172. Sub vectorSetVector (o As tVECTOR2d, v As tVECTOR2d)
1173.     o.x = v.x
1174.     o.y = v.y
1175. End Sub
1176.  
1177. Sub vectorNeg (v As tVECTOR2d)
1178.     v.x = -v.x
1179.     v.y = -v.y
1180. End Sub
1181.  
1182. Sub vectorNegND (o As tVECTOR2d, v As tVECTOR2d)
1183.     o.x = -v.x
1184.     o.y = -v.y
1185. End Sub
1186.  
1187. Sub vectorMultiplyScalar (v As tVECTOR2d, s As _Float)
1188.     v.x = v.x * s
1189.     v.y = v.y * s
1190. End Sub
1191.  
1192. Sub vectorMultiplyScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1193.     o.x = v.x * s
1194.     o.y = v.y * s
1195. End Sub
1196.  
1197. Sub vectorDivideScalar (v As tVECTOR2d, s As _Float)
1198.     v.x = v.x / s
1199.     v.y = v.y / s
1200. End Sub
1201.  
1202. Sub vectorDivideScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1203.     o.x = v.x / s
1204.     o.y = v.y / s
1205. End Sub
1206.  
1207. Sub vectorAddScalar (v As tVECTOR2d, s As _Float)
1208.     v.x = v.x + s
1209.     v.y = v.y + s
1210. End Sub
1211.  
1212. Sub vectorAddScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1213.     o.x = v.x + s
1214.     o.y = v.y + s
1215. End Sub
1216.  
1217. Sub vectorMultiplyVector (v As tVECTOR2d, m As tVECTOR2d)
1218.     v.x = v.x * m.x
1219.     v.y = v.y * m.y
1220. End Sub
1221.  
1222. Sub vectorMultiplyVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1223.     o.x = v.x * m.x
1224.     o.y = v.y * m.y
1225. End Sub
1226.  
1227. Sub vectorDivideVector (v As tVECTOR2d, m As tVECTOR2d)
1228.     v.x = v.x / m.x
1229.     v.y = v.y / m.y
1230. End Sub
1231.  
1232. Sub vectorAddVector (v As tVECTOR2d, m As tVECTOR2d)
1233.     v.x = v.x + m.x
1234.     v.y = v.y + m.y
1235. End Sub
1236.  
1237. Sub vectorAddVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1238.     o.x = v.x + m.x
1239.     o.y = v.y + m.y
1240. End Sub
1241.  
1242. Sub vectorAddVectorScalar (v As tVECTOR2d, m As tVECTOR2d, s As _Float)
1243.     v.x = v.x + m.x * s
1244.     v.y = v.y + m.y * s
1245. End Sub
1246.  
1247. Sub vectorAddVectorScalarND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d, s As _Float)
1248.     o.x = v.x + m.x * s
1249.     o.y = v.y + m.y * s
1250. End Sub
1251.  
1252. Sub vectorSubVector (v As tVECTOR2d, m As tVECTOR2d)
1253.     v.x = v.x - m.x
1254.     v.y = v.y - m.y
1255. End Sub
1256.  
1257. Sub vectorSubVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1258.     o.x = v.x - m.x
1259.     o.y = v.y - m.y
1260. End Sub
1261.  
1262. Function vectorLengthSq (v As tVECTOR2d)
1263.     vectorLengthSq = v.x * v.x + v.y * v.y
1264. End Function
1265.  
1266. Function vectorLength (v As tVECTOR2d)
1267.     vectorLength = Sqr(vectorLengthSq(v))
1268. End Function
1269.  
1270. Sub vectorRotate (v As tVECTOR2d, radians As _Float)
1271.     Dim c, s, xp, yp As _Float
1272.     c = Cos(radians)
1273.     s = Sin(radians)
1274.     xp = v.x * c - v.y * s
1275.     yp = v.x * s + v.y * c
1276.     v.x = xp
1277.     v.y = yp
1278. End Sub
1279.  
1280. Sub vectorNormalize (v As tVECTOR2d)
1281.     Dim lenSQ, invLen As _Float
1282.     lenSQ = vectorLengthSq(v)
1283.     If lenSQ > cEPSILON_SQ Then
1284.         invLen = 1.0 / Sqr(lenSQ)
1285.         v.x = v.x * invLen
1286.         v.y = v.y * invLen
1287.     End If
1288. End Sub
1289.  
1290. Sub vectorMin (a As tVECTOR2d, b As tVECTOR2d, o As tVECTOR2d)
1291.     o.x = scalarMin(a.x, b.x)
1292.     o.y = scalarMin(a.y, b.y)
1293. End Sub
1294.  
1295. Sub vectorMax (a As tVECTOR2d, b As tVECTOR2d, o As tVECTOR2d)
1296.     o.x = scalarMax(a.x, b.x)
1297.     o.y = scalarMax(a.y, b.y)
1298. End Sub
1299.  
1300. Function vectorDot (a As tVECTOR2d, b As tVECTOR2d)
1301.     vectorDot = a.x * b.x + a.y * b.y
1302. End Function
1303.  
1304. Function vectorSqDist (a As tVECTOR2d, b As tVECTOR2d)
1305.     Dim dx, dy As _Float
1306.     dx = b.x - a.x
1307.     dy = b.y - a.y
1308.     vectorSqDist = dx * dx + dy * dy
1309. End Function
1310.  
1311. Function vectorDistance (a As tVECTOR2d, b As tVECTOR2d)
1312.     vectorDistance = Sqr(vectorSqDist(a, b))
1313. End Function
1314.  
1315. Function vectorCross (a As tVECTOR2d, b As tVECTOR2d)
1316.     vectorCross = a.x * b.y - a.y * b.x
1317. End Function
1318.  
1319. Sub vectorCrossScalar (o As tVECTOR2d, v As tVECTOR2d, a As _Float)
1320.     o.x = v.y * -a
1321.     o.y = v.x * a
1322. End Sub
1323.  
1324. Function vectorArea (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1325.     vectorArea = (((b.x - a.x) * (c.y - a.y)) - ((c.x - a.x) * (b.y - a.y)))
1326. End Function
1327.  
1328. Function vectorLeft (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1329.     vectorLeft = vectorArea(a, b, c) > 0
1330. End Function
1331.  
1332. Function vectorLeftOn (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1333.     vectorLeftOn = vectorArea(a, b, c) >= 0
1334. End Function
1335.  
1336. Function vectorRight (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1337.     vectorRight = vectorArea(a, b, c) < 0
1338. End Function
1339.  
1340. Function vectorRightOn (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1341.     vectorRightOn = vectorArea(a, b, c) <= 0
1342. End Function
1343.  
1344. Function vectorCollinear (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d, thresholdAngle As _Float)
1345.     If (thresholdAngle = 0) Then
1346.         vectorCollinear = (vectorArea(a, b, c) = 0)
1347.     Else
1348.         Dim ab As tVECTOR2d
1349.         Dim bc As tVECTOR2d
1350.         Dim dot As _Float
1351.         Dim magA As _Float
1352.         Dim magB As _Float
1353.         Dim angle As _Float
1354.  
1355.         ab.x = b.x - a.x
1356.         ab.y = b.y - a.y
1357.         bc.x = c.x - b.x
1358.         bc.y = c.y - b.y
1359.  
1360.         dot = ab.x * bc.x + ab.y * bc.y
1361.         magA = Sqr(ab.x * ab.x + ab.y * ab.y)
1362.         magB = Sqr(bc.x * bc.x + bc.y * bc.y)
1363.         angle = _Acos(dot / (magA * magB))
1364.         vectorCollinear = angle < thresholdAngle
1365.     End If
1366. End Function
1367.  
1368. Sub vectorGetSupport (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, dir As tVECTOR2d, bestVertex As tVECTOR2d)
1369.     Dim bestProjection As _Float
1370.     Dim v As tVECTOR2d
1371.     Dim projection As _Float
1372.     Dim i As Integer
1373.     bestVertex.x = -9999999
1374.     bestVertex.y = -9999999
1375.     bestProjection = -9999999
1376.  
1377.     For i = 0 To pa(index).count
1378.         v = p(i + pa(index).start).vert
1379.         projection = vectorDot(v, dir)
1380.         If projection > bestProjection Then
1381.             bestVertex = v
1382.             bestProjection = projection
1383.         End If
1384.     Next
1385. End Sub
1386.  
1387. '**********************************************************************************************
1388. '   Matrix Stuff Ahead
1389. '**********************************************************************************************
1390.  
1391. Sub matrixSetRadians (m As tMATRIX2d, radians As _Float)
1392.     Dim c As _Float
1393.     Dim s As _Float
1394.     c = Cos(radians)
1395.     s = Sin(radians)
1396.     m.m00 = c
1397.     m.m01 = -s
1398.     m.m10 = s
1399.     m.m11 = c
1400. End Sub
1401.  
1402. Sub matrixSetScalar (m As tMATRIX2d, a As _Float, b As _Float, c As _Float, d As _Float)
1403.     m.m00 = a
1404.     m.m01 = b
1405.     m.m10 = c
1406.     m.m11 = d
1407. End Sub
1408.  
1409. Sub matrixAbs (m As tMATRIX2d, o As tMATRIX2d)
1410.     o.m00 = Abs(m.m00)
1411.     o.m01 = Abs(m.m01)
1412.     o.m10 = Abs(m.m10)
1413.     o.m11 = Abs(m.m11)
1414. End Sub
1415.  
1416. Sub matrixGetAxisX (m As tMATRIX2d, o As tVECTOR2d)
1417.     o.x = m.m00
1418.     o.y = m.m10
1419. End Sub
1420.  
1421. Sub matrixGetAxisY (m As tMATRIX2d, o As tVECTOR2d)
1422.     o.x = m.m01
1423.     o.y = m.m11
1424. End Sub
1425.  
1426. Sub matrixTransposeI (m As tMATRIX2d)
1427.     Swap m.m01, m.m10
1428. End Sub
1429.  
1430. Sub matrixTranspose (m As tMATRIX2d, o As tMATRIX2d)
1431.     o.m00 = m.m00
1432.     o.m01 = m.m10
1433.     o.m10 = m.m01
1434.     o.m11 = m.m11
1435. End Sub
1436.  
1437. Sub matrixMultiplyVector (m As tMATRIX2d, v As tVECTOR2d, o As tVECTOR2d)
1438.     Dim t As tVECTOR2d
1439.     t.x = m.m00 * v.x + m.m01 * v.y
1440.     t.y = m.m10 * v.x + m.m11 * v.y
1441.     o = t
1442. End Sub
1443.  
1444. Sub matrixMultiplyMatrix (m As tMATRIX2d, x As tMATRIX2d, o As tMATRIX2d)
1445.     o.m00 = m.m00 * x.m00 + m.m01 * x.m10
1446.     o.m01 = m.m00 * x.m01 + m.m01 * x.m11
1447.     o.m10 = m.m10 * x.m00 + m.m11 * x.m10
1448.     o.m11 = m.m10 * x.m01 + m.m11 * x.m11
1449. End Sub
1450.  
1451. '**********************************************************************************************
1452. '   Mostly Unused Stuff Ahead
1453. '**********************************************************************************************
1454.  
1455. Sub polygonMakeCCW (obj As tTRIANGLE)
1456.     If vectorLeft(obj.a, obj.b, obj.c) = 0 Then
1457.         Swap obj.a, obj.c
1458.     End If
1459. End Sub
1460.  
1461. Function polygonIsReflex (t As tTRIANGLE)
1462.     polygonIsReflex = vectorRight(t.a, t.b, t.c)
1463. End Function
1464.  
1465. Function scalarMin (a As _Float, b As _Float)
1466.     If a < b Then
1467.         scalarMin = a
1468.     Else
1469.         scalarMin = b
1470.     End If
1471. End Function
1472.  
1473. Function scalarMax (a As _Float, b As _Float)
1474.     If a > b Then
1475.         scalarMax = a
1476.     Else
1477.         scalarMax = b
1478.     End If
1479. End Function
1480.  
1481. Sub lineIntersection (l1 As tLINE2d, l2 As tLINE2d, o As tVECTOR2d)
1482.     Dim a1, b1, c1, a2, b2, c2, det As _Float
1483.     o.x = 0
1484.     o.y = 0
1485.     a1 = l1.b.y - l1.a.y
1486.     b1 = l1.a.x - l1.b.x
1487.     c1 = a1 * l1.a.x + b1 * l1.a.y
1488.     a2 = l2.b.y - l2.a.y
1489.     b2 = l2.a.x - l2.b.x
1490.     c2 = a2 * l2.a.x + b2 * l2.a.y
1491.     det = a1 * b2 - a2 * b1
1492.  
1493.     If Int(det * cPRECISION) <> 0 Then
1494.         o.x = (b2 * c1 - b1 * c2) / det
1495.         o.y = (a1 * c2 - a2 * c1) / det
1496.     End If
1497. End Sub
1498.  
1499. Function lineSegmentsIntersect (l1 As tLINE2d, l2 As tLINE2d)
1500.     Dim dx, dy, da, db, s, t As _Float
1501.     dx = l1.b.x - l1.a.x
1502.     dy = l1.b.y - l1.a.y
1503.     da = l2.b.x - l2.a.x
1504.     db = l2.b.y - l2.a.y
1505.     If da * dy - db * dx = 0 Then
1506.         lineSegmentsIntersect = 0
1507.     Else
1508.         s = (dx * (l2.a.y - l1.a.y) + dy * (l1.a.x - l2.a.x)) / (da * dy - db * dx)
1509.         t = (da * (l1.a.y - l2.a.y) + db * (l2.a.x - l1.a.x)) / (db * dx - da * dy)
1510.         lineSegmentsIntersect = (s >= 0 And s <= 1 And t >= 0 And t <= 1)
1511.     End If
1512. End Function
1513.  
1514. '**********************************************************************************************
1515. '   Impulse Specific Math Ahead
1516. '**********************************************************************************************
1517.  
1518. Function impulseEqual (a As _Float, b As _Float)
1519.     impulseEqual = Abs(a - b) <= cEPSILON
1520. End Function
1521.  
1522. Function impulseClamp (min As _Float, max As _Float, a As _Float)
1523.     If a < min Then
1524.         impulseClamp = min
1525.     Else If a > max Then
1526.             impulseClamp = max
1527.         Else
1528.             impulseClamp = a
1529.         End If
1530.     End If
1531. End Function
1532.  
1533. Function impulseRound (a As _Float)
1534.     impulseRound = Int(a + 0.5)
1535. End Function
1536.  
1537. Function impulseRandom_float (min As _Float, max As _Float)
1538.     impulseRandom_float = ((max - min) * Rnd + min)
1539. End Function
1540.  
1541. Function impulseRandomInteger (min As Integer, max As Integer)
1542.     impulseRandomInteger = Int((max - min) * Rnd + min)
1543. End Function
1544.  
1545. Function impulseGT (a As _Float, b As _Float)
1546.     impulseGT = (a >= b * cBIAS_RELATIVE + a * cBIAS_ABSOLUTE)
1547. End Function
1548.  
1549. '**********************************************************************************************
1550. '   Troubleshooting Tools
1551. '**********************************************************************************************
1552.  
1553.  
1554. Sub printMatrix (u As tMATRIX2d, n As Integer)
1555.     Print "---------------------------"
1556.     Print n; " u:"; u.m00; "|"; u.m10
1557.     Print "       "; u.m10; "|"; u.m11
1558. End Sub
1559.  
1560.  

[NOVARSEG]

looking at code

[bplus]

Well it is nice demo!

Welcome @justsomeguy

[justsomeguy]

Thank you for the feedback!

[Dimster]

That's pretty neat - maybe a new engine for a lottery machine. Seems to be a possible recursive pattern to the moving objects but getting hypnotized trying to see it.

[justsomeguy]

Hello

I have added textures to the objects and and added a FPS counter. I would be interested in what kind of performance that everyone is getting. I will appreciate any feedback good or bad.

Thanks

Code: QB64: [Select]

1. Option _Explicit
2. '/*
3. '    Copyright (c) 2013 Randy Gaul http://RandyGaul.net
4.  
5. '    This software is provided 'as-is', without any express or implied
6. '    warranty. In no event will the authors be held liable for any damages
7. '    arising from the use of this software.
8.  
9. '    Permission is granted to anyone to use this software for any purpose,
10. '    including commercial applications, and to alter it and redistribute it
11. '    freely, subject to the following restrictions:
12. '      1. The origin of this software must not be misrepresented; you must not
13. '         claim that you wrote the original software. If you use this software
14. '         in a product, an acknowledgment in the product documentation would be
15. '         appreciated but is not required.
16. '      2. Altered source versions must be plainly marked as such, and must not be
17. '         misrepresented as being the original software.
18. '      3. This notice may not be removed or altered from any source distribution.
19.  
20. '    Port to Java by Philip Diffenderfer http://magnos.org
21. '    Port to QB64 by justsomeguy
22. '*/
23. '
24.  
25. '**********************************************************************************************
26. '   Setup Types and Variables
27. '**********************************************************************************************
28. Type tVECTOR2d
29.     x As _Float
30.     y As _Float
31. End Type
32.  
33. Type tLINE2d ' Not used
34.     a As tVECTOR2d
35.     b As tVECTOR2d
36. End Type
37.  
38. Type tFACE2d ' Not used
39.     f0 As tVECTOR2d
40.     f1 As tVECTOR2d
41. End Type
42.  
43. Type tTRIANGLE ' Not used
44.     a As tVECTOR2d
45.     b As tVECTOR2d
46.     c As tVECTOR2d
47. End Type
48.  
49. Type tMATRIX2d
50.     m00 As _Float
51.     m01 As _Float
52.     m10 As _Float
53.     m11 As _Float
54. End Type
55.  
56. Type tSHAPE
57.     ty As Integer ' cSHAPE_CIRCLE = 1, cSHAPE_POLYGON = 2
58.     radius As _Float ' Only necessary for circle shapes
59.     u As tMATRIX2d ' Only neceassary for polygons
60.     texture As Long
61. End Type
62.  
63. Type tPOLY 'list of vertices for all objects in simulation
64.     vert As tVECTOR2d
65.     norm As tVECTOR2d
66. End Type
67.  
68. Type tPOLYATTRIB 'keep track of polys in monlithic list of vertices
69.     start As Integer ' starting vertex of the polygon
70.     count As Integer ' number of vertices in polygon
71. End Type
72.  
73. Type tBODY
74.     position As tVECTOR2d
75.     velocity As tVECTOR2d
76.     force As tVECTOR2d
77.     angularVelocity As _Float
78.     torque As _Float
79.     orient As _Float
80.     mass As _Float
81.     invMass As _Float
82.     inertia As _Float
83.     invInertia As _Float
84.     staticFriction As _Float
85.     dynamicFriction As _Float
86.     restitution As _Float
87.     shape As tSHAPE
88.     c As Long ' color
89.     visible As Integer 'Hide a body ;)
90. End Type
91.  
92. Type tMANIFOLD
93.     A As Integer
94.     B As Integer
95.     penetration As _Float
96.     normal As tVECTOR2d
97.     contactCount As Integer
98.     e As _Float
99.     df As _Float
100.     sf As _Float
101. End Type
102.  
103. Const cSHAPE_CIRCLE = 1
104. Const cSHAPE_POLYGON = 2
105. Const cPRECISION = 100
106. Const cMAXNUMOFTRIANGLES = 100
107. Const cMAXNUMBEROFOBJECTS = 1000 ' Max number of objects at one time
108. Const cMAXNUMBEROFPOLYGONS = 10000 ' Max number of total vertices included in all objects
109. Const cPI = 3.14159
110. Const cEPSILON = 0.0001
111. Const cEPSILON_SQ = cEPSILON * cEPSILON
112. Const cBIAS_RELATIVE = 0.95
113. Const cBIAS_ABSOLUTE = 0.01
114. Const cDT = 1.0 / 60.0
115. Const cITERATIONS = 10
116. Const cPENETRATION_ALLOWANCE = 0.05
117. Const cPENETRATION_CORRECTION = 0.4 ' misspelled in original code
118. Const cPARAMETER_POSITION = 1
119. Const cPARAMETER_VELOCITY = 2
120. Const cPARAMETER_FORCE = 3
121. Const cPARAMETER_ANGULARVELOCITY = 4
122. Const cPARAMETER_TORQUE = 5
123. Const cPARAMETER_ORIENT = 6
124. Const cPARAMETER_STATICFRICTION = 7
125. Const cPARAMETER_DYNAMICFRICTION = 8
126. Const cPARAMETER_COLOR = 9
127. Const cPARAMETER_VISIBLE = 10
128. Const cPARAMETER_STATIC = 11
129. Const cPARAMETER_TEXTURE = 12
130.  
131. Dim Shared sGRAVITY As tVECTOR2d: Call vectorSet(sGRAVITY, 0.0, 100.0)
132. Dim Shared sRESTING As _Float: Dim o As tVECTOR2d: Call vectorMultiplyScalarND(o, sGRAVITY, cDT): sRESTING = vectorLengthSq(o) + cEPSILON
133. Dim Shared sNUMBEROFBODIES As Integer: sNUMBEROFBODIES = 100 ' 0 is included - Don't go under 10 for the current scene
134.  
135. Dim poly(cMAXNUMBEROFPOLYGONS) As tPOLY
136. Dim polyattributes(cMAXNUMBEROFPOLYGONS) As tPOLYATTRIB
137. Dim body(cMAXNUMBEROFOBJECTS) As tBODY
138. Dim fps As Double
139.  
140. Const cSCENE_USER = 0
141. Const cSCENE_FLOOR = 1
142. Const cSCENE_SPINNEROFDEATH = 2
143. Const cSCENE_RIGHTRAMP = 3
144. Const cSCENE_LEFTRAMP = 4
145. Const cSCENE_DOZEROFDOOM = 5
146. Const cSCENE_ELEVATOROFTERROR = 6
147. Const cSCENE_RIGHTWALL = 7
148. Const cSCENE_ELEVATORKICKER = 8
149.  
150. '**********************************************************************************************
151. _Title "phyNGN"
152. Screen _NewImage(1024, 768, 32)
153. 'Randomize Timer
154. Call buildSimpleScene(poly(), polyattributes(), body())
155. '**********************************************************************************************
156. _PrintMode _KeepBackground
157. Do: fps = Timer(.001)
158.     Cls , _RGB32(28, 28, 22)
159.     Call animateScene(body())
160.     Call impulseStep(poly(), polyattributes(), body(), cDT, cITERATIONS)
161.     Call renderBodies(poly(), polyattributes(), body())
162.     Locate 1, 60: Print "FPS:"; Int(1 / (Timer(.001) - fps))
163.     _Display
164.     _Limit 240
165. Loop Until _KeyHit = 27
166. System
167. '**********************************************************************************************
168. '   End of Main loop
169. '**********************************************************************************************
170.  
171. '**********************************************************************************************
172. '   Scene Creation and Handling Ahead
173. '**********************************************************************************************
174.  
175. Sub animateScene (body() As tBODY)
176.     If _MouseInput Then ' Terrible user interaction
177.         Call vectorSet(body(cSCENE_USER).velocity, _MouseMovementX * 100, _MouseMovementY * 100)
178.     End If
179.  
180.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_SPINNEROFDEATH, body(cSCENE_SPINNEROFDEATH).orient + (cPI / 90), 0)
181.     If body(cSCENE_SPINNEROFDEATH).orient > 2 * cPI Then body(cSCENE_SPINNEROFDEATH).orient = 0
182.  
183.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_DOZEROFDOOM, body(cSCENE_DOZEROFDOOM).position.x - 1, _Height - 75)
184.     If body(cSCENE_DOZEROFDOOM).position.x < 120 Then body(cSCENE_DOZEROFDOOM).position.x = _Width
185.  
186.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_ELEVATOROFTERROR, 55, body(cSCENE_ELEVATOROFTERROR).position.y - 1)
187.     If body(cSCENE_ELEVATOROFTERROR).position.y < 50 Then body(cSCENE_ELEVATOROFTERROR).position.y = _Height - 25
188. End Sub
189.  
190. Sub buildSimpleScene (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY)
191.     Dim i, ty As Integer
192.     Dim bm(5) As Long
193.     Call generateBitmap(bm())
194.  
195.     Call createBoxBodies(p(), pa(), body(), cSCENE_USER, 10, 10)
196.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_USER, (_Width / 2), (_Height / 2))
197.     Call setBody(body(), cPARAMETER_VELOCITY, cSCENE_USER, 0, 0)
198.  
199.     Call createBoxBodies(p(), pa(), body(), cSCENE_FLOOR, 1000, 5)
200.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_FLOOR, (_Width / 2), (_Height - 20))
201.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_FLOOR, 0, 0)
202.  
203.     Call createBoxBodies(p(), pa(), body(), cSCENE_SPINNEROFDEATH, 75, 5)
204.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_SPINNEROFDEATH, (_Width / 2), (_Height - 100))
205.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_SPINNEROFDEATH, 0, 0)
206.  
207.     Call createBoxBodies(p(), pa(), body(), cSCENE_RIGHTRAMP, 350, 5)
208.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_RIGHTRAMP, (_Width * .75) + 35, (_Height / 2) + 105)
209.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_RIGHTRAMP, (cPI * .75), 0)
210.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_RIGHTRAMP, 0, 0)
211.  
212.     Call createBoxBodies(p(), pa(), body(), cSCENE_LEFTRAMP, 225, 5)
213.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_LEFTRAMP, (_Width * .25) + 55, (_Height / 2))
214.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_LEFTRAMP, (cPI * .1), 0)
215.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_LEFTRAMP, 0, 0)
216.  
217.     Call createBoxBodies(p(), pa(), body(), cSCENE_DOZEROFDOOM, 5, 50)
218.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_DOZEROFDOOM, 0, _Height - 75)
219.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_DOZEROFDOOM, 0, 0)
220.  
221.     Call createBoxBodies(p(), pa(), body(), cSCENE_ELEVATOROFTERROR, 50, 5)
222.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_ELEVATOROFTERROR, 55, _Height - 25)
223.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_ELEVATOROFTERROR, (cPI * .98), 0)
224.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_ELEVATOROFTERROR, 0, 0)
225.  
226.     Call createBoxBodies(p(), pa(), body(), cSCENE_RIGHTWALL, 5, 375)
227.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_RIGHTWALL, 5, _Height / 2 - 20)
228.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_RIGHTWALL, 0, 0)
229.  
230.     Call createBoxBodies(p(), pa(), body(), cSCENE_ELEVATORKICKER, 100, 5)
231.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_ELEVATORKICKER, 55, 120)
232.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_ELEVATORKICKER, (cPI * .70), 0)
233.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_ELEVATORKICKER, 0, 0)
234.  
235.     For i = cSCENE_ELEVATORKICKER + 1 To sNUMBEROFBODIES
236.         If Rnd > .25 Then ' Circles are must faster than polygons
237.             ty = cSHAPE_CIRCLE
238.         Else
239.             ty = cSHAPE_POLYGON
240.         End If
241.         Call createBodies(p(), pa(), body(), i, ty)
242.         Call setBody(body(), cPARAMETER_POSITION, i, (Rnd * _Width / 2) + (_Width / 4), ((Rnd * _Height / 2) + (_Height / 4)) - 200)
243.         Call setBody(body(), cPARAMETER_VELOCITY, i, Rnd * 100 - 50, Rnd * 100 - 50)
244.     Next
245.     For i = cSCENE_ELEVATORKICKER + 1 To sNUMBEROFBODIES
246.         If body(i).shape.ty = cSHAPE_CIRCLE Then
247.             Call setBody(body(), cPARAMETER_TEXTURE, i, bm(0), 0)
248.         Else
249.             Call setBody(body(), cPARAMETER_TEXTURE, i, bm(1), 0)
250.         End If
251.     Next
252. End Sub
253.  
254. Sub setBody (body() As tBODY, Parameter As Integer, Index As Integer, arg1 As _Float, arg2 As _Float)
255.     Select Case Parameter
256.         Case cPARAMETER_POSITION:
257.             Call vectorSet(body(Index).position, arg1, arg2)
258.         Case cPARAMETER_VELOCITY:
259.             Call vectorSet(body(Index).velocity, arg1, arg2)
260.         Case cPARAMETER_FORCE:
261.             Call vectorSet(body(Index).force, arg1, arg2)
262.         Case cPARAMETER_ANGULARVELOCITY:
263.             body(Index).angularVelocity = arg1
264.         Case cPARAMETER_TORQUE:
265.             body(Index).torque = arg1
266.         Case cPARAMETER_ORIENT:
267.             body(Index).orient = arg1
268.             Call matrixSetRadians(body(Index).shape.u, body(Index).orient)
269.         Case cPARAMETER_STATICFRICTION:
270.             body(Index).staticFriction = arg1
271.         Case cPARAMETER_DYNAMICFRICTION:
272.             body(Index).dynamicFriction = arg1
273.         Case cPARAMETER_COLOR:
274.             body(Index).c = arg1
275.         Case cPARAMETER_VISIBLE:
276.             body(Index).visible = arg1
277.         Case cPARAMETER_STATIC:
278.             Call bodySetStatic(body(Index))
279.         Case cPARAMETER_TEXTURE:
280.             body(Index).shape.texture = arg1
281.     End Select
282. End Sub
283.  
284. Sub createCircleBody (pa() As tPOLYATTRIB, body() As tBODY, index As Integer, radius As _Float)
285.     Dim shape As tSHAPE
286.     Call shapeCreate(shape, cSHAPE_CIRCLE, radius)
287.     Call bodyCreate(body(), index, shape)
288.     Call circleInitialize(body(), index)
289.     ' Even though circles do not have Polygons, they still must be included in the Vertices
290.     If index = 0 Then
291.         pa(index).start = 0
292.     Else
293.         pa(index).start = pa(index - 1).start + pa(index - 1).count + 1
294.     End If
295.     pa(index).count = 1
296.     body(index).c = _RGB32(255, 255, 255)
297. End Sub
298.  
299. Sub createBoxBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, index As Integer, xs As _Float, ys As _Float)
300.     Dim shape As tSHAPE
301.     Call shapeCreate(shape, cSHAPE_POLYGON, 0)
302.     Call bodyCreate(body(), index, shape)
303.     Call boxCreate(p(), pa(), index, xs, ys)
304.     Call polygonInitialize(body(), p(), pa(), index)
305.     body(index).c = _RGB32(255, 255, 255)
306. End Sub
307.  
308. Sub createBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, index As Integer, ty As Integer)
309.     If ty = cSHAPE_CIRCLE Then
310.         Call createCircleBody(pa(), body(), index, 10 + Rnd * 20)
311.     Else
312.         If ty = cSHAPE_POLYGON Then
313.             Call createBoxBodies(p(), pa(), body(), index, 10 + Rnd * 10, 10 + Rnd * 10)
314.         End If
315.     End If
316.     body(index).c = _RGB32(55 + Rnd * 200, 55 + Rnd * 200, 55 + Rnd * 200)
317. End Sub
318.  
319. '**********************************************************************************************
320. '   Physics and Collision Stuff Ahead
321. '**********************************************************************************************
322.  
323. Sub impulseIntegrateForces (b As tBODY, dt As _Float)
324.     If b.invMass = 0.0 Then Exit Sub
325.     Dim dts As _Float
326.     dts = dt * .5
327.     Call vectorAddVectorScalar(b.velocity, b.force, b.invMass * dts)
328.     Call vectorAddVectorScalar(b.velocity, sGRAVITY, dts)
329.     b.angularVelocity = b.angularVelocity + (b.torque * b.invInertia * dts)
330. End Sub
331.  
332. Sub impulseIntegrateVelocity (body As tBODY, dt As _Float)
333.     If body.invMass = 0.0 Then Exit Sub
334.     Call vectorAddVectorScalar(body.position, body.velocity, dt)
335.     body.orient = body.orient + (body.angularVelocity * dt)
336.     Call matrixSetRadians(body.shape.u, body.orient)
337.     Call impulseIntegrateForces(body, dt)
338. End Sub
339.  
340. Sub impulseStep (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, dt As _Float, iterations As Integer)
341.     Dim A As tBODY
342.     Dim B As tBODY
343.     Dim c(cMAXNUMBEROFOBJECTS) As tVECTOR2d
344.     Dim m As tMANIFOLD
345.     Dim manifolds(sNUMBEROFBODIES * sNUMBEROFBODIES) As tMANIFOLD
346.     Dim collisions(sNUMBEROFBODIES * sNUMBEROFBODIES, cMAXNUMBEROFOBJECTS) As tVECTOR2d
347.     Dim manifoldCount As Integer: manifoldCount = 0
348.     '    // Generate new collision info
349.     Dim i, j, k As Integer
350.     ' TODO: Implement hidden object logic
351.     For i = 0 To sNUMBEROFBODIES ' number of bodies
352.         A = body(i)
353.         For j = i + 1 To sNUMBEROFBODIES
354.             B = body(j)
355.             If A.invMass = 0.0 And B.invMass = 0.0 Then _Continue
356.             'Mainfold solve - handle collisions
357.             If A.shape.ty = cSHAPE_CIRCLE And B.shape.ty = cSHAPE_CIRCLE Then
358.                 Call collisionCCHandle(m, c(), A, B)
359.             Else
360.                 If A.shape.ty = cSHAPE_POLYGON And B.shape.ty = cSHAPE_POLYGON Then
361.                     Call collisionPPHandle(p(), pa(), body(), m, c(), i, j)
362.                 Else
363.                     If A.shape.ty = cSHAPE_CIRCLE And B.shape.ty = cSHAPE_POLYGON Then
364.                         Call collisionCPHandle(p(), pa(), body(), m, c(), i, j)
365.                     Else
366.                         If B.shape.ty = cSHAPE_CIRCLE And A.shape.ty = cSHAPE_POLYGON Then
367.                             Call collisionPCHandle(p(), pa(), body(), m, c(), i, j)
368.                         End If
369.                     End If
370.                 End If
371.             End If
372.             If m.contactCount > 0 Then
373.                 m.A = i 'identify the index of objects
374.                 m.B = j
375.                 manifolds(manifoldCount) = m
376.                 For k = 0 To m.contactCount
377.                     collisions(manifoldCount, k) = c(k)
378.                 Next
379.                 manifoldCount = manifoldCount + 1
380.             End If
381.         Next
382.     Next
383.     '   // Integrate forces
384.     For i = 0 To sNUMBEROFBODIES
385.         Call impulseIntegrateForces(body(i), dt)
386.     Next
387.     '   // Initialize collision
388.     For i = 0 To manifoldCount - 1
389.         ' this is the stupidest thing ever since QB will not let you split arrays
390.         For k = 0 To manifolds(i).contactCount - 1
391.             c(k) = collisions(i, k)
392.         Next
393.         Call manifoldInit(manifolds(i), body(), c())
394.     Next
395.     '// Solve collisions
396.     For j = 0 To iterations - 1
397.         For i = 0 To manifoldCount - 1
398.             For k = 0 To manifolds(i).contactCount - 1
399.                 c(k) = collisions(i, k)
400.             Next
401.             Call manifoldApplyImpulse(manifolds(i), body(), c())
402.         Next i
403.     Next j
404.     '// Integrate velocities
405.     For i = 0 To sNUMBEROFBODIES
406.         Call impulseIntegrateVelocity(body(i), dt)
407.     Next
408.     '// Correct positions
409.     For i = 0 To manifoldCount - 1
410.         Call manifoldPositionalCorrection(manifolds(i), body())
411.     Next
412.     '// Clear all forces
413.     For i = 0 To sNUMBEROFBODIES
414.         Call vectorSet(body(i).force, 0, 0)
415.         body(i).torque = 0
416.     Next
417. End Sub
418.  
419. Sub bodyApplyImpulse (body As tBODY, impulse As tVECTOR2d, contactVector As tVECTOR2d)
420.     Call vectorAddVectorScalar(body.velocity, impulse, body.invMass)
421.     body.angularVelocity = body.angularVelocity + body.invInertia * vectorCross(contactVector, impulse)
422. End Sub
423.  
424. Sub bodySetStatic (body As tBODY)
425.     body.inertia = 0.0
426.     body.invInertia = 0.0
427.     body.mass = 0.0
428.     body.invMass = 0.0
429. End Sub
430.  
431. Sub manifoldInit (m As tMANIFOLD, body() As tBODY, contacts() As tVECTOR2d)
432.     Dim ra As tVECTOR2d
433.     Dim rb As tVECTOR2d
434.     Dim rv As tVECTOR2d
435.     Dim tv1 As tVECTOR2d
436.     Dim tv2 As tVECTOR2d
437.     m.e = scalarMin(body(m.A).restitution, body(m.B).restitution)
438.     m.sf = Sqr(body(m.A).staticFriction * body(m.A).staticFriction)
439.     m.df = Sqr(body(m.A).dynamicFriction * body(m.A).dynamicFriction)
440.     Dim i As Integer
441.     For i = 0 To m.contactCount - 1
442.         Call vectorSubVectorND(contacts(i), body(m.A).position, ra)
443.         Call vectorSubVectorND(contacts(i), body(m.B).position, rb)
444.  
445.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
446.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
447.         Call vectorAddVector(tv1, body(m.B).velocity)
448.         Call vectorSubVectorND(tv2, body(m.A).velocity, tv2)
449.         Call vectorSubVectorND(rv, tv1, tv2)
450.  
451.         If vectorLengthSq(rv) < sRESTING Then
452.             m.e = 0.0
453.         End If
454.     Next
455. End Sub
456.  
457. Sub manifoldApplyImpulse (m As tMANIFOLD, body() As tBODY, contacts() As tVECTOR2d)
458.     Dim ra As tVECTOR2d
459.     Dim rb As tVECTOR2d
460.     Dim rv As tVECTOR2d
461.     Dim tv1 As tVECTOR2d
462.     Dim tv2 As tVECTOR2d
463.     Dim contactVel As _Float
464.  
465.     Dim raCrossN As _Float
466.     Dim rbCrossN As _Float
467.     Dim invMassSum As _Float
468.     Dim i As Integer
469.     Dim j As _Float
470.     Dim impulse As tVECTOR2d
471.  
472.     Dim t As tVECTOR2d
473.     Dim jt As _Float
474.     Dim tangentImpulse As tVECTOR2d
475.  
476.     If impulseEqual(body(m.A).invMass + body(m.B).invMass, 0.0) Then
477.         Call manifoldInfiniteMassCorrection(body(m.A), body(m.B))
478.         Exit Sub
479.     End If
480.  
481.     For i = 0 To m.contactCount - 1
482.         '// Calculate radii from COM to contact
483.         '// Vec2 ra = contacts[i] - A->position;
484.         '// Vec2 rb = contacts[i] - B->position;
485.         Call vectorSubVectorND(ra, contacts(i), body(m.A).position)
486.         Call vectorSubVectorND(rb, contacts(i), body(m.B).position)
487.  
488.         '// Relative velocity
489.         '// Vec2 rv = B->velocity + Cross( B->angularVelocity, rb ) - A->velocity - Cross( A->angularVelocity, ra );
490.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
491.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
492.         Call vectorAddVectorND(rv, tv1, body(m.B).velocity)
493.         Call vectorSubVector(rv, body(m.A).velocity)
494.         Call vectorSubVector(rv, tv2)
495.  
496.         '// Relative velocity along the normal
497.         '// real contactVel = Dot( rv, normal );
498.         contactVel = vectorDot(rv, m.normal)
499.  
500.         '// Do not resolve if velocities are separating
501.         If contactVel > 0 Then Exit Sub
502.  
503.         '// real raCrossN = Cross( ra, normal );
504.         '// real rbCrossN = Cross( rb, normal );
505.         '// real invMassSum = A->im + B->im + Sqr( raCrossN ) * A->iI + Sqr( rbCrossN ) * B->iI;
506.         raCrossN = vectorCross(ra, m.normal)
507.         rbCrossN = vectorCross(rb, m.normal)
508.         invMassSum = body(m.A).invMass + body(m.B).invMass + (raCrossN * raCrossN) * body(m.A).invInertia + (rbCrossN * rbCrossN) * body(m.B).invInertia
509.  
510.         '// Calculate impulse scalar
511.         j = -(1.0 + m.e) * contactVel
512.         j = j / invMassSum
513.         j = j / m.contactCount
514.  
515.         '// Apply impulse
516.         Call vectorMultiplyScalarND(impulse, m.normal, j)
517.  
518.         Call vectorNegND(tv1, impulse)
519.         Call bodyApplyImpulse(body(m.A), tv1, ra)
520.         Call bodyApplyImpulse(body(m.B), impulse, rb)
521.  
522.         '// Friction impulse
523.         '// rv = B->velocity + Cross( B->angularVelocity, rb ) - A->velocity - Cross( A->angularVelocity, ra );
524.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
525.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
526.         Call vectorAddVectorND(rv, tv1, body(m.B).velocity)
527.         Call vectorSubVector(rv, body(m.A).velocity)
528.         Call vectorSubVector(rv, tv2)
529.  
530.         '// Vec2 t = rv - (normal * Dot( rv, normal ));
531.         '// t.Normalize( );
532.         Call vectorMultiplyScalarND(t, m.normal, vectorDot(rv, m.normal))
533.         Call vectorSubVectorND(t, rv, t)
534.         Call vectorNormalize(t)
535.  
536.         '// j tangent magnitude
537.         jt = -vectorDot(rv, t)
538.         jt = jt / invMassSum
539.         jt = jt / m.contactCount
540.  
541.         '// Don't apply tiny friction impulses
542.         If impulseEqual(jt, 0.0) Then Exit Sub
543.  
544.         '// Coulumb's law
545.         If Abs(jt) < j * m.sf Then
546.             Call vectorMultiplyScalarND(tangentImpulse, t, jt)
547.         Else
548.             Call vectorMultiplyScalarND(tangentImpulse, t, -j * m.df)
549.         End If
550.  
551.         '// Apply friction impulse
552.         '// A->ApplyImpulse( -tangentImpulse, ra );
553.         '// B->ApplyImpulse( tangentImpulse, rb );
554.         Call vectorNegND(tv1, tangentImpulse)
555.         Call bodyApplyImpulse(body(m.A), tv1, ra)
556.         Call bodyApplyImpulse(body(m.B), tangentImpulse, rb)
557.     Next i
558. End Sub
559.  
560. Sub manifoldPositionalCorrection (m As tMANIFOLD, body() As tBODY)
561.     Dim correction As _Float
562.     correction = scalarMax(m.penetration - cPENETRATION_ALLOWANCE, 0.0) / (body(m.A).invMass + body(m.B).invMass) * cPENETRATION_CORRECTION
563.     Call vectorAddVectorScalar(body(m.A).position, m.normal, -body(m.A).invMass * correction)
564.     Call vectorAddVectorScalar(body(m.B).position, m.normal, body(m.B).invMass * correction)
565. End Sub
566.  
567. Sub manifoldInfiniteMassCorrection (A As tBODY, B As tBODY)
568.     Call vectorSet(A.velocity, 0, 0)
569.     Call vectorSet(B.velocity, 0, 0)
570. End Sub
571.  
572. '**********************************************************************************************
573. '   Collision Stuff Ahead
574. '**********************************************************************************************
575.  
576. Sub collisionCCHandle (m As tMANIFOLD, contacts() As tVECTOR2d, A As tBODY, B As tBODY)
577.     Dim normal As tVECTOR2d
578.     Dim dist_sqr As _Float
579.     Dim radius As _Float
580.  
581.     Call vectorSubVectorND(normal, B.position, A.position)
582.     dist_sqr = vectorLengthSq(normal)
583.     radius = A.shape.radius + B.shape.radius
584.  
585.     If (dist_sqr >= radius * radius) Then
586.         m.contactCount = 0
587.     Else
588.         Dim distance As _Float
589.         distance = Sqr(dist_sqr)
590.         m.contactCount = 1
591.  
592.         If distance = 0 Then
593.             m.penetration = A.shape.radius
594.             Call vectorSet(m.normal, 1.0, 0.0)
595.             Call vectorSetVector(contacts(0), A.position)
596.         Else
597.             m.penetration = radius - distance
598.             Call vectorDivideScalarND(m.normal, normal, distance)
599.  
600.             Call vectorMultiplyScalarND(contacts(0), m.normal, A.shape.radius)
601.             Call vectorAddVector(contacts(0), A.position)
602.         End If
603.     End If
604. End Sub
605.  
606. Sub collisionPCHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
607.     Call collisionCPHandle(p(), pa(), body(), m, contacts(), B, A)
608.     If m.contactCount > 0 Then
609.         Call vectorNeg(m.normal)
610.     End If
611. End Sub
612.  
613. Sub collisionCPHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
614.     'A is the Circle
615.     'B is the POLY
616.     m.contactCount = 0
617.     Dim center As tVECTOR2d
618.     Dim tm As tMATRIX2d
619.     Dim tv As tVECTOR2d
620.     Dim ARadius As _Float: ARadius = body(A).shape.radius
621.  
622.     Call vectorSubVectorND(center, body(A).position, body(B).position)
623.     Call matrixTranspose(body(B).shape.u, tm)
624.     Call matrixMultiplyVector(tm, center, center)
625.  
626.     Dim separation As _Float: separation = -9999999
627.     Dim faceNormal As Integer: faceNormal = 0
628.     Dim i As Integer
629.     Dim s As _Float
630.     For i = 0 To pa(B).count
631.         Call vectorSubVectorND(tv, center, p(pa(B).start + i).vert)
632.         s = vectorDot(p(pa(B).start + i).norm, tv)
633.         If s > ARadius Then Exit Sub
634.         If s > separation Then
635.             separation = s
636.             faceNormal = i
637.         End If
638.     Next
639.     Dim v1 As tVECTOR2d
640.     v1 = p(pa(B).start + faceNormal).vert
641.     Dim i2 As Integer
642.     i2 = pa(B).start + arrayNextIndex(faceNormal, pa(B).count)
643.     Dim v2 As tVECTOR2d
644.     v2 = p(i2).vert
645.  
646.     If separation < cEPSILON Then
647.         m.contactCount = 1
648.         Call matrixMultiplyVector(body(B).shape.u, p(pa(B).start + faceNormal).norm, m.normal)
649.         Call vectorNeg(m.normal)
650.         Call vectorMultiplyScalarND(contacts(0), m.normal, ARadius)
651.         Call vectorAddVector(contacts(0), body(A).position)
652.         m.penetration = ARadius
653.         Exit Sub
654.     End If
655.  
656.     Dim dot1 As _Float
657.     Dim dot2 As _Float
658.  
659.     Dim tv1 As tVECTOR2d
660.     Dim tv2 As tVECTOR2d
661.     Dim n As tVECTOR2d
662.     Call vectorSubVectorND(tv1, center, v1)
663.     Call vectorSubVectorND(tv2, v2, v1)
664.     dot1 = vectorDot(tv1, tv2)
665.     Call vectorSubVectorND(tv1, center, v2)
666.     Call vectorSubVectorND(tv2, v1, v2)
667.     dot2 = vectorDot(tv1, tv2)
668.     m.penetration = ARadius - separation
669.     If dot1 <= 0.0 Then
670.         If vectorSqDist(center, v1) > ARadius * ARadius Then Exit Sub
671.         m.contactCount = 1
672.         Call vectorSubVectorND(n, v1, center)
673.         Call matrixMultiplyVector(body(B).shape.u, n, n)
674.         Call vectorNormalize(n)
675.         m.normal = n
676.         Call matrixMultiplyVector(body(B).shape.u, v1, v1)
677.         Call vectorAddVectorND(v1, v1, body(B).position)
678.         contacts(0) = v1
679.     Else
680.         If dot2 <= 0.0 Then
681.             If vectorSqDist(center, v2) > ARadius * ARadius Then Exit Sub
682.             m.contactCount = 1
683.             Call vectorSubVectorND(n, v2, center)
684.             Call matrixMultiplyVector(body(B).shape.u, v2, v2)
685.             Call vectorAddVectorND(v2, v2, body(B).position)
686.             contacts(0) = v2
687.             Call matrixMultiplyVector(body(B).shape.u, n, n)
688.             Call vectorNormalize(n)
689.             m.normal = n
690.         Else
691.             n = p(pa(B).start + faceNormal).norm
692.             Call vectorSubVectorND(tv1, center, v1)
693.             If vectorDot(tv1, n) > ARadius Then Exit Sub
694.             m.contactCount = 1
695.             Call matrixMultiplyVector(body(B).shape.u, n, n)
696.             Call vectorNeg(n)
697.             m.normal = n
698.             Call vectorMultiplyScalarND(contacts(0), m.normal, ARadius)
699.             Call vectorAddVector(contacts(0), body(A).position)
700.         End If
701.     End If
702. End Sub
703.  
704. Function collisionPPClip (n As tVECTOR2d, c As _Float, face() As tVECTOR2d)
705.     Dim sp As Integer: sp = 0
706.     Dim o(cMAXNUMBEROFPOLYGONS) As tVECTOR2d
707.  
708.     o(0) = face(0)
709.     o(1) = face(1)
710.  
711.     Dim d1 As _Float: d1 = vectorDot(n, face(0)) - c
712.     Dim d2 As _Float: d2 = vectorDot(n, face(1)) - c
713.  
714.     If d1 <= 0.0 Then
715.         o(sp) = face(0)
716.         sp = sp + 1
717.     End If
718.  
719.     If d2 <= 0.0 Then
720.         o(sp) = face(1)
721.         sp = sp + 1
722.     End If
723.  
724.     If d1 * d2 < 0.0 Then
725.         Dim alpha As _Float: alpha = d1 / (d1 - d2)
726.         Dim tempv As tVECTOR2d
727.         'out[sp] = face[0] + alpha * (face[1] - face[0]);
728.         Call vectorSubVectorND(tempv, face(1), face(0))
729.         Call vectorMultiplyScalar(tempv, alpha)
730.         Call vectorAddVectorND(o(sp), tempv, face(0))
731.         sp = sp + 1
732.     End If
733.     face(0) = o(0)
734.     face(1) = o(1)
735.     collisionPPClip = sp
736. End Function
737.  
738. Sub collisionPPFindIncidentFace (p() As tPOLY, pa() As tPOLYATTRIB, b() As tBODY, v() As tVECTOR2d, RefPoly As Integer, IncPoly As Integer, referenceIndex As Integer)
739.     Dim referenceNormal As tVECTOR2d
740.     Dim uRef As tMATRIX2d: uRef = b(RefPoly).shape.u
741.     Dim uInc As tMATRIX2d: uInc = b(IncPoly).shape.u
742.     Dim uTemp As tMATRIX2d
743.     Dim i As Integer
744.     referenceNormal = p(pa(RefPoly).start + referenceIndex).norm
745.  
746.     '        // Calculate normal in incident's frame of reference
747.     '        // referenceNormal = RefPoly->u * referenceNormal; // To world space
748.     Call matrixMultiplyVector(uRef, referenceNormal, referenceNormal)
749.     '        // referenceNormal = IncPoly->u.Transpose( ) * referenceNormal; // To incident's model space
750.     Call matrixTranspose(uInc, uTemp)
751.     Call matrixMultiplyVector(uTemp, referenceNormal, referenceNormal)
752.  
753.     Dim incidentFace As Integer: incidentFace = 0
754.     Dim minDot As _Float: minDot = 9999999
755.     Dim dot As _Float
756.     For i = 0 To pa(IncPoly).count
757.         dot = vectorDot(referenceNormal, p(pa(IncPoly).start + i).norm)
758.         If (dot < minDot) Then
759.             minDot = dot
760.             incidentFace = i
761.         End If
762.     Next
763.  
764.     '// Assign face vertices for incidentFace
765.     '// v[0] = IncPoly->u * IncPoly->m_vertices[incidentFace] + IncPoly->body->position;
766.     Call matrixMultiplyVector(uInc, p(pa(IncPoly).start + incidentFace).vert, v(0))
767.     Call vectorAddVector(v(0), b(IncPoly).position)
768.  
769.     '// incidentFace = incidentFace + 1 >= (int32)IncPoly->m_vertexCount ? 0 : incidentFace + 1;
770.     incidentFace = arrayNextIndex(incidentFace, pa(IncPoly).count)
771.  
772.     '// v[1] = IncPoly->u * IncPoly->m_vertices[incidentFace] +  IncPoly->body->position;
773.     Call matrixMultiplyVector(uInc, p(pa(IncPoly).start + incidentFace).vert, v(1))
774.     Call vectorAddVector(v(1), b(IncPoly).position)
775. End Sub
776.  
777. Sub collisionPPHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
778.     m.contactCount = 0
779.  
780.     Dim faceA(100) As Integer
781.  
782.     Dim penetrationA As _Float
783.     penetrationA = collisionPPFindAxisLeastPenetration(p(), pa(), body(), faceA(), A, B)
784.     If penetrationA >= 0.0 Then Exit Sub
785.  
786.     Dim faceB(100) As Integer
787.  
788.     Dim penetrationB As _Float
789.     penetrationB = collisionPPFindAxisLeastPenetration(p(), pa(), body(), faceB(), B, A)
790.     If penetrationB >= 0.0 Then Exit Sub
791.  
792.  
793.     Dim referenceIndex As Integer
794.     Dim flip As Integer
795.  
796.     Dim RefPoly As Integer
797.     Dim IncPoly As Integer
798.  
799.     If impulseGT(penetrationA, penetrationB) Then
800.         RefPoly = A
801.         IncPoly = B
802.         referenceIndex = faceA(0)
803.         flip = 0
804.     Else
805.         RefPoly = B
806.         IncPoly = A
807.         referenceIndex = faceB(0)
808.         flip = 1
809.     End If
810.  
811.     Dim incidentFace(2) As tVECTOR2d
812.  
813.     Call collisionPPFindIncidentFace(p(), pa(), body(), incidentFace(), RefPoly, IncPoly, referenceIndex)
814.     Dim v1 As tVECTOR2d
815.     Dim v2 As tVECTOR2d
816.     Dim v1t As tVECTOR2d
817.     Dim v2t As tVECTOR2d
818.  
819.     v1 = p(pa(RefPoly).start + referenceIndex).vert
820.     referenceIndex = arrayNextIndex(referenceIndex, pa(RefPoly).count)
821.     v2 = p(pa(RefPoly).start + referenceIndex).vert
822.     '// Transform vertices to world space
823.     '// v1 = RefPoly->u * v1 + RefPoly->body->position;
824.     '// v2 = RefPoly->u * v2 + RefPoly->body->position;
825.     Call matrixMultiplyVector(body(RefPoly).shape.u, v1, v1t)
826.     Call vectorAddVectorND(v1, v1t, body(RefPoly).position)
827.     Call matrixMultiplyVector(body(RefPoly).shape.u, v2, v2t)
828.     Call vectorAddVectorND(v2, v2t, body(RefPoly).position)
829.  
830.     '// Calculate reference face side normal in world space
831.     '// Vec2 sidePlaneNormal = (v2 - v1);
832.     '// sidePlaneNormal.Normalize( );
833.     Dim sidePlaneNormal As tVECTOR2d
834.     Call vectorSubVectorND(sidePlaneNormal, v2, v1)
835.     Call vectorNormalize(sidePlaneNormal)
836.  
837.     '// Orthogonalize
838.     '// Vec2 refFaceNormal( sidePlaneNormal.y, -sidePlaneNormal.x );
839.     Dim refFaceNormal As tVECTOR2d
840.     Call vectorSet(refFaceNormal, sidePlaneNormal.y, -sidePlaneNormal.x)
841.  
842.     '// ax + by = c
843.     '// c is distance from origin
844.     '// real refC = Dot( refFaceNormal, v1 );
845.     '// real negSide = -Dot( sidePlaneNormal, v1 );
846.     '// real posSide = Dot( sidePlaneNormal, v2 );
847.     Dim refC As _Float: refC = vectorDot(refFaceNormal, v1)
848.     Dim negSide As _Float: negSide = -vectorDot(sidePlaneNormal, v1)
849.     Dim posSide As _Float: posSide = vectorDot(sidePlaneNormal, v2)
850.  
851.  
852.     '// Clip incident face to reference face side planes
853.     '// if(Clip( -sidePlaneNormal, negSide, incidentFace ) < 2)
854.     Dim negSidePlaneNormal As tVECTOR2d
855.     Call vectorNegND(negSidePlaneNormal, sidePlaneNormal)
856.  
857.     If collisionPPClip(negSidePlaneNormal, negSide, incidentFace()) < 2 Then Exit Sub
858.     If collisionPPClip(sidePlaneNormal, posSide, incidentFace()) < 2 Then Exit Sub
859.  
860.     Call vectorSet(m.normal, refFaceNormal.x, refFaceNormal.y)
861.     If flip Then Call vectorNeg(m.normal)
862.  
863.     '// Keep points behind reference face
864.     Dim cp As Integer: cp = 0 '// clipped points behind reference face
865.     Dim separation As _Float
866.     separation = vectorDot(refFaceNormal, incidentFace(0)) - refC
867.     If separation <= 0.0 Then
868.         contacts(cp) = incidentFace(0)
869.         m.penetration = -separation
870.         cp = cp + 1
871.     Else
872.         m.penetration = 0
873.     End If
874.  
875.     separation = vectorDot(refFaceNormal, incidentFace(1)) - refC
876.     If separation <= 0.0 Then
877.         contacts(cp) = incidentFace(1)
878.         m.penetration = m.penetration + -separation
879.         cp = cp + 1
880.         m.penetration = m.penetration / cp
881.     End If
882.     m.contactCount = cp
883. End Sub
884.  
885. Function collisionPPFindAxisLeastPenetration (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, faceIndex() As Integer, A As Integer, B As Integer)
886.     Dim bestDistance As _Float: bestDistance = -9999999
887.     Dim bestIndex As Integer: bestIndex = 0
888.  
889.     Dim n As tVECTOR2d
890.     Dim nw As tVECTOR2d
891.     Dim buT As tMATRIX2d
892.     Dim s As tVECTOR2d
893.     Dim nn As tVECTOR2d
894.     Dim v As tVECTOR2d
895.     Dim tv As tVECTOR2d
896.     Dim d As _Float
897.     Dim i, k As Integer
898.  
899.     For i = 0 To pa(A).count
900.         k = pa(A).start + i
901.  
902.         '// Retrieve a face normal from A
903.         '// Vec2 n = A->m_normals[i];
904.         '// Vec2 nw = A->u * n;
905.         n = p(k).norm
906.         Call matrixMultiplyVector(body(A).shape.u, n, nw)
907.  
908.  
909.         '// Transform face normal into B's model space
910.         '// Mat2 buT = B->u.Transpose( );
911.         '// n = buT * nw;
912.         Call matrixTranspose(body(B).shape.u, buT)
913.         Call matrixMultiplyVector(buT, nw, n)
914.  
915.         '// Retrieve support point from B along -n
916.         '// Vec2 s = B->GetSupport( -n );
917.         Call vectorNegND(nn, n)
918.         Call vectorGetSupport(p(), pa(), B, nn, s)
919.  
920.         '// Retrieve vertex on face from A, transform into
921.         '// B's model space
922.         '// Vec2 v = A->m_vertices[i];
923.         '// v = A->u * v + A->body->position;
924.         '// v -= B->body->position;
925.         '// v = buT * v;
926.  
927.         v = p(k).vert
928.         Call matrixMultiplyVector(body(A).shape.u, v, tv)
929.         Call vectorAddVectorND(v, tv, body(A).position)
930.  
931.         Call vectorSubVector(v, body(B).position)
932.         Call matrixMultiplyVector(buT, v, tv)
933.  
934.         Call vectorSubVector(s, tv)
935.         d = vectorDot(n, s)
936.  
937.         If d > bestDistance Then
938.             bestDistance = d
939.             bestIndex = i
940.         End If
941.  
942.     Next i
943.  
944.     faceIndex(0) = bestIndex
945.  
946.     collisionPPFindAxisLeastPenetration = bestDistance
947. End Function
948.  
949. '**********************************************************************************************
950. '   Shape Creation Ahead
951. '**********************************************************************************************
952.  
953. Sub shapeCreate (sh As tSHAPE, ty As Integer, radius As _Float)
954.     Dim u As tMATRIX2d
955.     Call matrixSetScalar(u, 1, 0, 0, 1)
956.     sh.ty = ty
957.     sh.radius = radius
958.     sh.u = u
959. End Sub
960.  
961. Sub bodyCreate (body() As tBODY, index As Integer, shape As tSHAPE)
962.     Call vectorSet(body(index).position, 0, 0)
963.     Call vectorSet(body(index).velocity, 0, 0)
964.     body(index).angularVelocity = 0.0
965.     body(index).torque = 0.0
966.     body(index).orient = impulseRandom_float(-cPI, cPI)
967.  
968.     Call vectorSet(body(index).force, 0, 0)
969.     body(index).staticFriction = 0.5
970.     body(index).dynamicFriction = 0.3
971.     body(index).restitution = 0.2
972.     body(index).shape = shape
973. End Sub
974.  
975. Sub boxCreate (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, sizex As _Float, sizey As _Float)
976.     Dim vertlength As Integer: vertlength = 3
977.     Dim verts(vertlength) As tVECTOR2d
978.  
979.     Call vectorSet(verts(0), -sizex, -sizey)
980.     Call vectorSet(verts(1), sizex, -sizey)
981.     Call vectorSet(verts(2), sizex, sizey)
982.     Call vectorSet(verts(3), -sizex, sizey)
983.  
984.     Call vertexSet(p(), pa(), index, verts(), vertlength)
985. End Sub
986.  
987. Sub vShapeCreate (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, sizex As _Float, sizey As _Float)
988.     Dim vertlength As Integer: vertlength = 7
989.     Dim verts(vertlength) As tVECTOR2d
990.  
991.     Call vectorSet(verts(0), -sizex, -sizey)
992.     Call vectorSet(verts(1), sizex, -sizey)
993.     Call vectorSet(verts(2), sizex, sizey)
994.     Call vectorSet(verts(3), -sizex, sizey)
995.     Call vectorSet(verts(4), -sizex, sizey / 2)
996.     Call vectorSet(verts(5), sizex / 2, sizey / 2)
997.     Call vectorSet(verts(6), sizex / 2, -sizey / 2)
998.     Call vectorSet(verts(7), -sizex, sizey / 2)
999.  
1000.     Call vertexSet(p(), pa(), index, verts(), vertlength)
1001. End Sub
1002.  
1003. Sub vertexSet (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, verts() As tVECTOR2d, vertLength As Integer)
1004.     Dim rightMost As Integer: rightMost = 0
1005.     Dim highestXCoord As _Float: highestXCoord = verts(0).x
1006.     Dim i As Integer
1007.     Dim x As _Float
1008.     For i = 1 To vertLength
1009.         x = verts(i).x
1010.         If x > highestXCoord Then
1011.             highestXCoord = x
1012.             rightMost = i
1013.         Else
1014.             If x = highestXCoord Then
1015.                 If verts(i).y < verts(rightMost).y Then
1016.                     rightMost = i
1017.                 End If
1018.             End If
1019.         End If
1020.     Next
1021.     Dim hull(cMAXNUMBEROFPOLYGONS) As Integer
1022.     Dim outCount As Integer: outCount = 0
1023.     Dim indexHull As Integer: indexHull = rightMost
1024.     Dim nextHullIndex As Integer
1025.     Dim e1 As tVECTOR2d
1026.     Dim e2 As tVECTOR2d
1027.     Dim c As _Float
1028.     Do
1029.         hull(outCount) = indexHull
1030.         nextHullIndex = 0
1031.         For i = 1 To vertLength
1032.             If nextHullIndex = indexHull Then
1033.                 nextHullIndex = i
1034.                 _Continue
1035.             End If
1036.             Call vectorSubVectorND(e1, verts(nextHullIndex), verts(hull(outCount)))
1037.             Call vectorSubVectorND(e2, verts(i), verts(hull(outCount)))
1038.             c = vectorCross(e1, e2)
1039.             If c < 0.0 Then nextHullIndex = i
1040.             If c = 0.0 And (vectorLengthSq(e2) > vectorLengthSq(e1)) Then
1041.                 nextHullIndex = i
1042.             End If
1043.         Next
1044.         outCount = outCount + 1
1045.         indexHull = nextHullIndex
1046.         If nextHullIndex = rightMost Then
1047.             pa(index).count = outCount - 1
1048.             Exit Do
1049.         End If
1050.     Loop
1051.  
1052.     If index = 0 Then
1053.         pa(index).start = 0
1054.     Else
1055.         pa(index).start = pa(index - 1).start + pa(index - 1).count + 1
1056.     End If
1057.  
1058.     For i = 0 To vertLength
1059.         p(pa(index).start + i).vert = verts(hull(i))
1060.     Next
1061.     Dim face As tVECTOR2d
1062.     For i = 0 To vertLength
1063.         Call vectorSubVectorND(face, p(pa(index).start + arrayNextIndex(i, pa(index).count)).vert, p(pa(index).start + i).vert)
1064.         Call vectorSet(p(pa(index).start + i).norm, face.y, -face.x)
1065.         Call vectorNormalize(p(pa(index).start + i).norm)
1066.     Next
1067. End Sub
1068.  
1069. Function arrayNextIndex (i As Integer, count As Integer)
1070.     arrayNextIndex = ((i + 1) Mod (count + 1))
1071. End Function
1072.  
1073. Sub renderBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY)
1074.     Dim i As Integer
1075.     For i = 0 To sNUMBEROFBODIES
1076.         'TODO: Put hidden object logic
1077.         If body(i).shape.ty = cSHAPE_CIRCLE Then
1078.             If body(i).shape.texture = 0 Then
1079.                 Call renderWireframeCircle(body(), i)
1080.             Else
1081.                 Call renderTexturedCircle(body(), i)
1082.             End If
1083.         Else If body(i).shape.ty = cSHAPE_POLYGON Then
1084.                 If body(i).shape.texture = 0 Then
1085.                     Call renderWireframePoly(p(), pa(), body(), i)
1086.                 Else
1087.                     Call renderTexturedBox(p(), pa(), body(), i)
1088.                 End If
1089.             End If
1090.         End If
1091.         If body(i).position.x < 0 Then body(i).position.x = _Width
1092.         If body(i).position.x > _Width Then body(i).position.x = 0
1093.         ' If b(index).position.y < 0 Then b(index).position.y = _Height
1094.         If body(i).position.y > _Height Then body(i).position.y = 0
1095.     Next
1096. End Sub
1097.  
1098. Sub renderWireframePoly (p() As tPOLY, pa() As tPOLYATTRIB, b() As tBODY, index As Integer)
1099.     Dim a As tVECTOR2d ' dummy vertices
1100.     Dim b As tVECTOR2d
1101.  
1102.     Dim i, element, element_next As Integer
1103.     For i = 0 To pa(index).count
1104.         element = pa(index).start + i
1105.         element_next = pa(index).start + arrayNextIndex(i, pa(index).count) ' wrap around back to first element
1106.         a = p(element).vert
1107.         b = p(element_next).vert
1108.  
1109.         Call matrixMultiplyVector(b(index).shape.u, a, a)
1110.         Call matrixMultiplyVector(b(index).shape.u, b, b)
1111.         Call vectorAddVector(a, b(index).position)
1112.         Call vectorAddVector(b, b(index).position)
1113.  
1114.         Line (a.x, a.y)-(b.x, b.y), b(index).c
1115.     Next
1116. End Sub
1117.  
1118. Sub renderTexturedBox (p() As tPOLY, pa() As tPOLYATTRIB, b() As tBODY, index As Integer)
1119.     Dim vert(3) As tVECTOR2d
1120.     Dim W, H As Integer
1121.     Dim bm As Long
1122.     bm = b(index).shape.texture
1123.     W = _Width(bm): H = _Height(bm)
1124.     Dim i As Integer
1125.     For i = 0 To 3
1126.         vert(i) = p(pa(index).start + i).vert
1127.         Call matrixMultiplyVector(b(index).shape.u, vert(i), vert(i))
1128.         Call vectorAddVector(vert(i), b(index).position)
1129.     Next
1130.     _MapTriangle (0, 0)-(W - 1, 0)-(W - 1, H - 1), bm To(vert(0).x, vert(0).y)-(vert(1).x, vert(1).y)-(vert(2).x, vert(2).y)
1131.     _MapTriangle (0, 0)-(0, H - 1)-(W - 1, H - 1), bm To(vert(0).x, vert(0).y)-(vert(3).x, vert(3).y)-(vert(2).x, vert(2).y)
1132.  
1133. End Sub
1134.  
1135. Sub renderWireframeCircle (b() As tBODY, index As Integer)
1136.     Circle (b(index).position.x, b(index).position.y), b(index).shape.radius, b(index).c
1137.     Line (b(index).position.x, b(index).position.y)-(b(index).position.x + Cos(b(index).orient) * b(index).shape.radius, b(index).position.y + Sin(b(index).orient) * b(index).shape.radius), b(index).c
1138. End Sub
1139.  
1140. Sub renderTexturedCircle (b() As tBODY, index As Integer)
1141.     Dim vert(3) As tVECTOR2d
1142.     Dim W, H As Integer
1143.     Dim bm As Long
1144.     bm = b(index).shape.texture
1145.     W = _Width(bm): H = _Height(bm)
1146.     Call vectorSet(vert(0), -b(index).shape.radius, -b(index).shape.radius)
1147.     Call vectorSet(vert(1), -b(index).shape.radius, b(index).shape.radius)
1148.     Call vectorSet(vert(2), b(index).shape.radius, b(index).shape.radius)
1149.     Call vectorSet(vert(3), b(index).shape.radius, -b(index).shape.radius)
1150.     Dim i As Integer
1151.     For i = 0 To 3
1152.         Call matrixMultiplyVector(b(index).shape.u, vert(i), vert(i))
1153.         Call vectorAddVector(vert(i), b(index).position)
1154.     Next
1155.     _MapTriangle (0, 0)-(0, H - 1)-(W - 1, H - 1), bm To(vert(0).x, vert(0).y)-(vert(1).x, vert(1).y)-(vert(2).x, vert(2).y)
1156.     _MapTriangle (0, 0)-(W - 1, 0)-(W - 1, H - 1), bm To(vert(0).x, vert(0).y)-(vert(3).x, vert(3).y)-(vert(2).x, vert(2).y)
1157.  
1158. End Sub
1159. Sub polygonSetOrient (b As tBODY, radians As _Float)
1160.     Call matrixSetRadians(b.shape.u, radians)
1161. End Sub
1162.  
1163. '**********************************************************************************************
1164. '   Object initialization Ahead
1165. '**********************************************************************************************
1166.  
1167. Sub circleInitialize (b() As tBODY, index As Integer)
1168.     Call circleComputeMass(b(), index, 1.0)
1169. End Sub
1170.  
1171. Sub circleComputeMass (b() As tBODY, index As Integer, density As _Float)
1172.     b(index).mass = cPI * b(index).shape.radius * b(index).shape.radius * density
1173.     If b(index).mass <> 0 Then
1174.         b(index).invMass = 1.0 / b(index).mass
1175.     Else
1176.         b(index).invMass = 0.0
1177.     End If
1178.  
1179.     b(index).inertia = b(index).mass * b(index).shape.radius * b(index).shape.radius
1180.  
1181.     If b(index).inertia <> 0 Then
1182.         b(index).invInertia = 1.0 / b(index).inertia
1183.     Else
1184.         b(index).invInertia = 0.0
1185.     End If
1186. End Sub
1187.  
1188. Sub polygonInitialize (body() As tBODY, p() As tPOLY, pa() As tPOLYATTRIB, index As Integer)
1189.     Call polygonComputeMass(body(), p(), pa(), index, 1.0)
1190. End Sub
1191.  
1192. Sub polygonComputeMass (b() As tBODY, p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, density As _Float)
1193.     Dim c As tVECTOR2d ' centroid
1194.     Dim p1 As tVECTOR2d
1195.     Dim p2 As tVECTOR2d
1196.     Dim area As _Float
1197.     Dim I As _Float
1198.     Dim k_inv3 As _Float
1199.     Dim D As _Float
1200.     Dim triangleArea As _Float
1201.     Dim weight As _Float
1202.     Dim intx2 As _Float
1203.     Dim inty2 As _Float
1204.     Dim ii As Integer
1205.  
1206.     k_inv3 = 1.0 / 3.0
1207.  
1208.     For ii = 0 To pa(index).count
1209.         p1 = p(pa(index).start + ii).vert
1210.         p2 = p(pa(index).start + arrayNextIndex(ii, pa(index).count)).vert
1211.         D = vectorCross(p1, p2)
1212.         triangleArea = .5 * D
1213.         area = area + triangleArea
1214.         weight = triangleArea * k_inv3
1215.         Call vectorAddVectorScalar(c, p1, weight)
1216.         Call vectorAddVectorScalar(c, p2, weight)
1217.         intx2 = p1.x * p1.x + p2.x * p1.x + p2.x * p2.x
1218.         inty2 = p1.y * p1.y + p2.y * p1.y + p2.y * p2.y
1219.         I = I + (0.25 * k_inv3 * D) * (intx2 + inty2)
1220.     Next ii
1221.  
1222.     Call vectorMultiplyScalar(c, 1.0 / area)
1223.  
1224.     For ii = 0 To pa(index).count
1225.         Call vectorSubVector(p(pa(index).start + ii).vert, c)
1226.     Next
1227.  
1228.     b(index).mass = density * area
1229.     If b(index).mass <> 0.0 Then
1230.         b(index).invMass = 1.0 / b(index).mass
1231.     Else
1232.         b(index).invMass = 0.0
1233.     End If
1234.  
1235.     b(index).inertia = I * density
1236.     If b(index).inertia <> 0 Then
1237.         b(index).invInertia = 1.0 / b(index).inertia
1238.     Else
1239.         b(index).invInertia = 0.0
1240.     End If
1241. End Sub
1242.  
1243. '**********************************************************************************************
1244. '   Vector Math Ahead
1245. '**********************************************************************************************
1246.  
1247. Sub vectorSet (v As tVECTOR2d, x As _Float, y As _Float)
1248.     v.x = x
1249.     v.y = y
1250. End Sub
1251.  
1252. Sub vectorSetVector (o As tVECTOR2d, v As tVECTOR2d)
1253.     o.x = v.x
1254.     o.y = v.y
1255. End Sub
1256.  
1257. Sub vectorNeg (v As tVECTOR2d)
1258.     v.x = -v.x
1259.     v.y = -v.y
1260. End Sub
1261.  
1262. Sub vectorNegND (o As tVECTOR2d, v As tVECTOR2d)
1263.     o.x = -v.x
1264.     o.y = -v.y
1265. End Sub
1266.  
1267. Sub vectorMultiplyScalar (v As tVECTOR2d, s As _Float)
1268.     v.x = v.x * s
1269.     v.y = v.y * s
1270. End Sub
1271.  
1272. Sub vectorMultiplyScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1273.     o.x = v.x * s
1274.     o.y = v.y * s
1275. End Sub
1276.  
1277. Sub vectorDivideScalar (v As tVECTOR2d, s As _Float)
1278.     v.x = v.x / s
1279.     v.y = v.y / s
1280. End Sub
1281.  
1282. Sub vectorDivideScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1283.     o.x = v.x / s
1284.     o.y = v.y / s
1285. End Sub
1286.  
1287. Sub vectorAddScalar (v As tVECTOR2d, s As _Float)
1288.     v.x = v.x + s
1289.     v.y = v.y + s
1290. End Sub
1291.  
1292. Sub vectorAddScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1293.     o.x = v.x + s
1294.     o.y = v.y + s
1295. End Sub
1296.  
1297. Sub vectorMultiplyVector (v As tVECTOR2d, m As tVECTOR2d)
1298.     v.x = v.x * m.x
1299.     v.y = v.y * m.y
1300. End Sub
1301.  
1302. Sub vectorMultiplyVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1303.     o.x = v.x * m.x
1304.     o.y = v.y * m.y
1305. End Sub
1306.  
1307. Sub vectorDivideVector (v As tVECTOR2d, m As tVECTOR2d)
1308.     v.x = v.x / m.x
1309.     v.y = v.y / m.y
1310. End Sub
1311.  
1312. Sub vectorAddVector (v As tVECTOR2d, m As tVECTOR2d)
1313.     v.x = v.x + m.x
1314.     v.y = v.y + m.y
1315. End Sub
1316.  
1317. Sub vectorAddVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1318.     o.x = v.x + m.x
1319.     o.y = v.y + m.y
1320. End Sub
1321.  
1322. Sub vectorAddVectorScalar (v As tVECTOR2d, m As tVECTOR2d, s As _Float)
1323.     v.x = v.x + m.x * s
1324.     v.y = v.y + m.y * s
1325. End Sub
1326.  
1327. Sub vectorAddVectorScalarND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d, s As _Float)
1328.     o.x = v.x + m.x * s
1329.     o.y = v.y + m.y * s
1330. End Sub
1331.  
1332. Sub vectorSubVector (v As tVECTOR2d, m As tVECTOR2d)
1333.     v.x = v.x - m.x
1334.     v.y = v.y - m.y
1335. End Sub
1336.  
1337. Sub vectorSubVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1338.     o.x = v.x - m.x
1339.     o.y = v.y - m.y
1340. End Sub
1341.  
1342. Function vectorLengthSq (v As tVECTOR2d)
1343.     vectorLengthSq = v.x * v.x + v.y * v.y
1344. End Function
1345.  
1346. Function vectorLength (v As tVECTOR2d)
1347.     vectorLength = Sqr(vectorLengthSq(v))
1348. End Function
1349.  
1350. Sub vectorRotate (v As tVECTOR2d, radians As _Float)
1351.     Dim c, s, xp, yp As _Float
1352.     c = Cos(radians)
1353.     s = Sin(radians)
1354.     xp = v.x * c - v.y * s
1355.     yp = v.x * s + v.y * c
1356.     v.x = xp
1357.     v.y = yp
1358. End Sub
1359.  
1360. Sub vectorNormalize (v As tVECTOR2d)
1361.     Dim lenSQ, invLen As _Float
1362.     lenSQ = vectorLengthSq(v)
1363.     If lenSQ > cEPSILON_SQ Then
1364.         invLen = 1.0 / Sqr(lenSQ)
1365.         v.x = v.x * invLen
1366.         v.y = v.y * invLen
1367.     End If
1368. End Sub
1369.  
1370. Sub vectorMin (a As tVECTOR2d, b As tVECTOR2d, o As tVECTOR2d)
1371.     o.x = scalarMin(a.x, b.x)
1372.     o.y = scalarMin(a.y, b.y)
1373. End Sub
1374.  
1375. Sub vectorMax (a As tVECTOR2d, b As tVECTOR2d, o As tVECTOR2d)
1376.     o.x = scalarMax(a.x, b.x)
1377.     o.y = scalarMax(a.y, b.y)
1378. End Sub
1379.  
1380. Function vectorDot (a As tVECTOR2d, b As tVECTOR2d)
1381.     vectorDot = a.x * b.x + a.y * b.y
1382. End Function
1383.  
1384. Function vectorSqDist (a As tVECTOR2d, b As tVECTOR2d)
1385.     Dim dx, dy As _Float
1386.     dx = b.x - a.x
1387.     dy = b.y - a.y
1388.     vectorSqDist = dx * dx + dy * dy
1389. End Function
1390.  
1391. Function vectorDistance (a As tVECTOR2d, b As tVECTOR2d)
1392.     vectorDistance = Sqr(vectorSqDist(a, b))
1393. End Function
1394.  
1395. Function vectorCross (a As tVECTOR2d, b As tVECTOR2d)
1396.     vectorCross = a.x * b.y - a.y * b.x
1397. End Function
1398.  
1399. Sub vectorCrossScalar (o As tVECTOR2d, v As tVECTOR2d, a As _Float)
1400.     o.x = v.y * -a
1401.     o.y = v.x * a
1402. End Sub
1403.  
1404. Function vectorArea (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1405.     vectorArea = (((b.x - a.x) * (c.y - a.y)) - ((c.x - a.x) * (b.y - a.y)))
1406. End Function
1407.  
1408. Function vectorLeft (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1409.     vectorLeft = vectorArea(a, b, c) > 0
1410. End Function
1411.  
1412. Function vectorLeftOn (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1413.     vectorLeftOn = vectorArea(a, b, c) >= 0
1414. End Function
1415.  
1416. Function vectorRight (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1417.     vectorRight = vectorArea(a, b, c) < 0
1418. End Function
1419.  
1420. Function vectorRightOn (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1421.     vectorRightOn = vectorArea(a, b, c) <= 0
1422. End Function
1423.  
1424. Function vectorCollinear (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d, thresholdAngle As _Float)
1425.     If (thresholdAngle = 0) Then
1426.         vectorCollinear = (vectorArea(a, b, c) = 0)
1427.     Else
1428.         Dim ab As tVECTOR2d
1429.         Dim bc As tVECTOR2d
1430.         Dim dot As _Float
1431.         Dim magA As _Float
1432.         Dim magB As _Float
1433.         Dim angle As _Float
1434.  
1435.         ab.x = b.x - a.x
1436.         ab.y = b.y - a.y
1437.         bc.x = c.x - b.x
1438.         bc.y = c.y - b.y
1439.  
1440.         dot = ab.x * bc.x + ab.y * bc.y
1441.         magA = Sqr(ab.x * ab.x + ab.y * ab.y)
1442.         magB = Sqr(bc.x * bc.x + bc.y * bc.y)
1443.         angle = _Acos(dot / (magA * magB))
1444.         vectorCollinear = angle < thresholdAngle
1445.     End If
1446. End Function
1447.  
1448. Sub vectorGetSupport (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, dir As tVECTOR2d, bestVertex As tVECTOR2d)
1449.     Dim bestProjection As _Float
1450.     Dim v As tVECTOR2d
1451.     Dim projection As _Float
1452.     Dim i As Integer
1453.     bestVertex.x = -9999999
1454.     bestVertex.y = -9999999
1455.     bestProjection = -9999999
1456.  
1457.     For i = 0 To pa(index).count
1458.         v = p(i + pa(index).start).vert
1459.         projection = vectorDot(v, dir)
1460.         If projection > bestProjection Then
1461.             bestVertex = v
1462.             bestProjection = projection
1463.         End If
1464.     Next
1465. End Sub
1466.  
1467. '**********************************************************************************************
1468. '   Matrix Stuff Ahead
1469. '**********************************************************************************************
1470.  
1471. Sub matrixSetRadians (m As tMATRIX2d, radians As _Float)
1472.     Dim c As _Float
1473.     Dim s As _Float
1474.     c = Cos(radians)
1475.     s = Sin(radians)
1476.     m.m00 = c
1477.     m.m01 = -s
1478.     m.m10 = s
1479.     m.m11 = c
1480. End Sub
1481.  
1482. Sub matrixSetScalar (m As tMATRIX2d, a As _Float, b As _Float, c As _Float, d As _Float)
1483.     m.m00 = a
1484.     m.m01 = b
1485.     m.m10 = c
1486.     m.m11 = d
1487. End Sub
1488.  
1489. Sub matrixAbs (m As tMATRIX2d, o As tMATRIX2d)
1490.     o.m00 = Abs(m.m00)
1491.     o.m01 = Abs(m.m01)
1492.     o.m10 = Abs(m.m10)
1493.     o.m11 = Abs(m.m11)
1494. End Sub
1495.  
1496. Sub matrixGetAxisX (m As tMATRIX2d, o As tVECTOR2d)
1497.     o.x = m.m00
1498.     o.y = m.m10
1499. End Sub
1500.  
1501. Sub matrixGetAxisY (m As tMATRIX2d, o As tVECTOR2d)
1502.     o.x = m.m01
1503.     o.y = m.m11
1504. End Sub
1505.  
1506. Sub matrixTransposeI (m As tMATRIX2d)
1507.     Swap m.m01, m.m10
1508. End Sub
1509.  
1510. Sub matrixTranspose (m As tMATRIX2d, o As tMATRIX2d)
1511.     o.m00 = m.m00
1512.     o.m01 = m.m10
1513.     o.m10 = m.m01
1514.     o.m11 = m.m11
1515. End Sub
1516.  
1517. Sub matrixMultiplyVector (m As tMATRIX2d, v As tVECTOR2d, o As tVECTOR2d)
1518.     Dim t As tVECTOR2d
1519.     t.x = m.m00 * v.x + m.m01 * v.y
1520.     t.y = m.m10 * v.x + m.m11 * v.y
1521.     o = t
1522. End Sub
1523.  
1524. Sub matrixMultiplyMatrix (m As tMATRIX2d, x As tMATRIX2d, o As tMATRIX2d)
1525.     o.m00 = m.m00 * x.m00 + m.m01 * x.m10
1526.     o.m01 = m.m00 * x.m01 + m.m01 * x.m11
1527.     o.m10 = m.m10 * x.m00 + m.m11 * x.m10
1528.     o.m11 = m.m10 * x.m01 + m.m11 * x.m11
1529. End Sub
1530.  
1531. '**********************************************************************************************
1532. '   Mostly Unused Stuff Ahead
1533. '**********************************************************************************************
1534.  
1535. Sub polygonMakeCCW (obj As tTRIANGLE)
1536.     If vectorLeft(obj.a, obj.b, obj.c) = 0 Then
1537.         Swap obj.a, obj.c
1538.     End If
1539. End Sub
1540.  
1541. Function polygonIsReflex (t As tTRIANGLE)
1542.     polygonIsReflex = vectorRight(t.a, t.b, t.c)
1543. End Function
1544.  
1545. Function scalarMin (a As _Float, b As _Float)
1546.     If a < b Then
1547.         scalarMin = a
1548.     Else
1549.         scalarMin = b
1550.     End If
1551. End Function
1552.  
1553. Function scalarMax (a As _Float, b As _Float)
1554.     If a > b Then
1555.         scalarMax = a
1556.     Else
1557.         scalarMax = b
1558.     End If
1559. End Function
1560.  
1561. Sub lineIntersection (l1 As tLINE2d, l2 As tLINE2d, o As tVECTOR2d)
1562.     Dim a1, b1, c1, a2, b2, c2, det As _Float
1563.     o.x = 0
1564.     o.y = 0
1565.     a1 = l1.b.y - l1.a.y
1566.     b1 = l1.a.x - l1.b.x
1567.     c1 = a1 * l1.a.x + b1 * l1.a.y
1568.     a2 = l2.b.y - l2.a.y
1569.     b2 = l2.a.x - l2.b.x
1570.     c2 = a2 * l2.a.x + b2 * l2.a.y
1571.     det = a1 * b2 - a2 * b1
1572.  
1573.     If Int(det * cPRECISION) <> 0 Then
1574.         o.x = (b2 * c1 - b1 * c2) / det
1575.         o.y = (a1 * c2 - a2 * c1) / det
1576.     End If
1577. End Sub
1578.  
1579. Function lineSegmentsIntersect (l1 As tLINE2d, l2 As tLINE2d)
1580.     Dim dx, dy, da, db, s, t As _Float
1581.     dx = l1.b.x - l1.a.x
1582.     dy = l1.b.y - l1.a.y
1583.     da = l2.b.x - l2.a.x
1584.     db = l2.b.y - l2.a.y
1585.     If da * dy - db * dx = 0 Then
1586.         lineSegmentsIntersect = 0
1587.     Else
1588.         s = (dx * (l2.a.y - l1.a.y) + dy * (l1.a.x - l2.a.x)) / (da * dy - db * dx)
1589.         t = (da * (l1.a.y - l2.a.y) + db * (l2.a.x - l1.a.x)) / (db * dx - da * dy)
1590.         lineSegmentsIntersect = (s >= 0 And s <= 1 And t >= 0 And t <= 1)
1591.     End If
1592. End Function
1593.  
1594. '**********************************************************************************************
1595. '   Impulse Specific Math Ahead
1596. '**********************************************************************************************
1597.  
1598. Function impulseEqual (a As _Float, b As _Float)
1599.     impulseEqual = Abs(a - b) <= cEPSILON
1600. End Function
1601.  
1602. Function impulseClamp (min As _Float, max As _Float, a As _Float)
1603.     If a < min Then
1604.         impulseClamp = min
1605.     Else If a > max Then
1606.             impulseClamp = max
1607.         Else
1608.             impulseClamp = a
1609.         End If
1610.     End If
1611. End Function
1612.  
1613. Function impulseRound (a As _Float)
1614.     impulseRound = Int(a + 0.5)
1615. End Function
1616.  
1617. Function impulseRandom_float (min As _Float, max As _Float)
1618.     impulseRandom_float = ((max - min) * Rnd + min)
1619. End Function
1620.  
1621. Function impulseRandomInteger (min As Integer, max As Integer)
1622.     impulseRandomInteger = Int((max - min) * Rnd + min)
1623. End Function
1624.  
1625. Function impulseGT (a As _Float, b As _Float)
1626.     impulseGT = (a >= b * cBIAS_RELATIVE + a * cBIAS_ABSOLUTE)
1627. End Function
1628.  
1629. '**********************************************************************************************
1630. '   Troubleshooting Tools
1631. '**********************************************************************************************
1632.  
1633. Sub printMatrix (u As tMATRIX2d, n As Integer)
1634.     Print "---------------------------"
1635.     Print n; " u:"; u.m00; "|"; u.m10
1636.     Print "       "; u.m10; "|"; u.m11
1637. End Sub
1638.  
1639.  
1640. '**********************************************************************************************
1641. '   Generate Bitmap
1642. '**********************************************************************************************
1643.  
1644. Sub generateBitmap (bm() As Long)
1645.     Dim cl As _Unsigned Long
1646.     Dim rleCount, y, x, i As Integer
1647.  
1648.     Data 0,30,4289110427,4,0,52,4289110427,15,0,44,4289110427,21,0,38,4289110427,7
1649.     Data 4281808695,11,4289110427,7,0,34,4289110427,5,4281808695,18,4289110427,5,0,30,4289110427,4
1650.     Data 4281808695,23,4289110427,4,0,28,4289110427,3,4281808695,27,4289110427,3,0,25,4289110427,3
1651.     Data 4281808695,31,4289110427,3,0,22,4289110427,3,4281808695,33,4289110427,3,0,20,4289110427,3
1652.     Data 4281808695,35,4289110427,3,0,18,4289110427,3,4281808695,38,4289110427,2,0,16,4289110427,3
1653.     Data 4281808695,40,4289110427,2,0,14,4289110427,3,4281808695,42,4289110427,2,0,13,4289110427,2
1654.     Data 4281808695,43,4289110427,3,0,11,4289110427,2,4281808695,45,4289110427,2,0,10,4289110427,2
1655.     Data 4281808695,47,4289110427,2,0,8,4289110427,2,4281808695,49,4289110427,2,0,7,4289110427,2
1656.     Data 4281808695,49,4289110427,2,0,6,4289110427,2,4281808695,51,4289110427,2,0,5,4289110427,2
1657.     Data 4281808695,51,4289110427,2,0,5,4289110427,1,4281808695,53,4289110427,2,0,3,4289110427,2
1658.     Data 4281808695,53,4289110427,2,0,3,4289110427,2,4281808695,54,4289110427,1,0,3,4289110427,1
1659.     Data 4281808695,7,4281084972,0,4279703319,0,4279637526,10,4280492835,0,4281808695,7,4279637526,14,4279834905,0
1660.     Data 4281742902,0,4281808695,8,4289110427,2,0,1,4289110427,2,4281808695,6,4279637526,15,4281808695,6
1661.     Data 4279637526,17,4281808695,7,4289110427,2,0,1,4289110427,2,4281808695,5,4279637526,1,4282412608,0
1662.     Data 4284394590,14,4281808695,5,4279637526,1,4284394590,15,4284394334,0,4281808695,7,4289110427,1,0,1
1663.     Data 4289110427,1,4281808695,6,4279637526,0,4280034076,0,4284394590,16,4281808695,4,4279637526,1,4284394590,16
1664.     Data 4284129114,0,4281808695,6,4289110427,1,0,1,4289110427,1,4281808695,6,4279637526,0,4284394590,17
1665.     Data 4283333454,0,4281808695,3,4279637526,1,4284394590,17,4281808695,6,4289110427,2,0,0,4289110427,1
1666.     Data 4281808695,6,4279637526,0,4284394590,3,4281808695,9,4279637526,0,4284394590,3,4281808695,3,4279637526,1
1667.     Data 4284394590,2,4281808695,9,4279637526,0,4284394590,3,4281808695,6,4289110427,2,0,0,4289110427,1
1668.     Data 4281808695,6,4279637526,0,4284394590,3,4281808695,9,4279637526,0,4284394590,3,4281808695,3,4279637526,1
1669.     Data 4284394590,2,4281808695,9,4279637526,0,4284394590,3,4281808695,6,4289110427,5,4281808695,6,4279637526,0
1670.     Data 4284394590,3,4281808695,9,4279637526,0,4284394590,3,4281808695,3,4279637526,1,4284394590,2,4281808695,9
1671.     Data 4279637526,0,4284394590,3,4281808695,6,4289110427,5,4281808695,6,4279637526,0,4284394590,3,4281808695,9
1672.     Data 4279637526,0,4284394590,3,4281808695,3,4279637526,1,4284394590,2,4279637526,10,4284394590,3,4281808695,6
1673.     Data 4289110427,5,4281808695,6,4279637526,0,4284394590,3,4281808695,9,4279637526,0,4284394590,3,4281808695,3
1674.     Data 4279637526,1,4284394590,17,4281808695,6,4289110427,5,4281808695,6,4279637526,0,4284394590,3,4281808695,9
1675.     Data 4279637526,0,4284394590,3,4281808695,3,4279637526,1,4284394590,16,4281808695,7,4289110427,5,4281808695,6
1676.     Data 4279637526,0,4284394590,3,4281808695,7,4281084972,0,4279703319,0,4279637526,0,4284394590,3,4281808695,3
1677.     Data 4279637526,1,4284394590,17,4281808695,6,4289110427,2,0,0,4289110427,1,4281808695,6,4279637526,0
1678.     Data 4284394590,3,4281808695,6,4279637526,3,4284394590,3,4281808695,3,4279637526,1,4284394590,17,4281808695,6
1679.     Data 4289110427,2,0,0,4289110427,1,4281808695,6,4279637526,0,4284394590,3,4281808695,5,4279637526,1
1680.     Data 4282412608,0,4284394590,5,4281808695,3,4279637526,1,4284394590,2,4281808695,9,4279637526,0,4284394590,3
1681.     Data 4281808695,6,4289110427,2,0,0,4289110427,1,4281808695,6,4279637526,0,4284394590,3,4281808695,5
1682.     Data 4279637526,0,4280034076,0,4284394590,6,4281808695,3,4279637526,1,4284394590,2,4281808695,9,4279637526,0
1683.     Data 4284394590,3,4281808695,6,4289110427,1,0,1,4289110427,2,4281808695,5,4279637526,0,4284394590,3
1684.     Data 4279637526,6,4284394590,7,4281808695,3,4279637526,1,4284394590,2,4279637526,10,4284394590,3,4281808695,6
1685.     Data 4289110427,1,0,1,4289110427,2,4281808695,5,4279637526,0,4284394590,16,4283532625,0,4281875000,0
1686.     Data 4281808695,3,4279637526,1,4284394590,17,4281808695,5,4289110427,2,0,2,4289110427,1,4281808695,6
1687.     Data 4284394590,15,4281808695,6,4279637526,1,4284394590,17,4281808695,5,4289110427,2,0,2,4289110427,1
1688.     Data 4281808695,7,4284394590,13,4281808695,7,4279637526,1,4284394590,16,4282803270,0,4281808695,5,4289110427,1
1689.     Data 0,3,4289110427,2,4281808695,7,4284394590,12,4281808695,9,4284394590,15,4282670916,0,4281808695,5
1690.     Data 4289110427,2,0,4,4289110427,1,4281808695,53,4289110427,2,0,4,4289110427,2,4281808695,52
1691.     Data 4289110427,1,0,5,4289110427,2,4281808695,51,4289110427,2,0,6,4289110427,2,4281808695,50
1692.     Data 4289110427,1,0,7,4289110427,2,4281808695,49,4289110427,2,0,8,4289110427,2,4281808695,47
1693.     Data 4289110427,2,0,10,4289110427,2,4281808695,46,4289110427,1,0,12,4289110427,2,4281808695,44
1694.     Data 4289110427,2,0,12,4289110427,2,4281808695,43,4289110427,2,0,14,4289110427,2,4281808695,41
1695.     Data 4289110427,2,0,16,4289110427,2,4281808695,39,4289110427,2,0,18,4289110427,3,4281808695,36
1696.     Data 4289110427,2,0,20,4289110427,3,4281808695,33,4289110427,3,0,22,4289110427,3,4281808695,31
1697.     Data 4289110427,3,0,24,4289110427,4,4281808695,28,4289110427,3,0,27,4289110427,4,4281808695,24
1698.     Data 4289110427,3,0,30,4289110427,5,4281808695,19,4289110427,5,0,33,4289110427,6,4281808695,13
1699.     Data 4289110427,6,0,37,4289110427,23,0,42,4289110427,17,0,49,4289110427,9,0,26
1700.  
1701.  
1702.     Data 4278190160,1484,4278650685,0,4279637527,0,4279637526,13,4278190160,5,4279637526,3,4278190160,10,4279637526,3
1703.     Data 4278190160,21,4279637526,16,4278190160,5,4279637526,3,4278190160,10,4279637526,3,4278190160,20,4279637526,1
1704.     Data 4286280720,0,4290950923,16,4278190160,3,4279637526,1,4290950923,2,4278190160,9,4279637526,0,4290950923,3
1705.     Data 4278190160,19,4279637526,0,4280624149,0,4290950923,17,4278190160,3,4279637526,1,4290950923,2,4278190160,9
1706.     Data 4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,18,4278190160,3,4279637526,1,4290950923,2
1707.     Data 4278190160,9,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3,4278190160,18,4279637526,1
1708.     Data 4290950923,2,4278190160,9,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3,4278190160,18
1709.     Data 4279637526,1,4290950923,2,4278190160,9,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3
1710.     Data 4278190160,18,4279637526,1,4290950923,2,4278190160,9,4279637526,0,4290950923,3,4278190160,19,4279637526,0
1711.     Data 4290950923,3,4279637526,10,4279505947,0,4278190160,6,4279374370,0,4279637526,0,4290950923,2,4279637526,10
1712.     Data 4290950923,3,4278190160,19,4279637526,0,4290950923,16,4278190160,6,4279637526,0,4290950923,17,4278190160,19
1713.     Data 4279637526,0,4290950923,17,4278190160,5,4278255950,0,4290950923,17,4278190160,19,4279637526,0,4290950923,17
1714.     Data 4282070843,0,4278190160,5,4278584910,0,4290950923,16,4278190160,19,4279637526,0,4290950923,17,4290622221,0
1715.     Data 4278190160,7,4286149157,0,4290950923,14,4278190160,19,4279637526,0,4290950923,3,4278190160,9,4279637526,0
1716.     Data 4290950923,3,4278190160,18,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3,4278190160,9
1717.     Data 4279637526,0,4290950923,3,4278190160,18,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3
1718.     Data 4279637526,10,4290950923,3,4278190160,18,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,17
1719.     Data 4290687756,0,4278190160,18,4279637526,0,4290950923,3,4278190160,20,4290950923,17,4282597176,0,4278190160,18
1720.     Data 4279637526,0,4290950923,3,4278190160,21,4290950923,16,4278190160,19,4279637526,0,4290950923,3,4278190160,21
1721.     Data 4278255952,0,4290950923,14,4278190160,21,4290950923,3,4278190160,1353
1722.  
1723.     For i = 0 To 1
1724.  
1725.         bm(i) = _NewImage(64, 64, 32)
1726.         _Dest bm(i)
1727.  
1728.         Read cl
1729.         Read rleCount
1730.  
1731.         For y = 0 To 63
1732.             For x = 0 To 63
1733.                 PSet (x, y), cl
1734.                 rleCount = rleCount - 1
1735.                 If rleCount < 0 Then
1736.                     Read cl
1737.                     Read rleCount
1738.                 End If
1739.             Next
1740.         Next
1741.     Next
1742.  
1743.     _Dest 0
1744. End Sub
1745.  

[Richard Frost]

I get 22 fps average, 35 tops on a 12 year old laptop running Win10. 

That's a great simulation of a terrible elevator system.  I'll take the
stairs.  Oh, the stairs are in there too.  Best to stay out of the building.

[AndyA]

That's a very well done physics engine!

I got between 90 and 200 FPS, it flickered so quickly, it was hard to read.

What method of indexing the objects did you use, a hash table or linked list? Maybe a blend of the two methods.

I looked at the code, but since I haven't use either, it kind of went over my head.

Oh well, maybe you could give a quick overview of how you keep track of everything.

It seems that this 2D physics engine could handle many different types of applications. Angry Birds, pinball, pachinko, etc. 

[justsomeguy]

Thanks for that!

As far as keeping track of objects it is merely an entry into a couple arrays. There is currently three arrays that handle the rigid bodies.
 

Code: QB64: [Select]

1. Dim poly(cMAXNUMBEROFPOLYGONS) As tPOLY
2. Dim polyattributes(cMAXNUMBEROFPOLYGONS) As tPOLYATTRIB
3. Dim body(cMAXNUMBEROFOBJECTS) As tBODY

• Poly is a monolithic list of vertices for all objects.
• Polyattributes is for keeping track of which vertices are for each object.
• Body is for keeping track of each rigid body (i.e. position, velocity etc.)

It's a bit of a mess and I plan on circling back to it and rethink,refactor and rename. I spent weeks of writing code without knowing how it would turn out or even being able to properly test it. So, not everything is optimal :)

Right now my focus is...

• Getting joints working properly, that will expand its range of uses (simple cars and motorcycles.)
• Making collision information easier access.
• Camera tools, so that games like angry birds can exceed the size of the screen
• Make it more approachable for a beginner to use. Simplify scene building and object management.
• Perhaps quad-trees to optimize the collision.
• Multithreading if I really want to punish myself.
• Whatever the community thinks it needs.

Thanks for the comment!

[AndyA]

Games like moto-cross, mario kart would be much easier with joints. For simple games with low poly counts (like billiards or pinball) the arrays seem like more than  enough to keep track of everything.

At any rate I'll be keeping an eye on your progress, as this would be a very nice addition to something like the 'QB64 tool box' (where SUBs/Functions and libraries) are posted for others to utilize. Whatever you do would be great as I haven't seen any physics engine on this board. So many possible applications for physics base simulations and such.

[justsomeguy]

Hello

I have a new update.

• Joints are now working, more work needs to be done with the management, and constraints.
• The demo is a bit more interactive, add a hedgehog that you can move around with arrow keys or WASD.
• Fixed the FPS counter.
• Set '_LIMIT 120' so that the hegehog wouldn't lag so bad.
• Renamed Engine to FzxNGN. Because vowels are obsolete.
• Added some collision query tools.

Please enjoy and share with me your feedback!

Thanks

Code: QB64: [Select]

1. Option _Explicit
2. '**********************************************************************************************
3. '   FzxNGN written by justsomeguy
4. '   Physics code ported from RandyGaul's Impulse Engine
5. '   https://github.com/RandyGaul/ImpulseEngine
6. '   http://RandyGaul.net
7. '**********************************************************************************************
8. '/*
9. '    Copyright (c) 2013 Randy Gaul http://RandyGaul.net
10.  
11. '    This software is provided 'as-is', without any express or implied
12. '    warranty. In no event will the authors be held liable for any damages
13. '    arising from the use of this software.
14.  
15. '    Permission is granted to anyone to use this software for any purpose,
16. '    including commercial applications, and to alter it and redistribute it
17. '    freely, subject to the following restrictions:
18. '      1. The origin of this software must not be misrepresented; you must not
19. '         claim that you wrote the original software. If you use this software
20. '         in a product, an acknowledgment in the product documentation would be
21. '         appreciated but is not required.
22. '      2. Altered source versions must be plainly marked as such, and must not be
23. '         misrepresented as being the original software.
24. '      3. This notice may not be removed or altered from any source distribution.
25. '
26. '    Port to QB64 by justsomeguy
27. '*/
28. '
29.  
30. '**********************************************************************************************
31. '   Setup Types and Variables
32. '**********************************************************************************************
33. Type tVECTOR2d
34.     x As _Float
35.     y As _Float
36. End Type
37.  
38. Type tLINE2d ' Not used
39.     a As tVECTOR2d
40.     b As tVECTOR2d
41. End Type
42.  
43. Type tFACE2d ' Not used
44.     f0 As tVECTOR2d
45.     f1 As tVECTOR2d
46. End Type
47.  
48. Type tTRIANGLE ' Not used
49.     a As tVECTOR2d
50.     b As tVECTOR2d
51.     c As tVECTOR2d
52. End Type
53.  
54. Type tMATRIX2d
55.     m00 As _Float
56.     m01 As _Float
57.     m10 As _Float
58.     m11 As _Float
59. End Type
60.  
61. Type tSHAPE
62.     ty As Integer ' cSHAPE_CIRCLE = 1, cSHAPE_POLYGON = 2
63.     radius As _Float ' Only necessary for circle shapes
64.     u As tMATRIX2d ' Only neceassary for polygons
65.     texture As Long
66.     flipTexture As Integer 'flag for flipping texture depending on direction
67. End Type
68.  
69. Type tPOLY 'list of vertices for all objects in simulation
70.     vert As tVECTOR2d
71.     norm As tVECTOR2d
72. End Type
73.  
74. Type tPOLYATTRIB 'keep track of polys in monlithic list of vertices
75.     start As Integer ' starting vertex of the polygon
76.     count As Integer ' number of vertices in polygon
77. End Type
78.  
79. Type tBODY
80.     position As tVECTOR2d
81.     velocity As tVECTOR2d
82.     force As tVECTOR2d
83.     angularVelocity As _Float
84.     torque As _Float
85.     orient As _Float
86.     mass As _Float
87.     invMass As _Float
88.     inertia As _Float
89.     invInertia As _Float
90.     staticFriction As _Float
91.     dynamicFriction As _Float
92.     restitution As _Float
93.     shape As tSHAPE
94.     c As Long ' color
95.     visible As Integer 'Hide a body ;)
96. End Type
97.  
98. Type tMANIFOLD
99.     A As Integer
100.     B As Integer
101.     penetration As _Float
102.     normal As tVECTOR2d
103.     contactCount As Integer
104.     e As _Float
105.     df As _Float
106.     sf As _Float
107. End Type
108.  
109. Type tHIT
110.     A As Integer
111.     B As Integer
112.     position As tVECTOR2d
113.     force As _Float
114. End Type
115.  
116. Type tJOINT
117.     M As tMATRIX2d
118.     localAnchor1 As tVECTOR2d
119.     localAnchor2 As tVECTOR2d
120.     r1 As tVECTOR2d
121.     r2 As tVECTOR2d
122.     bias As tVECTOR2d
123.     P As tVECTOR2d
124.     body1 As Integer
125.     body2 As Integer
126.     biasFactor As _Float
127.     softness As _Float
128. End Type
129.  
130. Const cSHAPE_CIRCLE = 1
131. Const cSHAPE_POLYGON = 2
132. Const cPRECISION = 100
133. Const cMAXNUMOFTRIANGLES = 100
134. Const cMAXNUMBEROFOBJECTS = 1000 ' Max number of objects at one time
135. Const cMAXNUMBEROFPOLYGONS = 10000 ' Max number of total vertices included in all objects
136. Const cMAXNUMBEROFJOINTS = 100
137. Const cMAXNUMBEROFHITS = 1000
138. Const cPI = 3.14159
139. Const cEPSILON = 0.0001
140. Const cEPSILON_SQ = cEPSILON * cEPSILON
141. Const cBIAS_RELATIVE = 0.95
142. Const cBIAS_ABSOLUTE = 0.01
143. Const cDT = 1.0 / 20.0
144. Const cITERATIONS = 10
145. Const cPENETRATION_ALLOWANCE = 0.05
146. Const cPENETRATION_CORRECTION = 0.4 ' misspelled in original code
147. Const cPARAMETER_POSITION = 1
148. Const cPARAMETER_VELOCITY = 2
149. Const cPARAMETER_FORCE = 3
150. Const cPARAMETER_ANGULARVELOCITY = 4
151. Const cPARAMETER_TORQUE = 5
152. Const cPARAMETER_ORIENT = 6
153. Const cPARAMETER_STATICFRICTION = 7
154. Const cPARAMETER_DYNAMICFRICTION = 8
155. Const cPARAMETER_COLOR = 9
156. Const cPARAMETER_VISIBLE = 10
157. Const cPARAMETER_STATIC = 11
158. Const cPARAMETER_TEXTURE = 12
159. Const cPARAMETER_FLIPTEXTURE = 13
160. Const cRENDER_JOINTS = 0
161. Const cRENDER_COLLISIONS = 0
162. Const cPLAYER_FORCE = 1000000
163.  
164. Dim Shared sGRAVITY As tVECTOR2d: Call vectorSet(sGRAVITY, 0.0, 50.0)
165. Dim Shared sRESTING As _Float: Dim o As tVECTOR2d: Call vectorMultiplyScalarND(o, sGRAVITY, cDT): sRESTING = vectorLengthSq(o) + cEPSILON
166. Dim Shared sNUMBEROFBODIES As Integer: sNUMBEROFBODIES = 50 ' 0 is included - Don't go under 25 for the current scene
167. Dim Shared sNUMBEROFJOINTS As Integer: sNUMBEROFJOINTS = 12 ' if zero then no joints at all
168.  
169. Dim poly(cMAXNUMBEROFPOLYGONS) As tPOLY
170. Dim polyattributes(cMAXNUMBEROFPOLYGONS) As tPOLYATTRIB
171. Dim body(cMAXNUMBEROFOBJECTS) As tBODY
172. Dim joints(cMAXNUMBEROFJOINTS) As tJOINT
173. Dim hits(cMAXNUMBEROFHITS) As tHIT
174.  
175. Dim timerOne As Integer
176. Dim Shared fps As Integer
177. Dim Shared fpsLast As Integer
178.  
179. Const cSCENE_USER = 0
180. Const cSCENE_FLOOR = 1
181. Const cSCENE_SPINNEROFDEATH = 2
182. Const cSCENE_RIGHTRAMP = 3
183. Const cSCENE_LEFTRAMP = 4
184. Const cSCENE_DOZEROFDOOM = 5
185. Const cSCENE_ELEVATOROFTERROR = 6
186. Const cSCENE_RIGHTWALL = 7
187. Const cSCENE_ELEVATORKICKER = 8
188. Const cSCENE_PIVOT = 9
189. Const cSCENE_PENDULUM = 10
190.  
191. '**********************************************************************************************
192. _Title "FzxNGN" ' vowels are obsolete
193. Screen _NewImage(1024, 768, 32)
194.  
195. timerOne = _FreeTimer
196. On Timer(timerOne, 1) renderFps
197. Timer(timerOne) On
198.  
199. Randomize Timer
200. Call buildSimpleScene(poly(), polyattributes(), body(), joints())
201. '**********************************************************************************************
202. _PrintMode _KeepBackground
203. Do: fps = fps + 1
204.     Cls , _RGB32(28, 28, 22)
205.     Call impulseStep(poly(), polyattributes(), body(), joints(), cDT, cITERATIONS, hits())
206.     Call renderBodies(poly(), polyattributes(), body(), joints(), hits())
207.     Call animateScene(body(), hits())
208.     Locate 1, 60: Print "FPS:"; (fpsLast)
209.     _Display
210.     _Limit 120
211. Loop Until _KeyHit = 27
212. System
213. '**********************************************************************************************
214. '   End of Main loop
215. '**********************************************************************************************
216.  
217. '**********************************************************************************************
218. '   Scene Creation and Handling Ahead
219. '**********************************************************************************************
220. Sub animateScene (body() As tBODY, hits() As tHIT)
221.  
222.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_USER, 0, 0)
223.     If _KeyDown(32) Or _KeyDown(87) Or _KeyDown(119) Or _KeyDown(18432) Then
224.         If isBodyTouching(hits(), cSCENE_USER) Then
225.             Call vectorSet(body(cSCENE_USER).force, 0, -cPLAYER_FORCE)
226.         End If
227.     End If
228.  
229.     If _KeyDown(65) Or _KeyDown(97) Or _KeyDown(19200) Then
230.         Call vectorSet(body(cSCENE_USER).force, -cPLAYER_FORCE / 10, 0)
231.     End If
232.  
233.     If _KeyDown(68) Or _KeyDown(100) Or _KeyDown(19712) Then
234.         Call vectorSet(body(cSCENE_USER).force, cPLAYER_FORCE / 10, 0)
235.     End If
236.  
237.     body(cSCENE_USER).velocity.x = impulseClamp(-100, 100, body(cSCENE_USER).velocity.x)
238.     body(cSCENE_USER).velocity.y = impulseClamp(-100, 100, body(cSCENE_USER).velocity.y)
239.  
240.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_SPINNEROFDEATH, body(cSCENE_SPINNEROFDEATH).orient + (cPI / 90), 0)
241.     If body(cSCENE_SPINNEROFDEATH).orient > 2 * cPI Then body(cSCENE_SPINNEROFDEATH).orient = 0
242.  
243.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_DOZEROFDOOM, body(cSCENE_DOZEROFDOOM).position.x - 1, _Height - 75)
244.     If body(cSCENE_DOZEROFDOOM).position.x < 120 Then body(cSCENE_DOZEROFDOOM).position.x = _Width
245.  
246.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_ELEVATOROFTERROR, 55, body(cSCENE_ELEVATOROFTERROR).position.y - 1)
247.     If body(cSCENE_ELEVATOROFTERROR).position.y < 50 Then body(cSCENE_ELEVATOROFTERROR).position.y = _Height - 25
248.  
249. End Sub
250.  
251. Sub buildSimpleScene (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, j() As tJOINT)
252.     Dim i, ty As Integer
253.     Dim bm(5) As Long ' array texture bitmaps
254.     Call generateBitmap(bm()) ' auto generated bitmaps can be substituted for whatever images you have
255.  
256.     Call createBoxBodies(p(), pa(), body(), cSCENE_USER, 20, 20)
257.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_USER, (20), (20))
258.     Call setBody(body(), cPARAMETER_VELOCITY, cSCENE_USER, 0, 0)
259.     Call setBody(body(), cPARAMETER_TEXTURE, cSCENE_USER, bm(2), 0)
260.     Call setBody(body(), cPARAMETER_FLIPTEXTURE, cSCENE_USER, 1, 0)
261.  
262.     Call createBoxBodies(p(), pa(), body(), cSCENE_FLOOR, 1000, 5)
263.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_FLOOR, (_Width / 2), (_Height - 20))
264.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_FLOOR, 0, 0)
265.  
266.     Call createBoxBodies(p(), pa(), body(), cSCENE_SPINNEROFDEATH, 75, 5)
267.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_SPINNEROFDEATH, (_Width / 2), (_Height - 100))
268.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_SPINNEROFDEATH, 0, 0)
269.  
270.     Call createBoxBodies(p(), pa(), body(), cSCENE_RIGHTRAMP, 350, 5)
271.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_RIGHTRAMP, (_Width * .75) + 35, (_Height / 2) + 105)
272.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_RIGHTRAMP, (cPI * .75), 0)
273.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_RIGHTRAMP, 0, 0)
274.  
275.     Call createBoxBodies(p(), pa(), body(), cSCENE_LEFTRAMP, 225, 5)
276.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_LEFTRAMP, (_Width * .25) + 55, (_Height / 2))
277.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_LEFTRAMP, (cPI * .1), 0)
278.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_LEFTRAMP, 0, 0)
279.  
280.     Call createBoxBodies(p(), pa(), body(), cSCENE_DOZEROFDOOM, 5, 50)
281.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_DOZEROFDOOM, 0, _Height - 75)
282.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_DOZEROFDOOM, 0, 0)
283.  
284.     Call createBoxBodies(p(), pa(), body(), cSCENE_ELEVATOROFTERROR, 50, 5)
285.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_ELEVATOROFTERROR, 55, _Height - 25)
286.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_ELEVATOROFTERROR, (cPI * .98), 0)
287.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_ELEVATOROFTERROR, 0, 0)
288.  
289.     Call createBoxBodies(p(), pa(), body(), cSCENE_RIGHTWALL, 5, 375)
290.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_RIGHTWALL, 5, _Height / 2 - 20)
291.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_RIGHTWALL, 0, 0)
292.  
293.     Call createBoxBodies(p(), pa(), body(), cSCENE_ELEVATORKICKER, 100, 5)
294.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_ELEVATORKICKER, 55, 120)
295.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_ELEVATORKICKER, (cPI * .70), 0)
296.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_ELEVATORKICKER, 0, 0)
297.     '********************************************************
298.     '   Make the Chain
299.     '********************************************************
300.  
301.     Call createBoxBodies(p(), pa(), body(), cSCENE_PIVOT, 20, 20)
302.     Call setBody(body(), cPARAMETER_POSITION, cSCENE_PIVOT, _Width / 2, 50)
303.     Call setBody(body(), cPARAMETER_ORIENT, cSCENE_PIVOT, (cPI * 1.5), 0)
304.     Call setBody(body(), cPARAMETER_STATIC, cSCENE_PIVOT, 0, 0)
305.  
306.     For i = 0 To sNUMBEROFJOINTS - 1
307.         Call createBoxBodies(p(), pa(), body(), cSCENE_PENDULUM + i, 12, 8)
308.         ' Call createCircleBody(pa(), body(), cSCENE_PENDULUM + i, 10)
309.         Call setBody(body(), cPARAMETER_ORIENT, cSCENE_PENDULUM + i, (cPI * 1.5), 0)
310.         Call setBody(body(), cPARAMETER_POSITION, cSCENE_PENDULUM + i, _Width / 2, 90 + (i * 30))
311.         Call jointSet(j(i + 1), body(), cSCENE_PENDULUM + i - 1, cSCENE_PENDULUM + i, body(cSCENE_PENDULUM + i - 1).position.x, body(cSCENE_PENDULUM + i - 1).position.y)
312.     Next i
313.  
314.     '********************************************************
315.     '   Make Random objects
316.     '********************************************************
317.     For i = cSCENE_PENDULUM + sNUMBEROFJOINTS To sNUMBEROFBODIES
318.         If Rnd > .35 Then ' Circles are much faster than polygons
319.             ty = cSHAPE_CIRCLE
320.         Else
321.             ty = cSHAPE_POLYGON
322.         End If
323.         Call createBodies(p(), pa(), body(), i, ty)
324.         Call setBody(body(), cPARAMETER_POSITION, i, (Rnd * _Width / 2) + (_Width / 4), ((Rnd * _Height / 2) + (_Height / 4)) - 200)
325.         Call setBody(body(), cPARAMETER_VELOCITY, i, Rnd * 100 - 50, Rnd * 100 - 50)
326.     Next
327.  
328.     '********************************************************
329.     '  Texture Bodies
330.     '********************************************************
331.     For i = cSCENE_ELEVATORKICKER + 1 To sNUMBEROFBODIES
332.         If body(i).shape.ty = cSHAPE_CIRCLE Then
333.             Call setBody(body(), cPARAMETER_TEXTURE, i, bm(0), 0)
334.         Else
335.             If body(i).shape.ty = cSHAPE_POLYGON Then
336.                 Call setBody(body(), cPARAMETER_TEXTURE, i, bm(1), 0)
337.             End If
338.         End If
339.     Next
340.  
341. End Sub
342. '**********************************************************************************************
343. '   Collision Helper Tools
344. '**********************************************************************************************
345. Function isBodyTouchingBody (hits() As tHIT, A As Integer, B As Integer)
346.     Dim hitcount As Integer: hitcount = 1
347.     isBodyTouchingBody = 0
348.     Do While hits(hitcount).A <> hits(hitcount).B
349.         If hits(hitcount).A = A And hits(hitcount).B = B Then
350.             isBodyTouchingBody = hitcount
351.             Exit Function
352.         End If
353.         hitcount = hitcount + 1: If hitcount > UBound(hits) Then Exit Function
354.     Loop
355. End Function
356.  
357. Function isBodyTouchingStatic (body() As tBODY, hits() As tHIT, A As Integer)
358.     Dim hitcount As Integer: hitcount = 1
359.     isBodyTouchingStatic = 0
360.     Do While hits(hitcount).A <> hits(hitcount).B
361.         If hits(hitcount).A = A Then
362.             If body(hits(hitcount).B).mass = 0 Then
363.                 isBodyTouchingStatic = hitcount
364.                 Exit Function
365.             End If
366.         End If
367.         hitcount = hitcount + 1: If hitcount > UBound(hits) Then Exit Function
368.     Loop
369. End Function
370.  
371. Function isBodyTouching (hits() As tHIT, A As Integer)
372.     Dim hitcount As Integer: hitcount = 1
373.     isBodyTouching = 0
374.     Do While hits(hitcount).A <> hits(hitcount).B
375.         If hits(hitcount).A = A Then
376.             isBodyTouching = hitcount
377.             Exit Function
378.         End If
379.         hitcount = hitcount + 1: If hitcount > UBound(hits) Then Exit Function
380.     Loop
381. End Function
382.  
383. '**********************************************************************************************
384. '   Scene Creation Tools ahead
385. '**********************************************************************************************
386.  
387. Sub setBody (body() As tBODY, Parameter As Integer, Index As Integer, arg1 As _Float, arg2 As _Float)
388.     Select Case Parameter
389.         Case cPARAMETER_POSITION:
390.             Call vectorSet(body(Index).position, arg1, arg2)
391.         Case cPARAMETER_VELOCITY:
392.             Call vectorSet(body(Index).velocity, arg1, arg2)
393.         Case cPARAMETER_FORCE:
394.             Call vectorSet(body(Index).force, arg1, arg2)
395.         Case cPARAMETER_ANGULARVELOCITY:
396.             body(Index).angularVelocity = arg1
397.         Case cPARAMETER_TORQUE:
398.             body(Index).torque = arg1
399.         Case cPARAMETER_ORIENT:
400.             body(Index).orient = arg1
401.             Call matrixSetRadians(body(Index).shape.u, body(Index).orient)
402.         Case cPARAMETER_STATICFRICTION:
403.             body(Index).staticFriction = arg1
404.         Case cPARAMETER_DYNAMICFRICTION:
405.             body(Index).dynamicFriction = arg1
406.         Case cPARAMETER_COLOR:
407.             body(Index).c = arg1
408.         Case cPARAMETER_VISIBLE:
409.             body(Index).visible = arg1
410.         Case cPARAMETER_STATIC:
411.             Call bodySetStatic(body(Index))
412.         Case cPARAMETER_TEXTURE:
413.             body(Index).shape.texture = arg1
414.         Case cPARAMETER_FLIPTEXTURE:
415.             body(Index).shape.flipTexture = arg1
416.     End Select
417. End Sub
418.  
419. Sub createCircleBody (pa() As tPOLYATTRIB, body() As tBODY, index As Integer, radius As _Float)
420.     Dim shape As tSHAPE
421.     Call shapeCreate(shape, cSHAPE_CIRCLE, radius)
422.     Call bodyCreate(body(), index, shape)
423.     Call circleInitialize(body(), index)
424.     ' Even though circles do not have Polygons, they still must be included in the Vertices
425.     If index = 0 Then
426.         pa(index).start = 0
427.     Else
428.         pa(index).start = pa(index - 1).start + pa(index - 1).count + 1
429.     End If
430.     pa(index).count = 1
431.     body(index).c = _RGB32(255, 255, 255)
432. End Sub
433.  
434. Sub createBoxBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, index As Integer, xs As _Float, ys As _Float)
435.     Dim shape As tSHAPE
436.     Call shapeCreate(shape, cSHAPE_POLYGON, 0)
437.     Call bodyCreate(body(), index, shape)
438.     Call boxCreate(p(), pa(), index, xs, ys)
439.     Call polygonInitialize(body(), p(), pa(), index)
440.     body(index).c = _RGB32(255, 255, 255)
441. End Sub
442.  
443. Sub createBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, index As Integer, ty As Integer)
444.     If ty = cSHAPE_CIRCLE Then
445.         Call createCircleBody(pa(), body(), index, 10 + Rnd * 20)
446.     Else
447.         If ty = cSHAPE_POLYGON Then
448.             Call createBoxBodies(p(), pa(), body(), index, 10 + Rnd * 10, 10 + Rnd * 10)
449.         End If
450.     End If
451.     body(index).c = _RGB32(55 + Rnd * 200, 55 + Rnd * 200, 55 + Rnd * 200)
452. End Sub
453.  
454. '**********************************************************************************************
455. '   Physics and Collision Stuff Ahead
456. '**********************************************************************************************
457.  
458. Sub impulseIntegrateForces (b As tBODY, dt As _Float)
459.     If b.invMass = 0.0 Then Exit Sub
460.     Dim dts As _Float
461.     dts = dt * .5
462.     Call vectorAddVectorScalar(b.velocity, b.force, b.invMass * dts)
463.     Call vectorAddVectorScalar(b.velocity, sGRAVITY, dts)
464.     b.angularVelocity = b.angularVelocity + (b.torque * b.invInertia * dts)
465. End Sub
466.  
467. Sub impulseIntegrateVelocity (body As tBODY, dt As _Float)
468.     If body.invMass = 0.0 Then Exit Sub
469.     Call vectorAddVectorScalar(body.position, body.velocity, dt)
470.     body.orient = body.orient + (body.angularVelocity * dt)
471.     Call matrixSetRadians(body.shape.u, body.orient)
472.     Call impulseIntegrateForces(body, dt)
473. End Sub
474.  
475. Sub impulseStep (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, j() As tJOINT, dt As _Float, iterations As Integer, hits() As tHIT)
476.     Dim A As tBODY
477.     Dim B As tBODY
478.     Dim c(cMAXNUMBEROFOBJECTS) As tVECTOR2d
479.     Dim m As tMANIFOLD
480.     Dim manifolds(sNUMBEROFBODIES * sNUMBEROFBODIES) As tMANIFOLD
481.     Dim collisions(sNUMBEROFBODIES * sNUMBEROFBODIES, cMAXNUMBEROFOBJECTS) As tVECTOR2d
482.     Dim manifoldCount As Integer: manifoldCount = 0
483.     '    // Generate new collision info
484.     Dim i, j, k As Integer
485.     Dim hitCount As Integer: hitCount = 0
486.     Dim dHit As tHIT
487.     ' // erase hitlist
488.     Do
489.         hits(hitCount) = dHit
490.         hitCount = hitCount + 1
491.     Loop Until hits(hitCount).A = hits(hitCount).B
492.     hitCount = 0
493.  
494.     ' TODO: Implement hidden object logic
495.     For i = 0 To sNUMBEROFBODIES ' number of bodies
496.         A = body(i)
497.         For j = i + 1 To sNUMBEROFBODIES
498.             B = body(j)
499.             If A.invMass = 0.0 And B.invMass = 0.0 Then _Continue
500.             'Mainfold solve - handle collisions
501.             If A.shape.ty = cSHAPE_CIRCLE And B.shape.ty = cSHAPE_CIRCLE Then
502.                 Call collisionCCHandle(m, c(), A, B)
503.             Else
504.                 If A.shape.ty = cSHAPE_POLYGON And B.shape.ty = cSHAPE_POLYGON Then
505.                     Call collisionPPHandle(p(), pa(), body(), m, c(), i, j)
506.                 Else
507.                     If A.shape.ty = cSHAPE_CIRCLE And B.shape.ty = cSHAPE_POLYGON Then
508.                         Call collisionCPHandle(p(), pa(), body(), m, c(), i, j)
509.                     Else
510.                         If B.shape.ty = cSHAPE_CIRCLE And A.shape.ty = cSHAPE_POLYGON Then
511.                             Call collisionPCHandle(p(), pa(), body(), m, c(), i, j)
512.                         End If
513.                     End If
514.                 End If
515.             End If
516.             If m.contactCount > 0 Then
517.                 m.A = i 'identify the index of objects
518.                 m.B = j
519.                 manifolds(manifoldCount) = m
520.                 For k = 0 To m.contactCount
521.                     hits(hitCount).A = i
522.                     hits(hitCount).B = j
523.                     hits(hitCount).position = c(k)
524.                     collisions(manifoldCount, k) = c(k)
525.                     hitCount = hitCount + 1
526.                 Next
527.                 manifoldCount = manifoldCount + 1
528.             End If
529.         Next
530.     Next
531.  
532.     '   // Integrate forces
533.     For i = 0 To sNUMBEROFBODIES
534.         Call impulseIntegrateForces(body(i), dt)
535.     Next
536.     '   // Initialize collision
537.     For i = 0 To manifoldCount - 1
538.         ' this is the stupidest thing ever since QB will not let you split arrays
539.         For k = 0 To manifolds(i).contactCount - 1
540.             c(k) = collisions(i, k)
541.         Next
542.         Call manifoldInit(manifolds(i), body(), c())
543.     Next
544.     ' joint pre Steps
545.  
546.     For i = 1 To sNUMBEROFJOINTS
547.         Call jointPrestep(j(i), body(), dt)
548.     Next
549.  
550.     '// Solve collisions
551.     For j = 0 To iterations - 1
552.  
553.         For i = 0 To manifoldCount - 1
554.             For k = 0 To manifolds(i).contactCount - 1
555.                 c(k) = collisions(i, k)
556.             Next
557.             Call manifoldApplyImpulse(manifolds(i), body(), c())
558.         Next
559.         For i = 1 To sNUMBEROFJOINTS
560.             Call jointApplyImpulse(j(i), body())
561.         Next
562.     Next
563.  
564.     '// Integrate velocities
565.     For i = 0 To sNUMBEROFBODIES
566.         Call impulseIntegrateVelocity(body(i), dt)
567.     Next
568.     '// Correct positions
569.     For i = 0 To manifoldCount - 1
570.         Call manifoldPositionalCorrection(manifolds(i), body())
571.     Next
572.     '// Clear all forces
573.     For i = 0 To sNUMBEROFBODIES
574.         Call vectorSet(body(i).force, 0, 0)
575.         body(i).torque = 0
576.     Next
577. End Sub
578.  
579. Sub bodyApplyImpulse (body As tBODY, impulse As tVECTOR2d, contactVector As tVECTOR2d)
580.     Call vectorAddVectorScalar(body.velocity, impulse, body.invMass)
581.     body.angularVelocity = body.angularVelocity + body.invInertia * vectorCross(contactVector, impulse)
582. End Sub
583.  
584. Sub bodySetStatic (body As tBODY)
585.     body.inertia = 0.0
586.     body.invInertia = 0.0
587.     body.mass = 0.0
588.     body.invMass = 0.0
589. End Sub
590.  
591. Sub manifoldInit (m As tMANIFOLD, body() As tBODY, contacts() As tVECTOR2d)
592.     Dim ra As tVECTOR2d
593.     Dim rb As tVECTOR2d
594.     Dim rv As tVECTOR2d
595.     Dim tv1 As tVECTOR2d
596.     Dim tv2 As tVECTOR2d
597.     m.e = scalarMin(body(m.A).restitution, body(m.B).restitution)
598.     m.sf = Sqr(body(m.A).staticFriction * body(m.A).staticFriction)
599.     m.df = Sqr(body(m.A).dynamicFriction * body(m.A).dynamicFriction)
600.     Dim i As Integer
601.     For i = 0 To m.contactCount - 1
602.         Call vectorSubVectorND(contacts(i), body(m.A).position, ra)
603.         Call vectorSubVectorND(contacts(i), body(m.B).position, rb)
604.  
605.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
606.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
607.         Call vectorAddVector(tv1, body(m.B).velocity)
608.         Call vectorSubVectorND(tv2, body(m.A).velocity, tv2)
609.         Call vectorSubVectorND(rv, tv1, tv2)
610.  
611.         If vectorLengthSq(rv) < sRESTING Then
612.             m.e = 0.0
613.         End If
614.     Next
615. End Sub
616.  
617. Sub manifoldApplyImpulse (m As tMANIFOLD, body() As tBODY, contacts() As tVECTOR2d)
618.     Dim ra As tVECTOR2d
619.     Dim rb As tVECTOR2d
620.     Dim rv As tVECTOR2d
621.     Dim tv1 As tVECTOR2d
622.     Dim tv2 As tVECTOR2d
623.     Dim contactVel As _Float
624.  
625.     Dim raCrossN As _Float
626.     Dim rbCrossN As _Float
627.     Dim invMassSum As _Float
628.     Dim i As Integer
629.     Dim j As _Float
630.     Dim impulse As tVECTOR2d
631.  
632.     Dim t As tVECTOR2d
633.     Dim jt As _Float
634.     Dim tangentImpulse As tVECTOR2d
635.  
636.     If impulseEqual(body(m.A).invMass + body(m.B).invMass, 0.0) Then
637.         Call manifoldInfiniteMassCorrection(body(m.A), body(m.B))
638.         Exit Sub
639.     End If
640.  
641.     For i = 0 To m.contactCount - 1
642.         '// Calculate radii from COM to contact
643.         '// Vec2 ra = contacts[i] - A->position;
644.         '// Vec2 rb = contacts[i] - B->position;
645.         Call vectorSubVectorND(ra, contacts(i), body(m.A).position)
646.         Call vectorSubVectorND(rb, contacts(i), body(m.B).position)
647.  
648.         '// Relative velocity
649.         '// Vec2 rv = B->velocity + Cross( B->angularVelocity, rb ) - A->velocity - Cross( A->angularVelocity, ra );
650.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
651.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
652.         Call vectorAddVectorND(rv, tv1, body(m.B).velocity)
653.         Call vectorSubVector(rv, body(m.A).velocity)
654.         Call vectorSubVector(rv, tv2)
655.  
656.         '// Relative velocity along the normal
657.         '// real contactVel = Dot( rv, normal );
658.         contactVel = vectorDot(rv, m.normal)
659.  
660.         '// Do not resolve if velocities are separating
661.         If contactVel > 0 Then Exit Sub
662.  
663.         '// real raCrossN = Cross( ra, normal );
664.         '// real rbCrossN = Cross( rb, normal );
665.         '// real invMassSum = A->im + B->im + Sqr( raCrossN ) * A->iI + Sqr( rbCrossN ) * B->iI;
666.         raCrossN = vectorCross(ra, m.normal)
667.         rbCrossN = vectorCross(rb, m.normal)
668.         invMassSum = body(m.A).invMass + body(m.B).invMass + (raCrossN * raCrossN) * body(m.A).invInertia + (rbCrossN * rbCrossN) * body(m.B).invInertia
669.  
670.         '// Calculate impulse scalar
671.         j = -(1.0 + m.e) * contactVel
672.         j = j / invMassSum
673.         j = j / m.contactCount
674.  
675.         '// Apply impulse
676.         Call vectorMultiplyScalarND(impulse, m.normal, j)
677.  
678.         Call vectorNegND(tv1, impulse)
679.         Call bodyApplyImpulse(body(m.A), tv1, ra)
680.         Call bodyApplyImpulse(body(m.B), impulse, rb)
681.  
682.         '// Friction impulse
683.         '// rv = B->velocity + Cross( B->angularVelocity, rb ) - A->velocity - Cross( A->angularVelocity, ra );
684.         Call vectorCrossScalar(tv1, rb, body(m.B).angularVelocity)
685.         Call vectorCrossScalar(tv2, ra, body(m.A).angularVelocity)
686.         Call vectorAddVectorND(rv, tv1, body(m.B).velocity)
687.         Call vectorSubVector(rv, body(m.A).velocity)
688.         Call vectorSubVector(rv, tv2)
689.  
690.         '// Vec2 t = rv - (normal * Dot( rv, normal ));
691.         '// t.Normalize( );
692.         Call vectorMultiplyScalarND(t, m.normal, vectorDot(rv, m.normal))
693.         Call vectorSubVectorND(t, rv, t)
694.         Call vectorNormalize(t)
695.  
696.         '// j tangent magnitude
697.         jt = -vectorDot(rv, t)
698.         jt = jt / invMassSum
699.         jt = jt / m.contactCount
700.  
701.         '// Don't apply tiny friction impulses
702.         If impulseEqual(jt, 0.0) Then Exit Sub
703.  
704.         '// Coulumb's law
705.         If Abs(jt) < j * m.sf Then
706.             Call vectorMultiplyScalarND(tangentImpulse, t, jt)
707.         Else
708.             Call vectorMultiplyScalarND(tangentImpulse, t, -j * m.df)
709.         End If
710.  
711.         '// Apply friction impulse
712.         '// A->ApplyImpulse( -tangentImpulse, ra );
713.         '// B->ApplyImpulse( tangentImpulse, rb );
714.         Call vectorNegND(tv1, tangentImpulse)
715.         Call bodyApplyImpulse(body(m.A), tv1, ra)
716.         Call bodyApplyImpulse(body(m.B), tangentImpulse, rb)
717.     Next i
718. End Sub
719.  
720. Sub manifoldPositionalCorrection (m As tMANIFOLD, body() As tBODY)
721.     Dim correction As _Float
722.     correction = scalarMax(m.penetration - cPENETRATION_ALLOWANCE, 0.0) / (body(m.A).invMass + body(m.B).invMass) * cPENETRATION_CORRECTION
723.     Call vectorAddVectorScalar(body(m.A).position, m.normal, -body(m.A).invMass * correction)
724.     Call vectorAddVectorScalar(body(m.B).position, m.normal, body(m.B).invMass * correction)
725. End Sub
726.  
727. Sub manifoldInfiniteMassCorrection (A As tBODY, B As tBODY)
728.     Call vectorSet(A.velocity, 0, 0)
729.     Call vectorSet(B.velocity, 0, 0)
730. End Sub
731.  
732. '**********************************************************************************************
733. '   Collision Stuff Ahead
734. '**********************************************************************************************
735.  
736. Sub collisionCCHandle (m As tMANIFOLD, contacts() As tVECTOR2d, A As tBODY, B As tBODY)
737.     Dim normal As tVECTOR2d
738.     Dim dist_sqr As _Float
739.     Dim radius As _Float
740.  
741.     Call vectorSubVectorND(normal, B.position, A.position)
742.     dist_sqr = vectorLengthSq(normal)
743.     radius = A.shape.radius + B.shape.radius
744.  
745.     If (dist_sqr >= radius * radius) Then
746.         m.contactCount = 0
747.     Else
748.         Dim distance As _Float
749.         distance = Sqr(dist_sqr)
750.         m.contactCount = 1
751.  
752.         If distance = 0 Then
753.             m.penetration = A.shape.radius
754.             Call vectorSet(m.normal, 1.0, 0.0)
755.             Call vectorSetVector(contacts(0), A.position)
756.         Else
757.             m.penetration = radius - distance
758.             Call vectorDivideScalarND(m.normal, normal, distance)
759.  
760.             Call vectorMultiplyScalarND(contacts(0), m.normal, A.shape.radius)
761.             Call vectorAddVector(contacts(0), A.position)
762.         End If
763.     End If
764. End Sub
765.  
766. Sub collisionPCHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
767.     Call collisionCPHandle(p(), pa(), body(), m, contacts(), B, A)
768.     If m.contactCount > 0 Then
769.         Call vectorNeg(m.normal)
770.     End If
771. End Sub
772.  
773. Sub collisionCPHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
774.     'A is the Circle
775.     'B is the POLY
776.     m.contactCount = 0
777.     Dim center As tVECTOR2d
778.     Dim tm As tMATRIX2d
779.     Dim tv As tVECTOR2d
780.     Dim ARadius As _Float: ARadius = body(A).shape.radius
781.  
782.     Call vectorSubVectorND(center, body(A).position, body(B).position)
783.     Call matrixTranspose(body(B).shape.u, tm)
784.     Call matrixMultiplyVector(tm, center, center)
785.  
786.     Dim separation As _Float: separation = -9999999
787.     Dim faceNormal As Integer: faceNormal = 0
788.     Dim i As Integer
789.     Dim s As _Float
790.     For i = 0 To pa(B).count
791.         Call vectorSubVectorND(tv, center, p(pa(B).start + i).vert)
792.         s = vectorDot(p(pa(B).start + i).norm, tv)
793.         If s > ARadius Then Exit Sub
794.         If s > separation Then
795.             separation = s
796.             faceNormal = i
797.         End If
798.     Next
799.     Dim v1 As tVECTOR2d
800.     v1 = p(pa(B).start + faceNormal).vert
801.     Dim i2 As Integer
802.     i2 = pa(B).start + arrayNextIndex(faceNormal, pa(B).count)
803.     Dim v2 As tVECTOR2d
804.     v2 = p(i2).vert
805.  
806.     If separation < cEPSILON Then
807.         m.contactCount = 1
808.         Call matrixMultiplyVector(body(B).shape.u, p(pa(B).start + faceNormal).norm, m.normal)
809.         Call vectorNeg(m.normal)
810.         Call vectorMultiplyScalarND(contacts(0), m.normal, ARadius)
811.         Call vectorAddVector(contacts(0), body(A).position)
812.         m.penetration = ARadius
813.         Exit Sub
814.     End If
815.  
816.     Dim dot1 As _Float
817.     Dim dot2 As _Float
818.  
819.     Dim tv1 As tVECTOR2d
820.     Dim tv2 As tVECTOR2d
821.     Dim n As tVECTOR2d
822.     Call vectorSubVectorND(tv1, center, v1)
823.     Call vectorSubVectorND(tv2, v2, v1)
824.     dot1 = vectorDot(tv1, tv2)
825.     Call vectorSubVectorND(tv1, center, v2)
826.     Call vectorSubVectorND(tv2, v1, v2)
827.     dot2 = vectorDot(tv1, tv2)
828.     m.penetration = ARadius - separation
829.     If dot1 <= 0.0 Then
830.         If vectorSqDist(center, v1) > ARadius * ARadius Then Exit Sub
831.         m.contactCount = 1
832.         Call vectorSubVectorND(n, v1, center)
833.         Call matrixMultiplyVector(body(B).shape.u, n, n)
834.         Call vectorNormalize(n)
835.         m.normal = n
836.         Call matrixMultiplyVector(body(B).shape.u, v1, v1)
837.         Call vectorAddVectorND(v1, v1, body(B).position)
838.         contacts(0) = v1
839.     Else
840.         If dot2 <= 0.0 Then
841.             If vectorSqDist(center, v2) > ARadius * ARadius Then Exit Sub
842.             m.contactCount = 1
843.             Call vectorSubVectorND(n, v2, center)
844.             Call matrixMultiplyVector(body(B).shape.u, v2, v2)
845.             Call vectorAddVectorND(v2, v2, body(B).position)
846.             contacts(0) = v2
847.             Call matrixMultiplyVector(body(B).shape.u, n, n)
848.             Call vectorNormalize(n)
849.             m.normal = n
850.         Else
851.             n = p(pa(B).start + faceNormal).norm
852.             Call vectorSubVectorND(tv1, center, v1)
853.             If vectorDot(tv1, n) > ARadius Then Exit Sub
854.             m.contactCount = 1
855.             Call matrixMultiplyVector(body(B).shape.u, n, n)
856.             Call vectorNeg(n)
857.             m.normal = n
858.             Call vectorMultiplyScalarND(contacts(0), m.normal, ARadius)
859.             Call vectorAddVector(contacts(0), body(A).position)
860.         End If
861.     End If
862. End Sub
863.  
864. Function collisionPPClip (n As tVECTOR2d, c As _Float, face() As tVECTOR2d)
865.     Dim sp As Integer: sp = 0
866.     Dim o(cMAXNUMBEROFPOLYGONS) As tVECTOR2d
867.  
868.     o(0) = face(0)
869.     o(1) = face(1)
870.  
871.     Dim d1 As _Float: d1 = vectorDot(n, face(0)) - c
872.     Dim d2 As _Float: d2 = vectorDot(n, face(1)) - c
873.  
874.     If d1 <= 0.0 Then
875.         o(sp) = face(0)
876.         sp = sp + 1
877.     End If
878.  
879.     If d2 <= 0.0 Then
880.         o(sp) = face(1)
881.         sp = sp + 1
882.     End If
883.  
884.     If d1 * d2 < 0.0 Then
885.         Dim alpha As _Float: alpha = d1 / (d1 - d2)
886.         Dim tempv As tVECTOR2d
887.         'out[sp] = face[0] + alpha * (face[1] - face[0]);
888.         Call vectorSubVectorND(tempv, face(1), face(0))
889.         Call vectorMultiplyScalar(tempv, alpha)
890.         Call vectorAddVectorND(o(sp), tempv, face(0))
891.         sp = sp + 1
892.     End If
893.     face(0) = o(0)
894.     face(1) = o(1)
895.     collisionPPClip = sp
896. End Function
897.  
898. Sub collisionPPFindIncidentFace (p() As tPOLY, pa() As tPOLYATTRIB, b() As tBODY, v() As tVECTOR2d, RefPoly As Integer, IncPoly As Integer, referenceIndex As Integer)
899.     Dim referenceNormal As tVECTOR2d
900.     Dim uRef As tMATRIX2d: uRef = b(RefPoly).shape.u
901.     Dim uInc As tMATRIX2d: uInc = b(IncPoly).shape.u
902.     Dim uTemp As tMATRIX2d
903.     Dim i As Integer
904.     referenceNormal = p(pa(RefPoly).start + referenceIndex).norm
905.  
906.     '        // Calculate normal in incident's frame of reference
907.     '        // referenceNormal = RefPoly->u * referenceNormal; // To world space
908.     Call matrixMultiplyVector(uRef, referenceNormal, referenceNormal)
909.     '        // referenceNormal = IncPoly->u.Transpose( ) * referenceNormal; // To incident's model space
910.     Call matrixTranspose(uInc, uTemp)
911.     Call matrixMultiplyVector(uTemp, referenceNormal, referenceNormal)
912.  
913.     Dim incidentFace As Integer: incidentFace = 0
914.     Dim minDot As _Float: minDot = 9999999
915.     Dim dot As _Float
916.     For i = 0 To pa(IncPoly).count
917.         dot = vectorDot(referenceNormal, p(pa(IncPoly).start + i).norm)
918.         If (dot < minDot) Then
919.             minDot = dot
920.             incidentFace = i
921.         End If
922.     Next
923.  
924.     '// Assign face vertices for incidentFace
925.     '// v[0] = IncPoly->u * IncPoly->m_vertices[incidentFace] + IncPoly->body->position;
926.     Call matrixMultiplyVector(uInc, p(pa(IncPoly).start + incidentFace).vert, v(0))
927.     Call vectorAddVector(v(0), b(IncPoly).position)
928.  
929.     '// incidentFace = incidentFace + 1 >= (int32)IncPoly->m_vertexCount ? 0 : incidentFace + 1;
930.     incidentFace = arrayNextIndex(incidentFace, pa(IncPoly).count)
931.  
932.     '// v[1] = IncPoly->u * IncPoly->m_vertices[incidentFace] +  IncPoly->body->position;
933.     Call matrixMultiplyVector(uInc, p(pa(IncPoly).start + incidentFace).vert, v(1))
934.     Call vectorAddVector(v(1), b(IncPoly).position)
935. End Sub
936.  
937. Sub collisionPPHandle (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, m As tMANIFOLD, contacts() As tVECTOR2d, A As Integer, B As Integer)
938.     m.contactCount = 0
939.  
940.     Dim faceA(100) As Integer
941.  
942.     Dim penetrationA As _Float
943.     penetrationA = collisionPPFindAxisLeastPenetration(p(), pa(), body(), faceA(), A, B)
944.     If penetrationA >= 0.0 Then Exit Sub
945.  
946.     Dim faceB(100) As Integer
947.  
948.     Dim penetrationB As _Float
949.     penetrationB = collisionPPFindAxisLeastPenetration(p(), pa(), body(), faceB(), B, A)
950.     If penetrationB >= 0.0 Then Exit Sub
951.  
952.  
953.     Dim referenceIndex As Integer
954.     Dim flip As Integer
955.  
956.     Dim RefPoly As Integer
957.     Dim IncPoly As Integer
958.  
959.     If impulseGT(penetrationA, penetrationB) Then
960.         RefPoly = A
961.         IncPoly = B
962.         referenceIndex = faceA(0)
963.         flip = 0
964.     Else
965.         RefPoly = B
966.         IncPoly = A
967.         referenceIndex = faceB(0)
968.         flip = 1
969.     End If
970.  
971.     Dim incidentFace(2) As tVECTOR2d
972.  
973.     Call collisionPPFindIncidentFace(p(), pa(), body(), incidentFace(), RefPoly, IncPoly, referenceIndex)
974.     Dim v1 As tVECTOR2d
975.     Dim v2 As tVECTOR2d
976.     Dim v1t As tVECTOR2d
977.     Dim v2t As tVECTOR2d
978.  
979.     v1 = p(pa(RefPoly).start + referenceIndex).vert
980.     referenceIndex = arrayNextIndex(referenceIndex, pa(RefPoly).count)
981.     v2 = p(pa(RefPoly).start + referenceIndex).vert
982.     '// Transform vertices to world space
983.     '// v1 = RefPoly->u * v1 + RefPoly->body->position;
984.     '// v2 = RefPoly->u * v2 + RefPoly->body->position;
985.     Call matrixMultiplyVector(body(RefPoly).shape.u, v1, v1t)
986.     Call vectorAddVectorND(v1, v1t, body(RefPoly).position)
987.     Call matrixMultiplyVector(body(RefPoly).shape.u, v2, v2t)
988.     Call vectorAddVectorND(v2, v2t, body(RefPoly).position)
989.  
990.     '// Calculate reference face side normal in world space
991.     '// Vec2 sidePlaneNormal = (v2 - v1);
992.     '// sidePlaneNormal.Normalize( );
993.     Dim sidePlaneNormal As tVECTOR2d
994.     Call vectorSubVectorND(sidePlaneNormal, v2, v1)
995.     Call vectorNormalize(sidePlaneNormal)
996.  
997.     '// Orthogonalize
998.     '// Vec2 refFaceNormal( sidePlaneNormal.y, -sidePlaneNormal.x );
999.     Dim refFaceNormal As tVECTOR2d
1000.     Call vectorSet(refFaceNormal, sidePlaneNormal.y, -sidePlaneNormal.x)
1001.  
1002.     '// ax + by = c
1003.     '// c is distance from origin
1004.     '// real refC = Dot( refFaceNormal, v1 );
1005.     '// real negSide = -Dot( sidePlaneNormal, v1 );
1006.     '// real posSide = Dot( sidePlaneNormal, v2 );
1007.     Dim refC As _Float: refC = vectorDot(refFaceNormal, v1)
1008.     Dim negSide As _Float: negSide = -vectorDot(sidePlaneNormal, v1)
1009.     Dim posSide As _Float: posSide = vectorDot(sidePlaneNormal, v2)
1010.  
1011.  
1012.     '// Clip incident face to reference face side planes
1013.     '// if(Clip( -sidePlaneNormal, negSide, incidentFace ) < 2)
1014.     Dim negSidePlaneNormal As tVECTOR2d
1015.     Call vectorNegND(negSidePlaneNormal, sidePlaneNormal)
1016.  
1017.     If collisionPPClip(negSidePlaneNormal, negSide, incidentFace()) < 2 Then Exit Sub
1018.     If collisionPPClip(sidePlaneNormal, posSide, incidentFace()) < 2 Then Exit Sub
1019.  
1020.     Call vectorSet(m.normal, refFaceNormal.x, refFaceNormal.y)
1021.     If flip Then Call vectorNeg(m.normal)
1022.  
1023.     '// Keep points behind reference face
1024.     Dim cp As Integer: cp = 0 '// clipped points behind reference face
1025.     Dim separation As _Float
1026.     separation = vectorDot(refFaceNormal, incidentFace(0)) - refC
1027.     If separation <= 0.0 Then
1028.         contacts(cp) = incidentFace(0)
1029.         m.penetration = -separation
1030.         cp = cp + 1
1031.     Else
1032.         m.penetration = 0
1033.     End If
1034.  
1035.     separation = vectorDot(refFaceNormal, incidentFace(1)) - refC
1036.     If separation <= 0.0 Then
1037.         contacts(cp) = incidentFace(1)
1038.         m.penetration = m.penetration + -separation
1039.         cp = cp + 1
1040.         m.penetration = m.penetration / cp
1041.     End If
1042.     m.contactCount = cp
1043. End Sub
1044.  
1045. Function collisionPPFindAxisLeastPenetration (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, faceIndex() As Integer, A As Integer, B As Integer)
1046.     Dim bestDistance As _Float: bestDistance = -9999999
1047.     Dim bestIndex As Integer: bestIndex = 0
1048.  
1049.     Dim n As tVECTOR2d
1050.     Dim nw As tVECTOR2d
1051.     Dim buT As tMATRIX2d
1052.     Dim s As tVECTOR2d
1053.     Dim nn As tVECTOR2d
1054.     Dim v As tVECTOR2d
1055.     Dim tv As tVECTOR2d
1056.     Dim d As _Float
1057.     Dim i, k As Integer
1058.  
1059.     For i = 0 To pa(A).count
1060.         k = pa(A).start + i
1061.  
1062.         '// Retrieve a face normal from A
1063.         '// Vec2 n = A->m_normals[i];
1064.         '// Vec2 nw = A->u * n;
1065.         n = p(k).norm
1066.         Call matrixMultiplyVector(body(A).shape.u, n, nw)
1067.  
1068.  
1069.         '// Transform face normal into B's model space
1070.         '// Mat2 buT = B->u.Transpose( );
1071.         '// n = buT * nw;
1072.         Call matrixTranspose(body(B).shape.u, buT)
1073.         Call matrixMultiplyVector(buT, nw, n)
1074.  
1075.         '// Retrieve support point from B along -n
1076.         '// Vec2 s = B->GetSupport( -n );
1077.         Call vectorNegND(nn, n)
1078.         Call vectorGetSupport(p(), pa(), B, nn, s)
1079.  
1080.         '// Retrieve vertex on face from A, transform into
1081.         '// B's model space
1082.         '// Vec2 v = A->m_vertices[i];
1083.         '// v = A->u * v + A->body->position;
1084.         '// v -= B->body->position;
1085.         '// v = buT * v;
1086.  
1087.         v = p(k).vert
1088.         Call matrixMultiplyVector(body(A).shape.u, v, tv)
1089.         Call vectorAddVectorND(v, tv, body(A).position)
1090.  
1091.         Call vectorSubVector(v, body(B).position)
1092.         Call matrixMultiplyVector(buT, v, tv)
1093.  
1094.         Call vectorSubVector(s, tv)
1095.         d = vectorDot(n, s)
1096.  
1097.         If d > bestDistance Then
1098.             bestDistance = d
1099.             bestIndex = i
1100.         End If
1101.  
1102.     Next i
1103.  
1104.     faceIndex(0) = bestIndex
1105.  
1106.     collisionPPFindAxisLeastPenetration = bestDistance
1107. End Function
1108.  
1109. '**********************************************************************************************
1110. '   Shape Creation Ahead
1111. '**********************************************************************************************
1112.  
1113. Sub shapeCreate (sh As tSHAPE, ty As Integer, radius As _Float)
1114.     Dim u As tMATRIX2d
1115.     Call matrixSetScalar(u, 1, 0, 0, 1)
1116.     sh.ty = ty
1117.     sh.radius = radius
1118.     sh.u = u
1119. End Sub
1120.  
1121. Sub bodyCreate (body() As tBODY, index As Integer, shape As tSHAPE)
1122.     Call vectorSet(body(index).position, 0, 0)
1123.     Call vectorSet(body(index).velocity, 0, 0)
1124.     body(index).angularVelocity = 0.0
1125.     body(index).torque = 0.0
1126.     body(index).orient = 0.0 ' impulseRandom_float(-cPI, cPI)
1127.  
1128.     Call vectorSet(body(index).force, 0, 0)
1129.     body(index).staticFriction = 0.5
1130.     body(index).dynamicFriction = 0.3
1131.     body(index).restitution = 0.2
1132.     body(index).shape = shape
1133. End Sub
1134.  
1135. Sub boxCreate (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, sizex As _Float, sizey As _Float)
1136.     Dim vertlength As Integer: vertlength = 3
1137.     Dim verts(vertlength) As tVECTOR2d
1138.  
1139.     Call vectorSet(verts(0), -sizex, -sizey)
1140.     Call vectorSet(verts(1), sizex, -sizey)
1141.     Call vectorSet(verts(2), sizex, sizey)
1142.     Call vectorSet(verts(3), -sizex, sizey)
1143.  
1144.     Call vertexSet(p(), pa(), index, verts(), vertlength)
1145. End Sub
1146.  
1147. Sub vShapeCreate (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, sizex As _Float, sizey As _Float)
1148.     Dim vertlength As Integer: vertlength = 7
1149.     Dim verts(vertlength) As tVECTOR2d
1150.  
1151.     Call vectorSet(verts(0), -sizex, -sizey)
1152.     Call vectorSet(verts(1), sizex, -sizey)
1153.     Call vectorSet(verts(2), sizex, sizey)
1154.     Call vectorSet(verts(3), -sizex, sizey)
1155.     Call vectorSet(verts(4), -sizex, sizey / 2)
1156.     Call vectorSet(verts(5), sizex / 2, sizey / 2)
1157.     Call vectorSet(verts(6), sizex / 2, -sizey / 2)
1158.     Call vectorSet(verts(7), -sizex, sizey / 2)
1159.  
1160.     Call vertexSet(p(), pa(), index, verts(), vertlength)
1161. End Sub
1162.  
1163. Sub vertexSet (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, verts() As tVECTOR2d, vertLength As Integer)
1164.     Dim rightMost As Integer: rightMost = 0
1165.     Dim highestXCoord As _Float: highestXCoord = verts(0).x
1166.     Dim i As Integer
1167.     Dim x As _Float
1168.     For i = 1 To vertLength
1169.         x = verts(i).x
1170.         If x > highestXCoord Then
1171.             highestXCoord = x
1172.             rightMost = i
1173.         Else
1174.             If x = highestXCoord Then
1175.                 If verts(i).y < verts(rightMost).y Then
1176.                     rightMost = i
1177.                 End If
1178.             End If
1179.         End If
1180.     Next
1181.     Dim hull(cMAXNUMBEROFPOLYGONS) As Integer
1182.     Dim outCount As Integer: outCount = 0
1183.     Dim indexHull As Integer: indexHull = rightMost
1184.     Dim nextHullIndex As Integer
1185.     Dim e1 As tVECTOR2d
1186.     Dim e2 As tVECTOR2d
1187.     Dim c As _Float
1188.     Do
1189.         hull(outCount) = indexHull
1190.         nextHullIndex = 0
1191.         For i = 1 To vertLength
1192.             If nextHullIndex = indexHull Then
1193.                 nextHullIndex = i
1194.                 _Continue
1195.             End If
1196.             Call vectorSubVectorND(e1, verts(nextHullIndex), verts(hull(outCount)))
1197.             Call vectorSubVectorND(e2, verts(i), verts(hull(outCount)))
1198.             c = vectorCross(e1, e2)
1199.             If c < 0.0 Then nextHullIndex = i
1200.             If c = 0.0 And (vectorLengthSq(e2) > vectorLengthSq(e1)) Then
1201.                 nextHullIndex = i
1202.             End If
1203.         Next
1204.         outCount = outCount + 1
1205.         indexHull = nextHullIndex
1206.         If nextHullIndex = rightMost Then
1207.             pa(index).count = outCount - 1
1208.             Exit Do
1209.         End If
1210.     Loop
1211.  
1212.     If index = 0 Then
1213.         pa(index).start = 0
1214.     Else
1215.         pa(index).start = pa(index - 1).start + pa(index - 1).count + 1
1216.     End If
1217.  
1218.     For i = 0 To vertLength
1219.         p(pa(index).start + i).vert = verts(hull(i))
1220.     Next
1221.     Dim face As tVECTOR2d
1222.     For i = 0 To vertLength
1223.         Call vectorSubVectorND(face, p(pa(index).start + arrayNextIndex(i, pa(index).count)).vert, p(pa(index).start + i).vert)
1224.         Call vectorSet(p(pa(index).start + i).norm, face.y, -face.x)
1225.         Call vectorNormalize(p(pa(index).start + i).norm)
1226.     Next
1227. End Sub
1228.  
1229. Function arrayNextIndex (i As Integer, count As Integer)
1230.     arrayNextIndex = ((i + 1) Mod (count + 1))
1231. End Function
1232.  
1233. '**********************************************************************************************
1234. '   Rendering Stuff Ahead
1235. '**********************************************************************************************
1236.  
1237. Sub renderFps
1238.     fpsLast = fps
1239.     fps = 0
1240. End Sub
1241.  
1242. Sub renderBodies (p() As tPOLY, pa() As tPOLYATTRIB, body() As tBODY, j() As tJOINT, hits() As tHIT)
1243.     Dim i As Integer
1244.     Dim hitcount As Integer
1245.  
1246.     For i = 0 To sNUMBEROFBODIES
1247.         'TODO: Put hidden object logic
1248.         If body(i).shape.ty = cSHAPE_CIRCLE Then
1249.             If body(i).shape.texture = 0 Then
1250.                 Call renderWireframeCircle(body(), i)
1251.             Else
1252.                 Call renderTexturedCircle(body(), i)
1253.             End If
1254.         Else If body(i).shape.ty = cSHAPE_POLYGON Then
1255.                 If body(i).shape.texture = 0 Then
1256.                     Call renderWireframePoly(p(), pa(), body(), i)
1257.                 Else
1258.                     Call renderTexturedBox(p(), pa(), body(), i)
1259.                 End If
1260.             End If
1261.         End If
1262.         If body(i).position.x < 0 Then body(i).position.x = _Width
1263.         If body(i).position.x > _Width Then body(i).position.x = 0
1264.         ' If b(index).position.y < 0 Then b(index).position.y = _Height
1265.         If body(i).position.y > _Height Then body(i).position.y = 0
1266.     Next
1267.     If cRENDER_JOINTS Then
1268.         For i = 1 To sNUMBEROFJOINTS
1269.             Call renderJoints(j(i), body())
1270.         Next
1271.     End If
1272.     If cRENDER_COLLISIONS Then
1273.         hitcount = 0
1274.         Do While hits(hitcount).A <> hits(hitcount).B
1275.             Circle (hits(hitcount).position.x, hits(hitcount).position.y), 5, _RGB(255, 6, 11)
1276.             hitcount = hitcount + 1
1277.         Loop
1278.     End If
1279.  
1280. End Sub
1281.  
1282. Sub renderJoints (j As tJOINT, b() As tBODY)
1283.     Dim b1 As tBODY: b1 = b(j.body1)
1284.     Dim b2 As tBODY: b2 = b(j.body2)
1285.     Dim R1 As tMATRIX2d: R1 = b1.shape.u 'Call matrixSetRadians(R1, b1.orient)
1286.     Dim R2 As tMATRIX2d: R2 = b2.shape.u ' Call matrixSetRadians(R2, b2.orient)
1287.  
1288.     Dim x1 As tVECTOR2d: x1 = b1.position
1289.     Dim p1 As tVECTOR2d: Call matrixMultiplyVector(R1, j.localAnchor1, p1)
1290.  
1291.     Call vectorAddVectorND(p1, p1, x1)
1292.  
1293.     Dim x2 As tVECTOR2d: x2 = b2.position
1294.     Dim p2 As tVECTOR2d: Call matrixMultiplyVector(R2, j.localAnchor2, p2)
1295.  
1296.     Call vectorAddVectorND(p2, p2, x2)
1297.  
1298.     'Line (x1.x, x1.y)-(p1.x, p1.y), _RGB(127, 127, 244) 'blue
1299.     Line (p1.x, p1.y)-(x2.x, x2.y), _RGB(255, 255, 127) 'yellow
1300.     ' Line (x2.x, x2.y)-(p2.x, p2.y), _RGB32(127, 255, 127) 'green
1301.     ' Line (p2.x, p2.y)-(x1.x, x1.y), _RGB(127, 6, 127) 'purple
1302. End Sub
1303.  
1304. Sub renderWireframePoly (p() As tPOLY, pa() As tPOLYATTRIB, b() As tBODY, index As Integer)
1305.     Dim a As tVECTOR2d ' dummy vertices
1306.     Dim b As tVECTOR2d
1307.  
1308.     Dim i, element, element_next As Integer
1309.     For i = 0 To pa(index).count
1310.         element = pa(index).start + i
1311.         element_next = pa(index).start + arrayNextIndex(i, pa(index).count) ' wrap around back to first element
1312.         a = p(element).vert
1313.         b = p(element_next).vert
1314.  
1315.         Call matrixMultiplyVector(b(index).shape.u, a, a)
1316.         Call matrixMultiplyVector(b(index).shape.u, b, b)
1317.         Call vectorAddVector(a, b(index).position)
1318.         Call vectorAddVector(b, b(index).position)
1319.  
1320.         Line (a.x, a.y)-(b.x, b.y), b(index).c
1321.     Next
1322. End Sub
1323.  
1324. Sub renderTexturedBox (p() As tPOLY, pa() As tPOLYATTRIB, b() As tBODY, index As Integer)
1325.     Dim vert(3) As tVECTOR2d
1326.     Dim W, H As Integer
1327.     Dim bm As Long
1328.     bm = b(index).shape.texture
1329.     W = _Width(bm): H = _Height(bm)
1330.     Dim i As Integer
1331.     For i = 0 To 3
1332.         vert(i) = p(pa(index).start + i).vert
1333.         Call matrixMultiplyVector(b(index).shape.u, vert(i), vert(i))
1334.         Call vectorAddVector(vert(i), b(index).position)
1335.     Next
1336.     If b(index).velocity.x > 1 Or b(index).shape.flipTexture = 0 Then
1337.         _MapTriangle (0, 0)-(W - 1, 0)-(W - 1, H - 1), bm To(vert(3).x, vert(3).y)-(vert(0).x, vert(0).y)-(vert(1).x, vert(1).y)
1338.         _MapTriangle (0, 0)-(0, H - 1)-(W - 1, H - 1), bm To(vert(3).x, vert(3).y)-(vert(2).x, vert(2).y)-(vert(1).x, vert(1).y)
1339.     Else
1340.         _MapTriangle (0, 0)-(W - 1, 0)-(W - 1, H - 1), bm To(vert(0).x, vert(0).y)-(vert(3).x, vert(3).y)-(vert(2).x, vert(2).y)
1341.         _MapTriangle (0, 0)-(0, H - 1)-(W - 1, H - 1), bm To(vert(0).x, vert(0).y)-(vert(1).x, vert(1).y)-(vert(2).x, vert(2).y)
1342.     End If
1343.  
1344. End Sub
1345.  
1346. Sub renderWireframeCircle (b() As tBODY, index As Integer)
1347.     Circle (b(index).position.x, b(index).position.y), b(index).shape.radius, b(index).c
1348.     Line (b(index).position.x, b(index).position.y)-(b(index).position.x + Cos(b(index).orient) * b(index).shape.radius, b(index).position.y + Sin(b(index).orient) * b(index).shape.radius), b(index).c
1349. End Sub
1350.  
1351. Sub renderTexturedCircle (b() As tBODY, index As Integer)
1352.     Dim vert(3) As tVECTOR2d
1353.     Dim W, H As Integer
1354.     Dim bm As Long
1355.     bm = b(index).shape.texture
1356.     W = _Width(bm): H = _Height(bm)
1357.     Call vectorSet(vert(0), -b(index).shape.radius, -b(index).shape.radius)
1358.     Call vectorSet(vert(1), -b(index).shape.radius, b(index).shape.radius)
1359.     Call vectorSet(vert(2), b(index).shape.radius, b(index).shape.radius)
1360.     Call vectorSet(vert(3), b(index).shape.radius, -b(index).shape.radius)
1361.     Dim i As Integer
1362.     For i = 0 To 3
1363.         Call matrixMultiplyVector(b(index).shape.u, vert(i), vert(i))
1364.         Call vectorAddVector(vert(i), b(index).position)
1365.     Next
1366.     _MapTriangle (0, 0)-(0, H - 1)-(W - 1, H - 1), bm To(vert(0).x, vert(0).y)-(vert(1).x, vert(1).y)-(vert(2).x, vert(2).y)
1367.     _MapTriangle (0, 0)-(W - 1, 0)-(W - 1, H - 1), bm To(vert(0).x, vert(0).y)-(vert(3).x, vert(3).y)-(vert(2).x, vert(2).y)
1368.  
1369. End Sub
1370. Sub polygonSetOrient (b As tBODY, radians As _Float)
1371.     Call matrixSetRadians(b.shape.u, radians)
1372. End Sub
1373.  
1374. '**********************************************************************************************
1375. '   Object initialization Ahead
1376. '**********************************************************************************************
1377.  
1378. Sub circleInitialize (b() As tBODY, index As Integer)
1379.     Call circleComputeMass(b(), index, 1.0)
1380. End Sub
1381.  
1382. Sub circleComputeMass (b() As tBODY, index As Integer, density As _Float)
1383.     b(index).mass = cPI * b(index).shape.radius * b(index).shape.radius * density
1384.     If b(index).mass <> 0 Then
1385.         b(index).invMass = 1.0 / b(index).mass
1386.     Else
1387.         b(index).invMass = 0.0
1388.     End If
1389.  
1390.     b(index).inertia = b(index).mass * b(index).shape.radius * b(index).shape.radius
1391.  
1392.     If b(index).inertia <> 0 Then
1393.         b(index).invInertia = 1.0 / b(index).inertia
1394.     Else
1395.         b(index).invInertia = 0.0
1396.     End If
1397. End Sub
1398.  
1399. Sub polygonInitialize (body() As tBODY, p() As tPOLY, pa() As tPOLYATTRIB, index As Integer)
1400.     Call polygonComputeMass(body(), p(), pa(), index, 1.0)
1401. End Sub
1402.  
1403. Sub polygonComputeMass (b() As tBODY, p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, density As _Float)
1404.     Dim c As tVECTOR2d ' centroid
1405.     Dim p1 As tVECTOR2d
1406.     Dim p2 As tVECTOR2d
1407.     Dim area As _Float
1408.     Dim I As _Float
1409.     Dim k_inv3 As _Float
1410.     Dim D As _Float
1411.     Dim triangleArea As _Float
1412.     Dim weight As _Float
1413.     Dim intx2 As _Float
1414.     Dim inty2 As _Float
1415.     Dim ii As Integer
1416.  
1417.     k_inv3 = 1.0 / 3.0
1418.  
1419.     For ii = 0 To pa(index).count
1420.         p1 = p(pa(index).start + ii).vert
1421.         p2 = p(pa(index).start + arrayNextIndex(ii, pa(index).count)).vert
1422.         D = vectorCross(p1, p2)
1423.         triangleArea = .5 * D
1424.         area = area + triangleArea
1425.         weight = triangleArea * k_inv3
1426.         Call vectorAddVectorScalar(c, p1, weight)
1427.         Call vectorAddVectorScalar(c, p2, weight)
1428.         intx2 = p1.x * p1.x + p2.x * p1.x + p2.x * p2.x
1429.         inty2 = p1.y * p1.y + p2.y * p1.y + p2.y * p2.y
1430.         I = I + (0.25 * k_inv3 * D) * (intx2 + inty2)
1431.     Next ii
1432.  
1433.     Call vectorMultiplyScalar(c, 1.0 / area)
1434.  
1435.     For ii = 0 To pa(index).count
1436.         Call vectorSubVector(p(pa(index).start + ii).vert, c)
1437.     Next
1438.  
1439.     b(index).mass = density * area
1440.     If b(index).mass <> 0.0 Then
1441.         b(index).invMass = 1.0 / b(index).mass
1442.     Else
1443.         b(index).invMass = 0.0
1444.     End If
1445.  
1446.     b(index).inertia = I * density
1447.     If b(index).inertia <> 0 Then
1448.         b(index).invInertia = 1.0 / b(index).inertia
1449.     Else
1450.         b(index).invInertia = 0.0
1451.     End If
1452. End Sub
1453. '**********************************************************************************************
1454. '   Joint Stuff Ahead
1455. '**********************************************************************************************
1456. Sub jointSet (j As tJOINT, body() As tBODY, b1 As Integer, b2 As Integer, x As _Float, y As _Float)
1457.     Dim anchor As tVECTOR2d
1458.     Call vectorSet(anchor, x, y)
1459.     Dim Rot1 As tMATRIX2d: Rot1 = body(b1).shape.u 'Call matrixSetRadians(Rot1, body(b1).orient)
1460.     Dim Rot2 As tMATRIX2d: Rot2 = body(b2).shape.u 'Call matrixSetRadians(Rot2, body(b2).orient)
1461.     Dim Rot1T As tMATRIX2d: Call matrixTranspose(Rot1, Rot1T)
1462.     Dim Rot2T As tMATRIX2d: Call matrixTranspose(Rot2, Rot2T)
1463.     Dim tv As tVECTOR2d
1464.  
1465.     j.body1 = b1
1466.     j.body2 = b2
1467.  
1468.     Call vectorSubVectorND(tv, anchor, body(b1).position)
1469.     Call matrixMultiplyVector(Rot1T, tv, j.localAnchor1)
1470.  
1471.     Call vectorSubVectorND(tv, anchor, body(b2).position)
1472.     Call matrixMultiplyVector(Rot2T, tv, j.localAnchor2)
1473.  
1474.     Call vectorSet(j.P, 0, 0)
1475.  
1476.     j.softness = 0
1477.     j.biasFactor = 100
1478.  
1479. End Sub
1480.  
1481. Sub jointPrestep (j As tJOINT, body() As tBODY, inv_dt As _Float)
1482.     Dim Rot1 As tMATRIX2d: Rot1 = body(j.body1).shape.u 'Call matrixSetRadians(Rot1, body(j.body1).orient)
1483.     Dim Rot2 As tMATRIX2d: Rot2 = body(j.body2).shape.u 'Call matrixSetRadians(Rot2, body(j.body2).orient)
1484.     Dim b1invMass As _Float
1485.     Dim b2invMass As _Float
1486.  
1487.     Dim b1invInertia As _Float
1488.     Dim b2invInertia As _Float
1489.  
1490.     Call matrixMultiplyVector(Rot1, j.localAnchor1, j.r1)
1491.     Call matrixMultiplyVector(Rot2, j.localAnchor2, j.r2)
1492.  
1493.     b1invMass = body(j.body1).invMass
1494.     b2invMass = body(j.body2).invMass
1495.  
1496.     b1invInertia = body(j.body1).invInertia
1497.     b2invInertia = body(j.body2).invInertia
1498.  
1499.     Dim K1 As tMATRIX2d
1500.     Call matrixSetScalar(K1, b1invMass + b2invMass, 0,_
1501.                                                 0, b1invMass + b2invMass)
1502.     Dim K2 As tMATRIX2d
1503.     Call matrixSetScalar(K2, b1invInertia * j.r1.y * j.r1.y, -b1invInertia * j.r1.x * j.r1.y,_
1504.                             -b1invInertia * j.r1.x * j.r1.y,  b1invInertia * j.r1.x * j.r1.x)
1505.  
1506.     Dim K3 As tMATRIX2d
1507.     Call matrixSetScalar(K3,  b2invInertia * j.r2.y * j.r2.y, - b2invInertia * j.r2.x * j.r2.y,_
1508.                              -b2invInertia * j.r2.x * j.r2.y,   b2invInertia * j.r2.x * j.r2.x)
1509.  
1510.     Dim K As tMATRIX2d
1511.     Call matrixAddMatrix(K1, K2, K)
1512.     Call matrixAddMatrix(K3, K, K)
1513.     K.m00 = K.m00 + j.softness
1514.     K.m11 = K.m11 + j.softness
1515.     Call matrixInvert(K, j.M)
1516.  
1517.     Dim p1 As tVECTOR2d: Call vectorAddVectorND(p1, body(j.body1).position, j.r1)
1518.     Dim p2 As tVECTOR2d: Call vectorAddVectorND(p2, body(j.body2).position, j.r2)
1519.     Dim dp As tVECTOR2d: Call vectorSubVectorND(dp, p2, p1)
1520.  
1521.     Call vectorMultiplyScalarND(j.bias, dp, -j.biasFactor * inv_dt)
1522.     'Call vectorSet(j.bias, 0, 0)
1523.     Call vectorSet(j.P, 0, 0)
1524. End Sub
1525.  
1526. Sub jointApplyImpulse (j As tJOINT, body() As tBODY)
1527.     Dim dv As tVECTOR2d
1528.     Dim impulse As tVECTOR2d
1529.     Dim cross1 As tVECTOR2d
1530.     Dim cross2 As tVECTOR2d
1531.     Dim tv As tVECTOR2d
1532.  
1533.  
1534.     'Vec2 dv = body2->velocity + Cross(body2->angularVelocity, r2) - body1->velocity - Cross(body1->angularVelocity, r1);
1535.     Call vectorCrossScalar(cross2, j.r2, body(j.body2).angularVelocity)
1536.     Call vectorCrossScalar(cross1, j.r1, body(j.body1).angularVelocity)
1537.     Call vectorAddVectorND(dv, body(j.body2).velocity, cross2)
1538.     Call vectorSubVectorND(dv, dv, body(j.body1).velocity)
1539.     Call vectorSubVectorND(dv, dv, cross1)
1540.  
1541.     ' impulse = M * (bias - dv - softness * P);
1542.     Call vectorMultiplyScalarND(tv, j.P, j.softness)
1543.     Call vectorSubVectorND(impulse, j.bias, dv)
1544.     Call vectorSubVectorND(impulse, impulse, tv)
1545.     Call matrixMultiplyVector(j.M, impulse, impulse)
1546.  
1547.     ' body1->velocity -= body1->invMass * impulse;
1548.  
1549.     Call vectorMultiplyScalarND(tv, impulse, body(j.body1).invMass)
1550.     Call vectorSubVectorND(body(j.body1).velocity, body(j.body1).velocity, tv)
1551.  
1552.     ' body1->angularVelocity -= body1->invI * Cross(r1, impulse);
1553.     Dim crossScalar As _Float
1554.     crossScalar = vectorCross(j.r1, impulse)
1555.     body(j.body1).angularVelocity = body(j.body1).angularVelocity - body(j.body1).invInertia * crossScalar
1556.  
1557.     Call vectorMultiplyScalarND(tv, impulse, body(j.body2).invMass)
1558.     Call vectorAddVectorND(body(j.body2).velocity, body(j.body2).velocity, tv)
1559.  
1560.     crossScalar = vectorCross(j.r2, impulse)
1561.     body(j.body2).angularVelocity = body(j.body2).angularVelocity + body(j.body2).invInertia * crossScalar
1562.  
1563.     Call vectorAddVectorND(j.P, j.P, impulse)
1564.  
1565. End Sub
1566.  
1567. '**********************************************************************************************
1568. '   Vector Math Ahead
1569. '**********************************************************************************************
1570.  
1571. Sub vectorSet (v As tVECTOR2d, x As _Float, y As _Float)
1572.     v.x = x
1573.     v.y = y
1574. End Sub
1575.  
1576. Sub vectorSetVector (o As tVECTOR2d, v As tVECTOR2d)
1577.     o.x = v.x
1578.     o.y = v.y
1579. End Sub
1580.  
1581. Sub vectorNeg (v As tVECTOR2d)
1582.     v.x = -v.x
1583.     v.y = -v.y
1584. End Sub
1585.  
1586. Sub vectorNegND (o As tVECTOR2d, v As tVECTOR2d)
1587.     o.x = -v.x
1588.     o.y = -v.y
1589. End Sub
1590.  
1591. Sub vectorMultiplyScalar (v As tVECTOR2d, s As _Float)
1592.     v.x = v.x * s
1593.     v.y = v.y * s
1594. End Sub
1595.  
1596. Sub vectorMultiplyScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1597.     o.x = v.x * s
1598.     o.y = v.y * s
1599. End Sub
1600.  
1601. Sub vectorDivideScalar (v As tVECTOR2d, s As _Float)
1602.     v.x = v.x / s
1603.     v.y = v.y / s
1604. End Sub
1605.  
1606. Sub vectorDivideScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1607.     o.x = v.x / s
1608.     o.y = v.y / s
1609. End Sub
1610.  
1611. Sub vectorAddScalar (v As tVECTOR2d, s As _Float)
1612.     v.x = v.x + s
1613.     v.y = v.y + s
1614. End Sub
1615.  
1616. Sub vectorAddScalarND (o As tVECTOR2d, v As tVECTOR2d, s As _Float)
1617.     o.x = v.x + s
1618.     o.y = v.y + s
1619. End Sub
1620.  
1621. Sub vectorMultiplyVector (v As tVECTOR2d, m As tVECTOR2d)
1622.     v.x = v.x * m.x
1623.     v.y = v.y * m.y
1624. End Sub
1625.  
1626. Sub vectorMultiplyVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1627.     o.x = v.x * m.x
1628.     o.y = v.y * m.y
1629. End Sub
1630.  
1631. Sub vectorDivideVector (v As tVECTOR2d, m As tVECTOR2d)
1632.     v.x = v.x / m.x
1633.     v.y = v.y / m.y
1634. End Sub
1635.  
1636. Sub vectorAddVector (v As tVECTOR2d, m As tVECTOR2d)
1637.     v.x = v.x + m.x
1638.     v.y = v.y + m.y
1639. End Sub
1640.  
1641. Sub vectorAddVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1642.     o.x = v.x + m.x
1643.     o.y = v.y + m.y
1644. End Sub
1645.  
1646. Sub vectorAddVectorScalar (v As tVECTOR2d, m As tVECTOR2d, s As _Float)
1647.     v.x = v.x + m.x * s
1648.     v.y = v.y + m.y * s
1649. End Sub
1650.  
1651. Sub vectorAddVectorScalarND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d, s As _Float)
1652.     o.x = v.x + m.x * s
1653.     o.y = v.y + m.y * s
1654. End Sub
1655.  
1656. Sub vectorSubVector (v As tVECTOR2d, m As tVECTOR2d)
1657.     v.x = v.x - m.x
1658.     v.y = v.y - m.y
1659. End Sub
1660.  
1661. Sub vectorSubVectorND (o As tVECTOR2d, v As tVECTOR2d, m As tVECTOR2d)
1662.     o.x = v.x - m.x
1663.     o.y = v.y - m.y
1664. End Sub
1665.  
1666. Function vectorLengthSq (v As tVECTOR2d)
1667.     vectorLengthSq = v.x * v.x + v.y * v.y
1668. End Function
1669.  
1670. Function vectorLength (v As tVECTOR2d)
1671.     vectorLength = Sqr(vectorLengthSq(v))
1672. End Function
1673.  
1674. Sub vectorRotate (v As tVECTOR2d, radians As _Float)
1675.     Dim c, s, xp, yp As _Float
1676.     c = Cos(radians)
1677.     s = Sin(radians)
1678.     xp = v.x * c - v.y * s
1679.     yp = v.x * s + v.y * c
1680.     v.x = xp
1681.     v.y = yp
1682. End Sub
1683.  
1684. Sub vectorNormalize (v As tVECTOR2d)
1685.     Dim lenSQ, invLen As _Float
1686.     lenSQ = vectorLengthSq(v)
1687.     If lenSQ > cEPSILON_SQ Then
1688.         invLen = 1.0 / Sqr(lenSQ)
1689.         v.x = v.x * invLen
1690.         v.y = v.y * invLen
1691.     End If
1692. End Sub
1693.  
1694. Sub vectorMin (a As tVECTOR2d, b As tVECTOR2d, o As tVECTOR2d)
1695.     o.x = scalarMin(a.x, b.x)
1696.     o.y = scalarMin(a.y, b.y)
1697. End Sub
1698.  
1699. Sub vectorMax (a As tVECTOR2d, b As tVECTOR2d, o As tVECTOR2d)
1700.     o.x = scalarMax(a.x, b.x)
1701.     o.y = scalarMax(a.y, b.y)
1702. End Sub
1703.  
1704. Function vectorDot (a As tVECTOR2d, b As tVECTOR2d)
1705.     vectorDot = a.x * b.x + a.y * b.y
1706. End Function
1707.  
1708. Function vectorSqDist (a As tVECTOR2d, b As tVECTOR2d)
1709.     Dim dx, dy As _Float
1710.     dx = b.x - a.x
1711.     dy = b.y - a.y
1712.     vectorSqDist = dx * dx + dy * dy
1713. End Function
1714.  
1715. Function vectorDistance (a As tVECTOR2d, b As tVECTOR2d)
1716.     vectorDistance = Sqr(vectorSqDist(a, b))
1717. End Function
1718.  
1719. Function vectorCross (a As tVECTOR2d, b As tVECTOR2d)
1720.     vectorCross = a.x * b.y - a.y * b.x
1721. End Function
1722.  
1723. Sub vectorCrossScalar (o As tVECTOR2d, v As tVECTOR2d, a As _Float)
1724.     o.x = v.y * -a
1725.     o.y = v.x * a
1726. End Sub
1727.  
1728. Function vectorArea (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1729.     vectorArea = (((b.x - a.x) * (c.y - a.y)) - ((c.x - a.x) * (b.y - a.y)))
1730. End Function
1731.  
1732. Function vectorLeft (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1733.     vectorLeft = vectorArea(a, b, c) > 0
1734. End Function
1735.  
1736. Function vectorLeftOn (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1737.     vectorLeftOn = vectorArea(a, b, c) >= 0
1738. End Function
1739.  
1740. Function vectorRight (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1741.     vectorRight = vectorArea(a, b, c) < 0
1742. End Function
1743.  
1744. Function vectorRightOn (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d)
1745.     vectorRightOn = vectorArea(a, b, c) <= 0
1746. End Function
1747.  
1748. Function vectorCollinear (a As tVECTOR2d, b As tVECTOR2d, c As tVECTOR2d, thresholdAngle As _Float)
1749.     If (thresholdAngle = 0) Then
1750.         vectorCollinear = (vectorArea(a, b, c) = 0)
1751.     Else
1752.         Dim ab As tVECTOR2d
1753.         Dim bc As tVECTOR2d
1754.         Dim dot As _Float
1755.         Dim magA As _Float
1756.         Dim magB As _Float
1757.         Dim angle As _Float
1758.  
1759.         ab.x = b.x - a.x
1760.         ab.y = b.y - a.y
1761.         bc.x = c.x - b.x
1762.         bc.y = c.y - b.y
1763.  
1764.         dot = ab.x * bc.x + ab.y * bc.y
1765.         magA = Sqr(ab.x * ab.x + ab.y * ab.y)
1766.         magB = Sqr(bc.x * bc.x + bc.y * bc.y)
1767.         angle = _Acos(dot / (magA * magB))
1768.         vectorCollinear = angle < thresholdAngle
1769.     End If
1770. End Function
1771.  
1772. Sub vectorGetSupport (p() As tPOLY, pa() As tPOLYATTRIB, index As Integer, dir As tVECTOR2d, bestVertex As tVECTOR2d)
1773.     Dim bestProjection As _Float
1774.     Dim v As tVECTOR2d
1775.     Dim projection As _Float
1776.     Dim i As Integer
1777.     bestVertex.x = -9999999
1778.     bestVertex.y = -9999999
1779.     bestProjection = -9999999
1780.  
1781.     For i = 0 To pa(index).count
1782.         v = p(i + pa(index).start).vert
1783.         projection = vectorDot(v, dir)
1784.         If projection > bestProjection Then
1785.             bestVertex = v
1786.             bestProjection = projection
1787.         End If
1788.     Next
1789. End Sub
1790.  
1791. '**********************************************************************************************
1792. '   Matrix Stuff Ahead
1793. '**********************************************************************************************
1794.  
1795. Sub matrixSetRadians (m As tMATRIX2d, radians As _Float)
1796.     Dim c As _Float
1797.     Dim s As _Float
1798.     c = Cos(radians)
1799.     s = Sin(radians)
1800.     m.m00 = c
1801.     m.m01 = -s
1802.     m.m10 = s
1803.     m.m11 = c
1804. End Sub
1805.  
1806. Sub matrixSetScalar (m As tMATRIX2d, a As _Float, b As _Float, c As _Float, d As _Float)
1807.     m.m00 = a
1808.     m.m01 = b
1809.     m.m10 = c
1810.     m.m11 = d
1811. End Sub
1812.  
1813. Sub matrixAbs (m As tMATRIX2d, o As tMATRIX2d)
1814.     o.m00 = Abs(m.m00)
1815.     o.m01 = Abs(m.m01)
1816.     o.m10 = Abs(m.m10)
1817.     o.m11 = Abs(m.m11)
1818. End Sub
1819.  
1820. Sub matrixGetAxisX (m As tMATRIX2d, o As tVECTOR2d)
1821.     o.x = m.m00
1822.     o.y = m.m10
1823. End Sub
1824.  
1825. Sub matrixGetAxisY (m As tMATRIX2d, o As tVECTOR2d)
1826.     o.x = m.m01
1827.     o.y = m.m11
1828. End Sub
1829.  
1830. Sub matrixTransposeI (m As tMATRIX2d)
1831.     Swap m.m01, m.m10
1832. End Sub
1833.  
1834. Sub matrixTranspose (m As tMATRIX2d, o As tMATRIX2d)
1835.     Dim tm As tMATRIX2d
1836.     tm.m00 = m.m00
1837.     tm.m01 = m.m10
1838.     tm.m10 = m.m01
1839.     tm.m11 = m.m11
1840.     o = tm
1841. End Sub
1842.  
1843. Sub matrixInvert (m As tMATRIX2d, o As tMATRIX2d)
1844.     Dim a, b, c, d, det As _Float
1845.     Dim tm As tMATRIX2d
1846.  
1847.     a = m.m00: b = m.m01: c = m.m10: d = m.m11
1848.     det = a * d - b * c
1849.     If det = 0 Then Exit Sub
1850.  
1851.     det = 1 / det
1852.     tm.m00 = det * d: tm.m01 = -det * b
1853.     tm.m10 = -det * c: tm.m11 = det * a
1854.     o = tm
1855. End Sub
1856.  
1857. Sub matrixMultiplyVector (m As tMATRIX2d, v As tVECTOR2d, o As tVECTOR2d)
1858.     Dim t As tVECTOR2d
1859.     t.x = m.m00 * v.x + m.m01 * v.y
1860.     t.y = m.m10 * v.x + m.m11 * v.y
1861.     o = t
1862. End Sub
1863.  
1864. Sub matrixAddMatrix (m As tMATRIX2d, x As tMATRIX2d, o As tMATRIX2d)
1865.     o.m00 = m.m00 + x.m00
1866.     o.m01 = m.m01 + x.m01
1867.     o.m10 = m.m10 + x.m10
1868.     o.m11 = m.m11 + x.m11
1869. End Sub
1870.  
1871. Sub matrixMultiplyMatrix (m As tMATRIX2d, x As tMATRIX2d, o As tMATRIX2d)
1872.     o.m00 = m.m00 * x.m00 + m.m01 * x.m10
1873.     o.m01 = m.m00 * x.m01 + m.m01 * x.m11
1874.     o.m10 = m.m10 * x.m00 + m.m11 * x.m10
1875.     o.m11 = m.m10 * x.m01 + m.m11 * x.m11
1876. End Sub
1877.  
1878. '**********************************************************************************************
1879. '   Mostly Unused Stuff Ahead
1880. '**********************************************************************************************
1881.  
1882. Sub polygonMakeCCW (obj As tTRIANGLE)
1883.     If vectorLeft(obj.a, obj.b, obj.c) = 0 Then
1884.         Swap obj.a, obj.c
1885.     End If
1886. End Sub
1887.  
1888. Function polygonIsReflex (t As tTRIANGLE)
1889.     polygonIsReflex = vectorRight(t.a, t.b, t.c)
1890. End Function
1891.  
1892. Function scalarMin (a As _Float, b As _Float)
1893.     If a < b Then
1894.         scalarMin = a
1895.     Else
1896.         scalarMin = b
1897.     End If
1898. End Function
1899.  
1900. Function scalarMax (a As _Float, b As _Float)
1901.     If a > b Then
1902.         scalarMax = a
1903.     Else
1904.         scalarMax = b
1905.     End If
1906. End Function
1907.  
1908. Sub lineIntersection (l1 As tLINE2d, l2 As tLINE2d, o As tVECTOR2d)
1909.     Dim a1, b1, c1, a2, b2, c2, det As _Float
1910.     o.x = 0
1911.     o.y = 0
1912.     a1 = l1.b.y - l1.a.y
1913.     b1 = l1.a.x - l1.b.x
1914.     c1 = a1 * l1.a.x + b1 * l1.a.y
1915.     a2 = l2.b.y - l2.a.y
1916.     b2 = l2.a.x - l2.b.x
1917.     c2 = a2 * l2.a.x + b2 * l2.a.y
1918.     det = a1 * b2 - a2 * b1
1919.  
1920.     If Int(det * cPRECISION) <> 0 Then
1921.         o.x = (b2 * c1 - b1 * c2) / det
1922.         o.y = (a1 * c2 - a2 * c1) / det
1923.     End If
1924. End Sub
1925.  
1926. Function lineSegmentsIntersect (l1 As tLINE2d, l2 As tLINE2d)
1927.     Dim dx, dy, da, db, s, t As _Float
1928.     dx = l1.b.x - l1.a.x
1929.     dy = l1.b.y - l1.a.y
1930.     da = l2.b.x - l2.a.x
1931.     db = l2.b.y - l2.a.y
1932.     If da * dy - db * dx = 0 Then
1933.         lineSegmentsIntersect = 0
1934.     Else
1935.         s = (dx * (l2.a.y - l1.a.y) + dy * (l1.a.x - l2.a.x)) / (da * dy - db * dx)
1936.         t = (da * (l1.a.y - l2.a.y) + db * (l2.a.x - l1.a.x)) / (db * dx - da * dy)
1937.         lineSegmentsIntersect = (s >= 0 And s <= 1 And t >= 0 And t <= 1)
1938.     End If
1939. End Function
1940.  
1941. '**********************************************************************************************
1942. '   Impulse Specific Math Ahead
1943. '**********************************************************************************************
1944.  
1945. Function impulseEqual (a As _Float, b As _Float)
1946.     impulseEqual = Abs(a - b) <= cEPSILON
1947. End Function
1948.  
1949. Function impulseClamp (min As _Float, max As _Float, a As _Float)
1950.     If a < min Then
1951.         impulseClamp = min
1952.     Else If a > max Then
1953.             impulseClamp = max
1954.         Else
1955.             impulseClamp = a
1956.         End If
1957.     End If
1958. End Function
1959.  
1960. Function impulseRound (a As _Float)
1961.     impulseRound = Int(a + 0.5)
1962. End Function
1963.  
1964. Function impulseRandom_float (min As _Float, max As _Float)
1965.     impulseRandom_float = ((max - min) * Rnd + min)
1966. End Function
1967.  
1968. Function impulseRandomInteger (min As Integer, max As Integer)
1969.     impulseRandomInteger = Int((max - min) * Rnd + min)
1970. End Function
1971.  
1972. Function impulseGT (a As _Float, b As _Float)
1973.     impulseGT = (a >= b * cBIAS_RELATIVE + a * cBIAS_ABSOLUTE)
1974. End Function
1975.  
1976. '**********************************************************************************************
1977. '   Troubleshooting Tools
1978. '**********************************************************************************************
1979.  
1980. Sub printMatrix (u As tMATRIX2d, n As Integer)
1981.     Print "---------------------------"
1982.     Print n; " u:"; u.m00; "|"; u.m10
1983.     Print "       "; u.m10; "|"; u.m11
1984.     Do
1985.     Loop Until _KeyHit = 27
1986. End Sub
1987.  
1988.  
1989. '**********************************************************************************************
1990. '   Generate Bitmap
1991. '**********************************************************************************************
1992.  
1993. Sub generateBitmap (bm() As Long)
1994.     Dim cl As _Unsigned Long
1995.     Dim rleCount, y, x, i As Integer
1996.  
1997.     'CIRCLE QB
1998.     Data 0,30,4289110427,4,0,52,4289110427,15,0,44,4289110427,21,0,38,4289110427,7
1999.     Data 4281808695,11,4289110427,7,0,34,4289110427,5,4281808695,18,4289110427,5,0,30,4289110427,4
2000.     Data 4281808695,23,4289110427,4,0,28,4289110427,3,4281808695,27,4289110427,3,0,25,4289110427,3
2001.     Data 4281808695,31,4289110427,3,0,22,4289110427,3,4281808695,33,4289110427,3,0,20,4289110427,3
2002.     Data 4281808695,35,4289110427,3,0,18,4289110427,3,4281808695,38,4289110427,2,0,16,4289110427,3
2003.     Data 4281808695,40,4289110427,2,0,14,4289110427,3,4281808695,42,4289110427,2,0,13,4289110427,2
2004.     Data 4281808695,43,4289110427,3,0,11,4289110427,2,4281808695,45,4289110427,2,0,10,4289110427,2
2005.     Data 4281808695,47,4289110427,2,0,8,4289110427,2,4281808695,49,4289110427,2,0,7,4289110427,2
2006.     Data 4281808695,49,4289110427,2,0,6,4289110427,2,4281808695,51,4289110427,2,0,5,4289110427,2
2007.     Data 4281808695,51,4289110427,2,0,5,4289110427,1,4281808695,53,4289110427,2,0,3,4289110427,2
2008.     Data 4281808695,53,4289110427,2,0,3,4289110427,2,4281808695,54,4289110427,1,0,3,4289110427,1
2009.     Data 4281808695,7,4281084972,0,4279703319,0,4279637526,10,4280492835,0,4281808695,7,4279637526,14,4279834905,0
2010.     Data 4281742902,0,4281808695,8,4289110427,2,0,1,4289110427,2,4281808695,6,4279637526,15,4281808695,6
2011.     Data 4279637526,17,4281808695,7,4289110427,2,0,1,4289110427,2,4281808695,5,4279637526,1,4282412608,0
2012.     Data 4284394590,14,4281808695,5,4279637526,1,4284394590,15,4284394334,0,4281808695,7,4289110427,1,0,1
2013.     Data 4289110427,1,4281808695,6,4279637526,0,4280034076,0,4284394590,16,4281808695,4,4279637526,1,4284394590,16
2014.     Data 4284129114,0,4281808695,6,4289110427,1,0,1,4289110427,1,4281808695,6,4279637526,0,4284394590,17
2015.     Data 4283333454,0,4281808695,3,4279637526,1,4284394590,17,4281808695,6,4289110427,2,0,0,4289110427,1
2016.     Data 4281808695,6,4279637526,0,4284394590,3,4281808695,9,4279637526,0,4284394590,3,4281808695,3,4279637526,1
2017.     Data 4284394590,2,4281808695,9,4279637526,0,4284394590,3,4281808695,6,4289110427,2,0,0,4289110427,1
2018.     Data 4281808695,6,4279637526,0,4284394590,3,4281808695,9,4279637526,0,4284394590,3,4281808695,3,4279637526,1
2019.     Data 4284394590,2,4281808695,9,4279637526,0,4284394590,3,4281808695,6,4289110427,5,4281808695,6,4279637526,0
2020.     Data 4284394590,3,4281808695,9,4279637526,0,4284394590,3,4281808695,3,4279637526,1,4284394590,2,4281808695,9
2021.     Data 4279637526,0,4284394590,3,4281808695,6,4289110427,5,4281808695,6,4279637526,0,4284394590,3,4281808695,9
2022.     Data 4279637526,0,4284394590,3,4281808695,3,4279637526,1,4284394590,2,4279637526,10,4284394590,3,4281808695,6
2023.     Data 4289110427,5,4281808695,6,4279637526,0,4284394590,3,4281808695,9,4279637526,0,4284394590,3,4281808695,3
2024.     Data 4279637526,1,4284394590,17,4281808695,6,4289110427,5,4281808695,6,4279637526,0,4284394590,3,4281808695,9
2025.     Data 4279637526,0,4284394590,3,4281808695,3,4279637526,1,4284394590,16,4281808695,7,4289110427,5,4281808695,6
2026.     Data 4279637526,0,4284394590,3,4281808695,7,4281084972,0,4279703319,0,4279637526,0,4284394590,3,4281808695,3
2027.     Data 4279637526,1,4284394590,17,4281808695,6,4289110427,2,0,0,4289110427,1,4281808695,6,4279637526,0
2028.     Data 4284394590,3,4281808695,6,4279637526,3,4284394590,3,4281808695,3,4279637526,1,4284394590,17,4281808695,6
2029.     Data 4289110427,2,0,0,4289110427,1,4281808695,6,4279637526,0,4284394590,3,4281808695,5,4279637526,1
2030.     Data 4282412608,0,4284394590,5,4281808695,3,4279637526,1,4284394590,2,4281808695,9,4279637526,0,4284394590,3
2031.     Data 4281808695,6,4289110427,2,0,0,4289110427,1,4281808695,6,4279637526,0,4284394590,3,4281808695,5
2032.     Data 4279637526,0,4280034076,0,4284394590,6,4281808695,3,4279637526,1,4284394590,2,4281808695,9,4279637526,0
2033.     Data 4284394590,3,4281808695,6,4289110427,1,0,1,4289110427,2,4281808695,5,4279637526,0,4284394590,3
2034.     Data 4279637526,6,4284394590,7,4281808695,3,4279637526,1,4284394590,2,4279637526,10,4284394590,3,4281808695,6
2035.     Data 4289110427,1,0,1,4289110427,2,4281808695,5,4279637526,0,4284394590,16,4283532625,0,4281875000,0
2036.     Data 4281808695,3,4279637526,1,4284394590,17,4281808695,5,4289110427,2,0,2,4289110427,1,4281808695,6
2037.     Data 4284394590,15,4281808695,6,4279637526,1,4284394590,17,4281808695,5,4289110427,2,0,2,4289110427,1
2038.     Data 4281808695,7,4284394590,13,4281808695,7,4279637526,1,4284394590,16,4282803270,0,4281808695,5,4289110427,1
2039.     Data 0,3,4289110427,2,4281808695,7,4284394590,12,4281808695,9,4284394590,15,4282670916,0,4281808695,5
2040.     Data 4289110427,2,0,4,4289110427,1,4281808695,53,4289110427,2,0,4,4289110427,2,4281808695,52
2041.     Data 4289110427,1,0,5,4289110427,2,4281808695,51,4289110427,2,0,6,4289110427,2,4281808695,50
2042.     Data 4289110427,1,0,7,4289110427,2,4281808695,49,4289110427,2,0,8,4289110427,2,4281808695,47
2043.     Data 4289110427,2,0,10,4289110427,2,4281808695,46,4289110427,1,0,12,4289110427,2,4281808695,44
2044.     Data 4289110427,2,0,12,4289110427,2,4281808695,43,4289110427,2,0,14,4289110427,2,4281808695,41
2045.     Data 4289110427,2,0,16,4289110427,2,4281808695,39,4289110427,2,0,18,4289110427,3,4281808695,36
2046.     Data 4289110427,2,0,20,4289110427,3,4281808695,33,4289110427,3,0,22,4289110427,3,4281808695,31
2047.     Data 4289110427,3,0,24,4289110427,4,4281808695,28,4289110427,3,0,27,4289110427,4,4281808695,24
2048.     Data 4289110427,3,0,30,4289110427,5,4281808695,19,4289110427,5,0,33,4289110427,6,4281808695,13
2049.     Data 4289110427,6,0,37,4289110427,23,0,42,4289110427,17,0,49,4289110427,9,0,26
2050.  
2051.     'BOX 64
2052.     Data 4278190160,1484,4278650685,0,4279637527,0,4279637526,13,4278190160,5,4279637526,3,4278190160,10,4279637526,3
2053.     Data 4278190160,21,4279637526,16,4278190160,5,4279637526,3,4278190160,10,4279637526,3,4278190160,20,4279637526,1
2054.     Data 4286280720,0,4290950923,16,4278190160,3,4279637526,1,4290950923,2,4278190160,9,4279637526,0,4290950923,3
2055.     Data 4278190160,19,4279637526,0,4280624149,0,4290950923,17,4278190160,3,4279637526,1,4290950923,2,4278190160,9
2056.     Data 4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,18,4278190160,3,4279637526,1,4290950923,2
2057.     Data 4278190160,9,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3,4278190160,18,4279637526,1
2058.     Data 4290950923,2,4278190160,9,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3,4278190160,18
2059.     Data 4279637526,1,4290950923,2,4278190160,9,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3
2060.     Data 4278190160,18,4279637526,1,4290950923,2,4278190160,9,4279637526,0,4290950923,3,4278190160,19,4279637526,0
2061.     Data 4290950923,3,4279637526,10,4279505947,0,4278190160,6,4279374370,0,4279637526,0,4290950923,2,4279637526,10
2062.     Data 4290950923,3,4278190160,19,4279637526,0,4290950923,16,4278190160,6,4279637526,0,4290950923,17,4278190160,19
2063.     Data 4279637526,0,4290950923,17,4278190160,5,4278255950,0,4290950923,17,4278190160,19,4279637526,0,4290950923,17
2064.     Data 4282070843,0,4278190160,5,4278584910,0,4290950923,16,4278190160,19,4279637526,0,4290950923,17,4290622221,0
2065.     Data 4278190160,7,4286149157,0,4290950923,14,4278190160,19,4279637526,0,4290950923,3,4278190160,9,4279637526,0
2066.     Data 4290950923,3,4278190160,18,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3,4278190160,9
2067.     Data 4279637526,0,4290950923,3,4278190160,18,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,3
2068.     Data 4279637526,10,4290950923,3,4278190160,18,4279637526,0,4290950923,3,4278190160,19,4279637526,0,4290950923,17
2069.     Data 4290687756,0,4278190160,18,4279637526,0,4290950923,3,4278190160,20,4290950923,17,4282597176,0,4278190160,18
2070.     Data 4279637526,0,4290950923,3,4278190160,21,4290950923,16,4278190160,19,4279637526,0,4290950923,3,4278190160,21
2071.     Data 4278255952,0,4290950923,14,4278190160,21,4290950923,3,4278190160,1353
2072.  
2073.     'Hedgehog CC0 - from Frogatto & Friends team - www.frogatto.com
2074.     Data 0,148,4282268723,0,4280889648,0,4282145364,0,4282541920,1,0,58,4282663478,0,4282143050,0
2075.     Data 4284656026,0,4285714365,0,4285914054,0,4290832070,0,4293848006,0,4293780935,0,4293650117,0,4293454274,0
2076.     Data 4293651396,0,4292602567,0,4288996553,0,4285375122,0,4282467390,0,4281546805,0,4281548088,0,0,48
2077.     Data 4281546546,0,4281822563,0,4283351467,0,4285519038,0,4286698443,0,4286229455,0,4285246658,0,4283876010,0
2078.     Data 4285518780,0,4288209609,0,4292471495,0,4294240706,0,4294042300,0,4289452478,0,4285250988,0,4281946187,0
2079.     Data 4282137394,0,0,48,4281225803,0,4284394139,0,4285847238,0,4284333241,0,4283611312,0,4283154601,0
2080.     Data 4288272314,0,4292733639,0,4294241734,0,4294963142,1,4293389510,0,4291224001,0,4286362786,0,4283662710,0
2081.     Data 4282072630,0,4283716160,0,0,46,4280360993,0,4284061579,0,4285716932,0,4283745711,0,4283614638,0
2082.     Data 4284534199,0,4290371775,0,4294963142,4,4294307270,0,4291291336,0,4288988330,0,4286939503,0,4284965458,0
2083.     Data 4283518782,0,4284768842,0,0,44,4280101432,0,4283931540,0,4285782725,0,4284205748,0,4285255865,0
2084.     Data 4287881930,0,4291881415,0,4294963142,8,4288190851,0,4281812801,0,4283520581,0,0,37,4280953127,0
2085.     Data 4280360993,4,4279842904,0,4279195808,0,4283608250,0,4286308299,1,4289521097,0,4294963142,10,4290635720,0
2086.     Data 4285515701,0,4282211158,0,4281940016,0,0,33,4281611053,1,0,0,4284391314,0,4287607966,0
2087.     Data 4291279772,3,4288330924,0,4284530112,0,4284138423,0,4283942833,1,4288075449,0,4294963142,8,4292930503,0
2088.     Data 4288865225,0,4290635720,0,4291219890,0,4284243796,0,4281940016,0,0,33,4283596917,0,4286285172,0
2089.     Data 4288389000,0,4290239421,0,4292471495,0,4294963142,3,4293061575,0,4290635720,0,4286896319,0,4284007093,0
2090.     Data 4281833640,0,4284131499,0,4289058743,0,4292338879,0,4294963142,1,4293323974,0,4290897864,0,4290635720,2
2091.     Data 4288733123,0,4285059258,0,4289847232,0,4293452220,0,4286947983,0,4283198818,0,0,32,4286225290,0
2092.     Data 4288865225,0,4292930503,0,4294963142,4,4294373062,0,4293192647,0,4293717190,0,4294963142,0,4290897864,0
2093.     Data 4287025091,0,4282355120,0,4281371305,0,4282164902,0,4288138425,0,4292799431,1,4290307784,0,4286701514,0
2094.     Data 4286308299,0,4286176969,0,4285716932,0,4284927421,0,4283807923,0,4288270525,0,4292209351,0,4289783240,0
2095.     Data 4285900437,0,4281350198,0,0,27,4281089595,0,4282880899,0,4287156403,0,4293060802,0,4294635206,0
2096.     Data 4294963142,6,4292799431,0,4287881930,0,4289848776,0,4294373062,1,4292798661,0,4287551427,0,4283474867,0
2097.     Data 4279325850,0,4283145392,0,4286174401,0,4286239939,0,4286240966,0,4286242506,0,4286176713,0,4285716933,0
2098.     Data 4283942322,0,4284002999,0,4285373646,0,4285906126,0,4287357386,0,4292209351,0,4290358930,0,4282136885,0
2099.     Data 0,25,4281545260,0,4283200618,0,4286103725,0,4290369721,0,4291224771,0,4288471752,0,4291422408,0
2100.     Data 4294963142,6,4292799431,0,4287881930,0,4286963914,0,4287881930,1,4286890933,0,4283457136,0,4281939800,0
2101.     Data 4281149267,0,4282924625,0,4284698708,0,4285616229,0,4286088592,0,4286240453,0,4284862651,0,4283875762,0
2102.     Data 4284721858,0,4285243083,0,4285504208,0,4285906126,0,4287357386,0,4292209351,0,4290358930,0,4282136885,0
2103.     Data 0,25,4283598459,0,4287412644,0,4291028936,0,4290373320,0,4288865225,0,4286767050,0,4290635720,0
2104.     Data 4294963142,4,4294635206,0,4291881415,0,4288667588,0,4285518523,0,4285121729,0,4285839566,0,4284451740,0
2105.     Data 4284375669,0,4286853466,0,4287570514,1,4288161614,0,4288555854,0,4288359511,0,4287449708,0,4286216070,0
2106.     Data 4284707957,0,4283855987,0,4285042614,0,4284387016,0,4282152887,0,4283212214,0,4285190329,0,4288339651,0
2107.     Data 4287211418,0,4282136134,0,4281806644,0,4282597686,1,4283321404,0,0,20,4284319354,0,4288535490,0
2108.     Data 4290635720,0,4291487943,0,4288144073,0,4287094986,0,4288668617,0,4291946951,0,4294963142,4,4294373062,0
2109.     Data 4289521097,0,4285519810,0,4283745711,0,4283604646,0,4284314276,0,4284235628,0,4285735502,0,4290717275,0
2110.     Data 4292290655,1,4292424285,0,4292295515,0,4291443803,0,4290002521,0,4288430166,0,4287313226,0,4286264909,0
2111.     Data 4284834187,0,4282934425,0,4280174724,0,4281891996,0,4284201400,0,4285518276,0,4285047966,0,4282792271,0
2112.     Data 4282196791,0,4282000433,0,4281147437,0,4281478192,0,4283452991,0,0,17,4280955955,0,4284259728,0
2113.     Data 4287876020,0,4292662449,0,4289318579,0,4285515701,1,4287876537,0,4292008383,0,4293190337,0,4293454274,0
2114.     Data 4293716933,0,4294110662,0,4294766278,0,4294438598,0,4293389510,0,4289127625,0,4285585603,0,4284008626,0
2115.     Data 4282809213,0,4281867840,0,4286981714,0,4290390622,0,4291635294,0,4291503964,0,4290783063,0,4291315025,0
2116.     Data 4291714381,1,4292238672,0,4293090900,0,4292689754,0,4291044955,0,4285014091,0,4282654021,1,4283847810,0
2117.     Data 4285108670,0,4285510587,0,4285110159,0,4284170819,0,4284952389,0,4285738325,0,4283310922,0,4281671227,0
2118.     Data 4280557349,0,4282597686,0,0,16,4280427043,0,4280889648,0,4281415734,0,4282071349,0,4281612341,0
2119.     Data 4281087798,1,4281091928,0,4281099414,0,4282882216,0,4284794798,0,4286503105,0,4289258697,0,4293979590,0
2120.     Data 4291619015,0,4287291594,0,4286701514,0,4286176969,0,4285979591,0,4284911494,0,4283641140,0,4287638350,0
2121.     Data 4290062942,0,4290259550,0,4287113034,0,4281803048,0,4281869607,0,4281935911,1,4285868859,0,4291768154,0
2122.     Data 4292291422,0,4291831902,0,4289800283,0,4288948570,1,4285540951,0,4282068051,0,4282134867,0,4282725193,0
2123.     Data 4283707447,0,4284952389,0,4285935190,0,4285607253,0,4284164423,0,4280951079,0,4282597686,0,0,22
2124.     Data 4281347882,0,4279972168,0,4279325072,0,4279921569,0,4280713124,0,4281435820,0,4283276465,0,4286826675,0
2125.     Data 4286107572,0,4284139445,0,4282753970,0,4282220961,0,4283067520,0,4285287524,0,4287769677,0,4289145687,0
2126.     Data 4288883030,0,4285080895,0,4284428600,0,4285154873,0,4286473550,0,4287719510,0,4288489531,0,4287304755,0
2127.     Data 4285079863,0,4289013070,0,4292159582,0,4291635294,0,4291438942,1,4289865305,0,4288095060,0,4287308883,0
2128.     Data 4285473868,0,4282983231,0,4283574590,0,4284952386,0,4287311186,0,4287376213,0,4284426565,0,4283183419,0
2129.     Data 4282466100,0,4284242501,0,0,21,4281426545,0,4281560742,0,4280378537,0,4279261856,0,4280185506,0
2130.     Data 4282356647,0,4286695345,0,4287549875,0,4287417779,0,4286032304,0,4284183443,0,4282200406,0,4285276750,0
2131.     Data 4290063198,0,4287768655,0,4285802818,0,4283839540,0,4285551169,0,4289429342,0,4290682227,0,4292121461,0
2132.     Data 4293340491,0,4290709299,0,4285927978,0,4286717242,0,4288226634,0,4290521176,0,4291438942,1,4291831902,0
2133.     Data 4291962974,0,4290718302,0,4288358488,0,4285407822,0,4285474631,0,4286459204,0,4288818005,0,4289407836,0
2134.     Data 4287835482,0,4284556870,0,4281082671,0,4283715395,0,0,19,4281224777,0,4282817418,0,4283937975,0
2135.     Data 4284257476,0,4282417079,0,4280776360,0,4283805100,0,4287746740,0,4293716675,0,4294241734,0,4293323719,0
2136.     Data 4293190599,0,4290293414,0,4283777115,0,4285276750,0,4290063198,0,4283966519,0,4281937450,0,4287192905,0
2137.     Data 4290088298,0,4292329616,1,4292582527,0,4293472334,0,4293918777,1,4287439157,0,4283185463,0,4286786890,0
2138.     Data 4288751958,0,4289931869,0,4290914654,0,4291635294,0,4290587230,0,4290063198,1,4290259550,0,4290456158,3
2139.     Data 4287440212,0,4283638343,0,4284171847,0,0,17,4280953126,0,4281822562,0,4283349669,0,4285124796,0
2140.     Data 4284069053,0,4280380583,0,4282685877,0,4286371784,0,4291552709,0,4294372548,0,4294831813,0,4291356872,0
2141.     Data 4286766027,0,4286363598,0,4284972716,0,4282397788,0,4285276750,0,4290063198,0,4283966519,0,4282399538,0
2142.     Data 4289369454,0,4292724376,0,4294699969,1,4294557608,0,4294064731,0,4293918777,1,4292239711,0,4289764210,0
2143.     Data 4283450171,0,4283769654,0,4289473114,0,4290128478,1,4290062942,0,4290063198,1,4291045726,0,4292094046,3
2144.     Data 4291897182,0,4290914137,0,4284753209,0,4280624164,3,4283650368,0,0,12,4282222713,0,4283740575,0
2145.     Data 4284795582,0,4282621107,0,4282225330,0,4283739835,0,4288139202,0,4292405959,0,4294110662,0,4293455046,0
2146.     Data 4289717705,0,4286830783,0,4284074163,0,4283940020,0,4283272856,0,4282005591,0,4285276750,0,4290063198,0
2147.     Data 4283966519,0,4282465331,0,4289567089,0,4292920220,0,4294957510,0,4289303942,0,4284830284,0,4284622899,0
2148.     Data 4288089390,0,4293329207,0,4293881980,0,4292194975,0,4283713861,0,4283376436,0,4289407578,0,4290063198,4
2149.     Data 4290390622,0,4290849118,0,4291766366,0,4292424285,0,4292889944,0,4293022295,0,4292760150,0,4290662731,0
2150.     Data 4289286212,1,4288953671,0,4288554315,0,4284428602,0,4282597686,0,4284769098,0,0,10,4287809964,0
2151.     Data 4286567352,0,4284203704,0,4280974760,0,4282549420,0,4288730307,0,4292471495,0,4294700742,0,4292340423,0
2152.     Data 4290897864,0,4290176712,0,4287617985,0,4284468152,0,4284267193,0,4283533980,0,4282070872,0,4285276750,0
2153.     Data 4290063198,0,4286588744,0,4284953409,0,4286342483,0,4287592556,0,4289101964,0,4286532958,0,4284556347,1
2154.     Data 4286061372,0,4288286012,0,4288499297,0,4287788661,0,4284235081,0,4285081412,0,4289604187,0,4290063198,5
2155.     Data 4290194014,0,4291569758,0,4292556636,0,4293221973,0,4293355092,4,4293088854,0,4292756314,0,4287639623,0
2156.     Data 4284296251,0,4283450427,0,4284045123,0,0,8,4285365355,0,4294042813,0,4288531126,0,4281966759,0
2157.     Data 4281305001,0,4285308595,0,4293189826,0,4294963142,0,4294504134,0,4290438856,0,4290045640,0,4294110662,0
2158.     Data 4291160264,0,4286241483,0,4285838286,0,4284578477,0,4282331996,0,4284358731,0,4287899479,0,4289210715,0
2159.     Data 4288686421,0,4284097592,0,4283113785,0,4283703113,0,4287571284,0,4290456158,0,4290194014,0,4287637078,0
2160.     Data 4284096586,0,4283179323,0,4283311157,0,4285934414,0,4287966554,0,4289866589,0,4290063198,0,4290128478,0
2161.     Data 4290390622,1,4290128478,0,4290063198,0,4290194014,0,4291569758,0,4292490076,0,4292956247,0,4293156181,0
2162.     Data 4293355092,3,4293222229,0,4293088854,0,4289869910,0,4286522700,0,4281737515,0,4281742638,0,4284176709,0
2163.     Data 4284900427,0,0,5,4282423431,0,4286828210,0,4294175940,0,4287079347,0,4280051877,0,4284069053,0
2164.     Data 4288996553,0,4293848518,0,4294963142,4,4291160264,0,4286241483,0,4285838286,0,4284578477,0,4282331996,0
2165.     Data 4281605186,1,4286850387,0,4290063198,3,4291307870,0,4291831902,0,4290587230,0,4290063198,7,4290325086,0
2166.     Data 4291569758,1,4290325086,0,4290063198,0,4290194014,0,4291569758,0,4292290655,1,4292756314,0,4293355092,3
2167.     Data 4292889176,0,4292290655,0,4285603916,0,4281343035,0,4280557351,0,4280360993,1,4283190076,0,0,5
2168.     Data 4289049239,0,4290108346,0,4286434737,0,4283071608,0,0,0,4288786333,0,4293455046,0,4294635206,0
2169.     Data 4294963142,2,4293323974,0,4289258697,0,4287488458,0,4286043332,0,4283988107,0,4283119456,0,4284427605,0
2170.     Data 4285805134,0,4286987595,0,4286985043,0,4287573337,0,4289473373,0,4290063198,1,4291307870,0,4292159582,0
2171.     Data 4291831902,0,4291045726,0,4290128478,0,4285933124,0,4282786352,1,4285015358,0,4289604187,0,4290063198,0
2172.     Data 4290392157,0,4292102233,0,4292626521,0,4291898973,0,4290849118,0,4290062942,0,4290390622,0,4290980190,0
2173.     Data 4292028510,0,4292756314,0,4293355092,3,4292103000,0,4290587230,0,4284948812,0,4282985029,0,4287650386,0
2174.     Data 4288174414,0,4286660162,0,4283840566,0,4281611053,0,0,4,4291279772,0,4290824103,0,4282546027,0
2175.     Data 0,1,4290358930,0,4293586118,0,4291160264,0,4290635720,0,4290897864,0,4293586118,0,4292799431,0
2176.     Data 4287357386,0,4285585603,0,4284531890,0,4282736495,0,4283049030,0,4286264911,0,4287971664,0,4288825678,0
2177.     Data 4287905872,0,4287117138,0,4286130256,0,4287374933,0,4290063198,0,4291307870,0,4292028510,0,4291438942,0
2178.     Data 4288882770,0,4285539649,0,4286007112,0,4285880905,0,4281937964,0,4283703860,0,4290455642,0,4290587230,0
2179.     Data 4290458204,0,4292301655,0,4293155925,0,4292889176,0,4289017420,0,4285211967,1,4286654023,0,4290390362,0
2180.     Data 4292100953,0,4293355092,1,4293221973,0,4292889688,0,4290722649,0,4288032090,0,4283966027,0,4283642443,0
2181.     Data 4290477417,0,4291461222,0,4289748818,0,4284824127,0,4280950321,0,0,4,4287859318,0,4287727987,0
2182.     Data 0,2,4290358930,0,4292209351,0,4287357386,0,4286308299,0,4286635978,0,4290373320,0,4290174149,0
2183.     Data 4285053886,0,4283083699,0,4281833375,0,4281683303,0,4283245382,0,4286920016,0,4288430416,0,4288825678,1
2184.     Data 4287841100,0,4284755783,0,4285016391,0,4286981962,0,4289538134,0,4290717786,0,4288161615,0,4286002245,0
2185.     Data 4284499774,0,4289231969,0,4291991925,0,4286472269,0,4285611586,0,4288292682,0,4289603412,0,4291047773,0
2186.     Data 4292498263,0,4293355092,1,4286988863,0,4280951084,0,4283186231,0,4285087811,0,4286982738,0,4289542742,0
2187.     Data 4292367191,0,4292760151,0,4292626521,0,4291833949,0,4288489560,0,4284623184,0,4284955474,0,4286666844,0
2188.     Data 4291597173,0,4292450418,0,4291462242,0,4285876560,0,4281605186,0,0,9,4290358930,0,4292077252,0
2189.     Data 4287026881,0,4285911745,0,4285977282,1,4284330936,0,4280116383,0,4279325850,0,4279455892,0,4280693091,0
2190.     Data 4282784840,0,4285537368,0,4287442519,0,4288693839,0,4288759630,0,4288825678,1,4285807166,0,4280885795,0
2191.     Data 4285736515,0,4287899729,0,4283049009,0,4285420357,0,4292320375,0,4293109117,2,4289297761,0,4281740585,0
2192.     Data 4286260800,0,4291767900,0,4292759383,0,4293026132,0,4292698451,0,4287447628,0,4282985545,0,4289690731,0
2193.     Data 4290348143,0,4283642956,0,4285474383,0,4289669468,0,4291111005,0,4291438686,0,4289997148,0,4286326353,0
2194.     Data 4282196548,0,4289033319,0,4293109117,3,4286601051,0,4281605186,0,0,9,4290358930,0,4290689436,0
2195.     Data 4283128145,0,4281942606,0,4282466395,1,4282137177,0,4281281108,0,4281149267,0,4281149010,0,4281409608,0
2196.     Data 4281801795,0,4282391622,0,4284555088,0,4287177819,0,4288166739,0,4288825678,1,4288169546,0,4287185221,0
2197.     Data 4284951878,0,4283901254,0,4286199877,0,4289422938,0,4292714105,0,4293109117,2,4291727725,0,4289030479,0
2198.     Data 4286136905,0,4284686410,0,4289670230,0,4289736789,0,4284885832,0,4287322715,0,4291071090,0,4292385913,0
2199.     Data 4292517498,0,4291202675,0,4287519583,0,4283637576,0,4287702613,0,4288620376,0,4284555339,0,4286136658,0
2200.     Data 4290014816,0,4291924082,0,4293109117,3,4286601051,0,4281605186,0,0,6,4279844709,0,0,1
2201.     Data 4284702290,0,4285233770,0,4282481260,0,4281031538,0,4280302451,0,4281149010,0,4282785349,0,4285735759,0
2202.     Data 4286325841,4,4285276240,0,4283898958,0,4286261332,0,4287902805,0,4288562255,0,4288825678,1,4286987595,0
2203.     Data 4286200137,0,4287972428,0,4290143323,0,4292185198,0,4292779127,0,4292977275,0,4292580980,0,4291922024,0
2204.     Data 4290803543,0,4288701009,0,4286662733,0,4286394190,0,4286064460,0,4285739593,0,4289359202,0,4293109117,3
2205.     Data 4290609772,0,4287386198,0,4286921804,0,4286789450,0,4287253844,0,4289423454,0,4291986024,0,4292646773,0
2206.     Data 4293109117,1,4292844920,0,4292448625,0,4286336854,0,4281605186,0,0,5,4280504174,0,4281697706,0
2207.     Data 4282218888,0,4282410591,0,4281753431,0,4281429869,0,4281635227,0,4280643211,0,4279910510,0,4283116631,0
2208.     Data 4286260048,0,4290127964,0,4290849118,4,4288161366,0,4284752204,0,4284816977,0,4285473108,0,4287443540,0
2209.     Data 4288298577,0,4288825678,3,4289813589,0,4291328608,0,4292119660,0,4292514930,0,4291789926,0,4291263325,0
2210.     Data 4290737750,1,4290014804,0,4286795597,0,4286400075,0,4288960080,0,4291264359,0,4293109117,3,4292580723,0
2211.     Data 4291657317,0,4288831827,0,4288306769,0,4291330920,0,4292382575,1,4292844664,0,4293109117,1,4292449906,0
2212.     Data 4291460449,0,4285679432,0,4281081141,0,0,4,4280965251,0,4282617263,0,4285584580,0,4285914054,0
2213.     Data 4285454018,0,4283613105,0,4281570464,0,4279721363,0,4280432988,0,4282065195,0,4287571789,0,4290783582,0
2214.     Data 4292028510,0,4292291422,0,4292423517,3,4291505501,0,4290325086,0,4284817740,0,4282457158,0,4285275222,0
2215.     Data 4287048279,0,4288562000,1,4288562255,0,4288759630,0,4289419088,0,4290342228,0,4291197278,0,4291657571,0
2216.     Data 4291000409,0,4290737750,5,4290869079,0,4291923049,0,4292976762,0,4293043068,1,4292977018,0,4292514674,0
2217.     Data 4291986024,1,4292250221,0,4292845177,0,4293109117,2,4293043324,0,4292977018,0,4291595370,0,4289424207,0
2218.     Data 4284630584,0,4280953127,0,0,4,4289834393,0,4290041019,0,4284138926,0,4283548589,0,4283021483,0
2219.     Data 4280844964,0,4279849342,0,4280102462,0,4284491843,0,4289014102,0,4290979932,0,4292028510,0,4292225118,0
2220.     Data 4292689754,0,4293221973,3,4292691545,0,4291962974,0,4285472844,0,4281670722,0,4282129476,0,4284030542,0
2221.     Data 4287045980,1,4287375706,0,4288364369,0,4288891726,0,4289023566,0,4290078036,0,4290869079,0,4290737750,5
2222.     Data 4291066202,0,4291657571,0,4291920744,0,4292184171,0,4292778871,0,4292844920,0,4292184684,0,4292052073,0
2223.     Data 4291986024,1,4292250221,0,4292845177,0,4293109117,2,4292910969,0,4292250734,0,4288177233,0,4281608743,0
2224.     Data 4283451963,0,4284834635,0,0,1,4282466100,0,4286281058,0,4289440144,0,4289516728,0,4287551935,0
2225.     Data 4283548331,0,4282224254,0,4281161555,0,4280369489,0,4281151820,0,4283378244,0,4287637840,0,4291373406,0
2226.     Data 4291045726,0,4291242334,0,4292094046,0,4292756314,0,4293355092,3,4293155669,0,4292955736,0,4289999701,0
2227.     Data 4286980688,0,4282850629,0,4281998398,0,4282785336,1,4283638078,0,4286327120,0,4287573080,1,4288628308,0
2228.     Data 4289682769,0,4290408020,0,4290737750,4,4291066203,0,4291788901,0,4291986024,1,4292250477,1,4291986280,0
2229.     Data 4291986024,2,4292052329,0,4292316270,0,4292712565,0,4293109117,1,4292515702,0,4290538334,0,4286334531,0
2230.     Data 4280360993,0,4283190076,0,0,2,4280624164,0,4288517245,0,4293848518,0,4288472009,0,4284923821,0
2231.     Data 4282155123,0,4283256660,0,4284359995,0,4283377209,0,4283771202,0,4285541715,0,4289145691,0,4292094046,0
2232.     Data 4290718302,0,4290325086,0,4291111262,0,4291966812,0,4292889688,0,4293155669,0,4293355092,3,4292689754,0
2233.     Data 4290258265,0,4283571783,0,4281081141,0,4280360993,0,4281409318,0,4282588719,0,4283571517,0,4283964739,1
2234.     Data 4284623678,0,4285217338,0,4285876797,0,4287057735,0,4288826968,0,4289419350,0,4290012499,0,4290802522,0
2235.     Data 4291460449,0,4291854694,0,4291986024,9,4292250221,0,4292580723,0,4292252270,0,4290740066,0,4286400323,0
2236.     Data 4284169016,0,4282597686,0,4284176965,0,0,2,4280624164,0,4287599230,0,4292273603,0,4287219634,0
2237.     Data 4284189571,0,4282329908,0,4286064197,0,4289604445,0,4287769946,0,4286393941,0,4285738833,0,4288949079,0
2238.     Data 4292094046,0,4290718302,0,4290063198,1,4290849118,0,4291898206,0,4292364377,0,4292827733,0,4293024342,0
2239.     Data 4293155414,1,4292557403,0,4290389594,0,4284227914,0,4282064700,0,4281540396,0,4283637047,0,4284620347,0
2240.     Data 4282721326,0,4282000426,0,4282064941,0,4281802540,0,4281540396,1,4282785336,0,4285340752,0,4286394188,0
2241.     Data 4287514440,0,4288962900,0,4289752922,1,4290540382,0,4291393379,0,4291591524,0,4291788901,0,4291920231,0
2242.     Data 4291986024,2,4291920231,0,4291788901,0,4291591267,0,4291393379,0,4289752148,0,4287388485,0,4282660912,0
2243.     Data 4282860856,0,0,4,4280624164,0,4283993216,0,4286040502,0,4282210387,0,4283444026,0,4288883287,0
2244.     Data 4289735260,0,4289997661,0,4289866589,0,4287966288,0,4284755770,0,4288162634,0,4292094046,0,4290718302,0
2245.     Data 4290063198,1,4290062942,0,4290194270,0,4290194781,0,4290784605,0,4291963998,0,4292356958,1,4292290910,0
2246.     Data 4291045725,0,4286917719,0,4285933399,0,4286389339,0,4286585947,0,4286981209,0,4287839055,0,4288559186,0
2247.     Data 4288947293,0,4287569500,0,4286389339,1,4284620106,0,4281081640,0,4280820004,0,4280886052,0,4281017636,0
2248.     Data 4281083429,1,4285020474,0,4289089360,0,4290210132,0,4291066203,0,4291788901,0,4291986024,2,4291657571,0
2249.     Data 4291000410,0,4290012243,0,4289023055,0,4283970612,0,4281741612,0,4284373830,0,4285229391,0,0,4
2250.     Data 4280624164,0,4281352510,0,4282799444,0,4285805645,0,4287965264,0,4289866332,0,4290783582,0,4291569758,1
2251.     Data 4289211217,0,4284886840,0,4287311176,0,4290783582,0,4291307870,0,4291176798,0,4290194014,0,4290063198,2
2252.     Data 4290194014,0,4290587230,0,4291373406,0,4292290655,0,4291307870,0,4289275994,0,4284425036,0,4283899718,0
2253.     Data 4285471812,0,4286983500,0,4288562003,0,4289616979,0,4289681235,0,4289085268,0,4288559955,0,4288231253,0
2254.     Data 4288554590,0,4288094299,0,4286783823,0,4286652750,2,4284686400,0,4281147430,0,4281673256,0,4282985775,0
2255.     Data 4283381296,0,4283644722,0,4283907638,0,4283973175,2,4283841845,0,4283644722,0,4283315248,0,4282985519,0
2256.     Data 4283516218,0,4284176708,0,4285163598,0,0,3,4282926649,0,4283775547,0,4285015871,0,4285211967,0
2257.     Data 4285802051,0,4288817494,0,4290063198,1,4291443035,0,4292756314,0,4292424029,0,4289997398,0,4285869640,0
2258.     Data 4286000710,0,4287245641,0,4289866327,0,4291176798,1,4290652766,0,4290063198,1,4290325086,0,4290914654,0
2259.     Data 4291176798,1,4287833429,0,4285801296,1,4284817480,0,4283243581,0,4286330182,0,4289155407,0,4290210388,0
2260.     Data 4290342228,0,4289814610,0,4289748818,0,4289945685,0,4290929256,0,4291322736,2,4291190893,0,4290532194,0
2261.     Data 4288495188,0,4285605445,0,4282982201,0,4281212466,0,4283835195,0,4283966519,0,4280950820,0,4281148196,0
2262.     Data 4282132522,1,4281673255,0,4280688930,0,4281479211,0,4282926649,0,0,6,4280360993,0,4283966519,0
2263.     Data 4289407578,0,4290325086,0,4290587230,3,4291971161,0,4293222485,0,4292757081,0,4290786395,0,4287704921,0
2264.     Data 4286197323,0,4285607487,0,4287179087,0,4288882520,0,4291242077,0,4291242334,0,4290587230,1,4290849118,0
2265.     Data 4291504478,0,4290062427,0,4287899479,0,4285276750,0,4284883276,0,4288817242,0,4287244117,0,4282654791,0
2266.     Data 4285083977,0,4287382603,0,4288698189,0,4289421138,0,4289683287,0,4290012501,0,4290473815,0,4291593577,0
2267.     Data 4292186481,0,4292450419,0,4292516211,0,4292186991,0,4290935133,0,4290008152,0,4289669985,0,4285603666,0
2268.     Data 4282064195,0,4286719828,0,4286851405,0,4281409832,0,4281935656,0,4283969331,0,4284231480,0,4283640886,0
2269.     Data 4281804329,0,4282530611,0,0,7,4280360993,0,4283966519,0,4289407578,0,4291307870,0,4292290655,3
2270.     Data 4292822873,0,4293355092,1,4292301655,0,4290458204,0,4290063198,0,4289473116,0,4284227658,0,4283703113,0
2271.     Data 4288948570,0,4290980190,0,4292290655,1,4291700830,0,4290456158,0,4286325841,0,4281605186,0,4286850387,0
2272.     Data 4290063198,1,4288490587,0,4286000983,0,4283507787,0,4282195008,0,4284030010,0,4285602886,0,4286717020,0
2273.     Data 4287903061,0,4288825678,1,4289419088,0,4290605909,0,4290737750,0,4290474069,0,4289419088,0,4289018964,0
2274.     Data 4289472096,0,4285603666,0,4281867587,0,4284623184,0,4284558153,0,4281016615,0,4281935656,0,4284034869,0
2275.     Data 4285214537,0,4285476686,0,4284297017,0,4282329387,0,4280360993,0,0,6,4280360993,0,4282852661,0
2276.     Data 4286590293,0,4285474128,0,4284489799,0,4285606464,0,4286000702,1,4286133564,0,4286463294,0,4287315021,0
2277.     Data 4289283414,0,4291908438,0,4291248474,0,4289473114,0,4283572793,0,4281147179,0,4282458671,0,4282982960,0
2278.     Data 4283375922,0,4283899967,0,4284096329,0,4283768649,0,4284228684,0,4284885585,0,4288096857,0,4290063198,1
2279.     Data 4288490587,0,4286000983,0,4283507787,0,4282720835,0,4286264646,0,4288498254,0,4289617239,0,4290012501,0
2280.     Data 4290341717,0,4290933086,0,4291592039,0,4292384370,0,4292516211,0,4292450163,0,4292186481,0,4291526505,0
2281.     Data 4290602588,0,4288696146,0,4286724938,0,4284033352,0,4282064957,0,4280623141,0,4282590772,0,4285673294,0
2282.     Data 4287704406,0,4288883802,0,4288621652,0,4284950077,0,4280360993,0,0,6,4280360993,0,4281540912,0
2283.     Data 4283311176,0,4285080654,0,4286457168,0,4287114060,0,4287769675,0,4288555851,0,4288621387,0,4288162890,0
2284.     Data 4286000709,0,4286199368,0,4288627795,0,4286854472,0,4284359739,0,4282130230,0,4280884782,0,4280426275,0
2285.     Data 4280622889,0,4281081140,0,4281343036,0,4281933375,0,4282656059,0,4283771453,0,4284821314,0,4288097363,0
2286.     Data 4290063198,1,4289342300,0,4288228442,0,4284490572,0,4282917956,0,4286987595,0,4289485137,0,4290605909,0
2287.     Data 4291131739,0,4291526498,0,4292317038,0,4292713078,0,4293043324,0,4293109117,2,4292779639,0,4292186990,0
2288.     Data 4290935135,0,4289355089,0,4284166471,0,4281277753,0,4280491813,0,4282787384,0,4286197335,0,4288490587,0
2289.     Data 4288817242,0,4286194769,0,4283441218,0,4281015603,0,4282004533,0,4283124027,0,4284900427,0,0,3
2290.     Data 4280360993,0,4281802800,0,4283965512,0,4287506005,0,4290063198,1,4290718302,0,4292094046,0,4292424029,0
2291.     Data 4291574103,0,4287050567,0,4285017925,0,4285804371,0,4285152330,0,4284368958,0,4284629064,0,4283708482,0
2292.     Data 4280886054,0,4280884783,0,4281605186,1,4282196286,0,4283509813,0,4283641141,0,4283181367,0,4286655310,0
2293.     Data 4289014876,0,4289801053,0,4290063198,1,4285276750,0,4282917956,0,4286987595,0,4289485137,0,4290605909,0
2294.     Data 4291394656,0,4292118122,0,4292779127,0,4293109117,6,4292054892,0,4290474842,0,4284561738,0,4281277753,0
2295.     Data 4280491813,0,4282787384,0,4286066262,0,4286851413,0,4286325586,0,4283964748,0,4284034639,0,4285154900,0
2296.     Data 4284432706,0,4283908665,0,4283846719,0,4284439879,0,0,2,4280360993,0,4283966519,0,4289407578,0
2297.     Data 4290063198,0,4290062942,0,4290128478,0,4290849118,0,4292159582,0,4292822873,0,4292370260,0,4288168020,0
2298.     Data 4286001237,0,4286198358,0,4289752684,0,4293109632,0,4292382576,0,4289096535,0,4281805866,0,4281015856,0
2299.     Data 4281867587,1,4282458431,0,4283837496,0,4283377467,0,4282129475,0,4284360526,0,4286459223,0,4289014620,0
2300.     Data 4289866589,0,4290063198,0,4285276750,0,4282917700,0,4287052619,0,4289484625,0,4290474069,0,4291328863,0
2301.     Data 4292118122,0,4292779127,0,4293109117,4,4293043324,0,4293043067,0,4292448881,0,4291263076,0,4284824397,0
2302.     Data 4281343290,0,4280688678,0,4282787384,0,4285475924,0,4283376713,0,4283309897,0,4286128473,0,4289748333,0
2303.     Data 4293175681,0,4292448882,0,4289818971,0,4282528302,0,4282268723,0,0,2,4280360993,0,4283966519,0
2304.     Data 4289407578,0,4290063198,0,4290259550,0,4291373406,0,4291962974,0,4292225118,0,4292822873,0,4292173648,0
2305.     Data 4287119425,0,4286005570,0,4289159506,0,4292191113,0,4294498744,0,4293374606,0,4289756771,0,4281872172,0
2306.     Data 4282459446,0,4285147987,1,4286065491,0,4288162645,0,4288686679,0,4288424024,0,4284686924,0,4283179593,0
2307.     Data 4285934420,0,4287966554,0,4290063198,0,4285276750,0,4283047495,0,4287440215,0,4289345625,0,4289154640,0
2308.     Data 4290735197,0,4292118122,0,4292779127,0,4293109117,4,4292779127,0,4292250734,0,4291526754,0,4290343511,0
2309.     Data 4284495945,0,4281999421,0,4283050545,0,4282853177,0,4282720582,0,4285543497,0,4288104782,0,4289486421,0
2310.     Data 4291991939,0,4294565308,0,4293506706,0,4290545256,0,4282660657,0,4282268723,0,0,2,4280360993,0
2311.     Data 4283966519,0,4289407578,0,4290783582,0,4291636573,0,4292560217,0,4292955736,1,4292822873,0,4291575125,0
2312.     Data 4286657599,0,4286072125,0,4289883473,0,4292254328,0,4293639062,0,4292254069,0,4288965976,0,4282395195,0
2313.     Data 4283245892,0,4286197335,0,4288425050,0,4290259548,0,4291111262,0,4290783582,0,4290063198,0,4288030551,0
2314.     Data 4286194769,0,4283900747,0,4284819279,0,4287507801,0,4284162892,0,4282260037,0,4284225102,0,4285537867,0
2315.     Data 4286262081,0,4287707475,0,4288956258,0,4290011488,0,4290802785,0,4291528036,0,4291594084,2,4291461986,0
2316.     Data 4291198045,0,4290341462,0,4289025616,0,4284034886,0,4283113540,0,4286982732,0,4284687935,0,4281278767,0
2317.     Data 4285806913,0,4289287248,0,4290342228,0,4292056691,0,4293771162,0,4292385912,0,4289492055,0,4282463021,0
2318.     Data 4282268723,0,0,2,4280360993,0,4283114545,0,4287310923,0,4288555854,0,4289343311,0,4290201427,0
2319.     Data 4290335056,0,4289876296,0,4289478219,0,4288490315,0,4285541947,0,4285480254,0,4288304465,0,4289686114,0
2320.     Data 4290213483,0,4287914064,0,4285942084,0,4283640136,0,4285081424,0,4287769945,0,4290456156,0,4292357469,0
2321.     Data 4292557403,0,4292034650,0,4291248474,0,4291048028,0,4289144665,0,4283309639,0,4283245385,0,4286000983,0
2322.     Data 4283507787,0,4282195267,0,4284031304,0,4285409094,0,4286262336,0,4287707475,0,4288956258,0,4290011488,0
2323.     Data 4290802785,0,4291528036,0,4291594084,4,4288831319,0,4286002761,0,4285147211,0,4286063440,0,4289341787,0
2324.     Data 4285802051,0,4280820004,0,4285148993,0,4288364373,0,4289023576,0,4289880420,0,4290736497,0,4288307283,0
2325.     Data 4285944127,0,4283121973,0,4283452990,0,0,2,4280953127,0,4281936682,0,4283313456,0,4284232756,0
2326.     Data 4284954427,0,4285936462,0,4285542475,0,4283903031,0,4284297782,0,4284823863,0,4284955706,0,4285545283,0
2327.     Data 4286396499,0,4286001749,0,4285082449,0,4281934641,0,4281738030,0,4285279568,0,4287835482,0,4290456158,0
2328.     Data 4291504222,0,4292556636,0,4293155414,0,4293355092,1,4292689754,0,4290324057,0,4283834437,0,4283179847,0
2329.     Data 4285410388,0,4283638604,0,4283442247,0,4287184203,0,4288825678,1,4290472027,0,4291921000,0,4292647029,0
2330.     Data 4292977019,0,4293043324,0,4293109117,2,4292977531,0,4292845432,0,4287192413,0,4282129475,0,4287374933,0
2331.     Data 4290063198,1,4285802051,0,4280754212,0,4284555590,0,4287112029,0,4287243869,0,4287177821,0,4287045980,0
2332.     Data 4282851383,0,4281282090,0,0,4,4284834635,0,4283320892,0,4281017893,0,4285877309,0,4289685585,0
2333.     Data 4288827215,0,4286592332,0,4282979397,0,4286267211,0,4290081109,0,4291200356,0,4291265893,0,4290343256,0
2334.     Data 4286137677,0,4281998914,0,4280885036,0,4281738030,0,4285279568,0,4288621658,0,4292028510,0,4292159582,0
2335.     Data 4292556636,0,4293155414,0,4293355092,1,4292689754,0,4290652503,0,4285279292,0,4283049786,0,4282129988,0
2336.     Data 4284423505,0,4286653528,0,4288167249,0,4288825678,1,4289946451,0,4291000666,0,4291789414,0,4292382576,0
2337.     Data 4293043067,0,4293109117,2,4292450418,0,4291264863,0,4286270286,0,4282129475,0,4287374933,0,4290063198,1
2338.     Data 4285802051,0,4280820259,0,4285478462,0,4288957777,0,4289880917,0,4289485140,0,4288562000,0,4283378994,0
2339.     Data 4281282090,0,0,5,4283519039,0,4280624164,0,4285414971,0,4289287504,0,4288957518,0,4286789196,0
2340.     Data 4282847304,0,4285936204,0,4289616978,0,4290802778,0,4291198556,0,4290803543,0,4285680192,0,4280950572,0
2341.     Data 4283115069,0,4285344331,0,4288162905,0,4289604444,0,4290849118,0,4291700830,0,4292357214,0,4292556636,0
2342.     Data 4292623195,1,4291440733,0,4289473366,0,4285214267,0,4282722608,0,4280688171,0,4284161352,0,4287307614,0
2343.     Data 4288686429,0,4289149015,0,4288825166,0,4289155151,0,4289616721,0,4290670936,0,4291198301,0,4291396705,0
2344.     Data 4291462242,0,4291264609,0,4290539358,0,4288108623,0,4284366902,0,4285476931,0,4287571541,0,4289210715,0
2345.     Data 4290063198,1,4285802051,0,4280885795,0,4285610301,0,4288957518,0,4289287248,0,4286596161,0,4282985519,0
2346.     Data 4283516218,0,0,6,4284374086,0,4282729527,0,4283972408,0,4285085498,1,4283968569,0,4281734967,0
2347.     Data 4283311672,0,4285217338,0,4285810749,0,4286140478,1,4283512631,0,4281278258,0,4285605964,0,4287901018,0
2348.     Data 4288162906,0,4289014620,0,4290128478,0,4290783582,0,4291307870,3,4290521694,0,4288883541,0,4285083451,0
2349.     Data 4282918450,0,4281276210,0,4283307589,0,4285536087,0,4287503454,0,4288620637,0,4289082967,0,4289148759,0
2350.     Data 4289215830,0,4289681235,0,4289880658,1,4288043336,0,4286008638,0,4285414971,0,4284363065,0,4283050040,0
2351.     Data 4286392395,0,4290063198,1,4289604445,0,4288490587,0,4284753729,0,4280623394,0,4283313712,0,4285085498,1
2352.     Data 4283972408,0,4282597686,0,4284374086,0,0,8,4283124027,0,4281282090,1,4281018663,0,4280360993,0
2353.     Data 4280889648,0,4281615424,0,4282533184,0,4282268216,0,4280886314,0,4280950321,0,4281867581,0,4287309395,0
2354.     Data 4289014876,0,4286459479,0,4287442265,0,4289276764,5,4289735517,0,4288752469,0,4284558392,0,4282786358,0
2355.     Data 4282060864,1,4282716740,0,4284684622,0,4286520918,0,4287897692,0,4288094300,0,4287964250,0,4287576144,0
2356.     Data 4287381577,0,4287250757,0,4284101172,0,4281017124,1,4282525236,0,4285345104,0,4287638873,0,4289342300,0
2357.     Data 4289801053,0,4288752473,0,4285541455,0,4283313469,0,4281282090,3,4283124027,0,0,14,4280624163,0
2358.     Data 4283136368,0,4286895295,0,4291485117,0,4290094229,0,4283053135,0,4280950321,0,4281016358,0,4287047499,0
2359.     Data 4289014876,0,4286459479,0,4286066263,0,4286197335,5,4288621659,0,4288227666,0,4282327597,0,4280492066,0
2360.     Data 4280491555,2,4280688420,0,4281212464,0,4281998402,0,4282063940,0,4282063939,0,4282064451,0,4281671481,0
2361.     Data 4280951333,0,4282263594,0,4283707185,1,4284428093,0,4285673298,0,4286066263,0,4286459479,0,4288818267,0
2362.     Data 4287703119,0,4281868843,0,4282662966,0,4285163598,3,4285295183,0,0,16,4282077259,0,4283322954,0
2363.     Data 4284110155,0,4284438604,0,4282399799,0,4280623138,0,4283836980,0,4285607492,0,4285935187,0,4286000983,4
2364.     Data 4287311193,0,4289014876,0,4287769946,0,4285737806,0,4281606699,0,4280360993,1,4279842646,0,4279454336,1
2365.     Data 4279908703,0,4280557870,0,4281146679,0,4281605186,1,4281999675,0,4282919727,0,4283510320,0,4283969587,1
2366.     Data 4283509561,0,4282851908,0,4282654791,0,4282720327,0,4283375688,0,4282851135,0,4280753958,0,4280887334,0
2367.     Data 4281611053,1,4282597686,0,4284768842,0,0,17,4282926649,1,4283716160,0,4285163598,0,4282926649,0
2368.     Data 4280426529,0,4281541927,0,4282853680,0,4284624449,0,4284952389,4,4285082434,0,4285211967,0,4284294471,0
2369.     Data 4283114564,0,4280951081,0,4280360993,1,4279971652,0,4279648620,0,4279325072,0,4279583600,0,4280230696,0
2370.     Data 4281672495,0,4282787386,1,4283115832,0,4283838259,0,4283378486,0,4282787386,1,4282918972,0,4283182656,0
2371.     Data 4284232004,0,4285215304,1,4284230467,0,4281866806,0,4283182391,0,4285483323,0,4284890169,0,4284168503,0
2372.     Data 4283188024,0,4284045123,0,0,20,4282926649,0,4280492321,0,4282134058,0,4283512113,0,4284888632,0
2373.     Data 4284428089,0,4283705400,0,4284823354,0,4285809726,0,4286139203,0,4284892221,0,4283250738,0,4282328125,0
2374.     Data 4281932607,0,4282328624,0,4282592813,0,4282922286,0,4281477414,0,4280166194,0,4279648104,0,4279777884,0
2375.     Data 4280295974,0,4281869864,0,4283050799,0,4283247412,0,4283378486,1,4282853436,0,4282393921,1,4283445058,0
2376.     Data 4285415491,0,4287317576,0,4288825678,0,4289089615,0,4287710541,0,4283834695,0,4286399053,0,4290605909,0
2377.     Data 4289814610,0,4287055684,0,4282001705,0,4282597686,0,0,20,4282926649,0,4280952100,0,4287454021,0
2378.     Data 4290210388,0,4289023567,0,4286000715,0,4282913608,0,4287581776,0,4291330399,0,4292648053,0,4292580723,0
2379.     Data 4291986024,0,4286003284,0,4283635785,0,4287577420,0,4289485137,0,4290737750,0,4284892472,0,4280360993,4
2380.     Data 4280491813,0,4281277753,0,4281605186,1,4283248449,0,4284891968,1,4286071876,0,4288301132,0,4288825678,0
2381.     Data 4288891726,0,4290078547,0,4289227088,0,4285614402,0,4287387977,0,4290737750,1,4288110664,0,4282265642,0
2382.     Data 4282597686,0,0,20,4282926649,0,4280952100,0,4287454021,0,4290605909,0,4290408020,0,4287714892,0
2383.     Data 4284890948,0,4289558114,0,4292714103,0,4292977531,0,4292977275,0,4292845177,0,4287585878,0,4285678663,0
2384.     Data 4290079580,0,4291525219,0,4291723108,0,4285286718,0,4281084712,0,4283452990,0,4284505672,1,4282137394,0
2385.     Data 4280820516,0,4283249720,0,4284234560,1,4284563264,0,4284891968,1,4286071876,0,4288301132,0,4288825678,1
2386.     Data 4289023567,0,4287578701,0,4283637319,0,4285608010,0,4289155407,1,4286924099,0,4282001705,0,4282597686,0
2387.     Data 0,20,4282926649,0,4280952100,0,4287454021,0,4290408276,0,4289748818,0,4286923851,0,4284033606,0
2388.     Data 4288635994,0,4291923049,0,4292317295,0,4292448625,1,4286860629,0,4284756040,0,4288894549,0,4290866526,0
2389.     Data 4291986024,0,4285418048,0,4281282090,0,4284176709,0,0,1,4284176965,0,4283123514,0,4282529329,0
2390.     Data 4282330926,4,4282855472,0,4283838771,0,4284035380,2,4283312948,0,4281604658,0,4282458931,0,4284035380,1
2391.     Data 4283840566,0,4283385402,0,4284176965,0,0,20,4283716160,0,4282268209,0,4285747262,0,4287124292,0
2392.     Data 4286332992,0,4284230206,0,4282128188,0,4285349953,0,4287651144,0,4288176463,0,4288308049,1,4284232004,0
2393.     Data 4282587708,0,4285346879,0,4286990918,0,4288308049,0,4284697406,0,4282597686,0,4284571464,0,0,2
2394.     Data 4285032012,0,4282795320,0,4281940016,14,4282795320,0,4284769098,0,0,22,4285163598,0,4281940016,0
2395.     Data 4280360993,13,4283190076,0,0,32
2396.  
2397.     For i = 0 To 2
2398.  
2399.         bm(i) = _NewImage(64, 64, 32)
2400.         _Dest bm(i)
2401.  
2402.         Read cl
2403.         Read rleCount
2404.  
2405.         For y = 0 To 63
2406.             For x = 0 To 63
2407.                 PSet (x, y), cl
2408.                 rleCount = rleCount - 1
2409.                 If rleCount < 0 Then
2410.                     Read cl
2411.                     Read rleCount
2412.                 End If
2413.             Next
2414.         Next
2415.     Next
2416.  
2417.     _Dest 0
2418. End Sub
2419.  

[NOVARSEG]

justsomeguy

Is vector addition useful for 2D collisions of balls?    The balls have velocity and direction. When they collide do the vectors pass through the centers of the balls?

The other thing is that the result of the addition is a single vector of a certain magnitude and direction but how doe that apply to new directions and velocity after the collision?

Can the math for a 2 ball collision be derived from vector addition alone?

[johnno56]

THIS is REALLY impressive.... Well done!!

J

[justsomeguy]

Hello

I hope I can answer your questions correctly.

Is vector addition useful for 2D collisions of balls?

I will say that vector math is essential for the 2d collision of balls or circles in this case. Vectors are simply a data type that I use that hold two numbers. The vectors can be used as a position, a velocity ( x axis speed, y axis speed), or a vertex of a polygon.

Code: QB64: [Select]

1. Type tVECTOR2d
2.     x As _Float
3.     y As _Float
4. End Type

A collision between two circles can be derived when the distance between the circles is less than both of their radius added together.

Code: QB64: [Select]

1.     Call vectorSubVectorND(normal, B.position, A.position) ' Subtract two vectors position A and position B
2.     dist_sqr = vectorLengthSq(normal)  ' Calculate the distance between the balls or circles
3.     radius = A.shape.radius + B.shape.radius ' Add both circle A and circle B radius
4.  
5.     If (dist_sqr >= radius * radius) Then ' Deterime if they have collided
6.               'No collision
7.     Else
8.               'Collision has occured
9.  

Code: QB64: [Select]

1. Function vectorLengthSq (v As tVECTOR2d)
2.     vectorLengthSq = v.x * v.x + v.y * v.y
3. End Function

The method employed is a faster method of calculating collisions because it does not use square roots.

The balls have velocity and direction. When they collide do the vectors pass through the centers of the balls?

Not necessarily. A glancing blow from two balls must also be accounted for. A ball hitting another ball straight on versus a glancing blow will result in very different trajectories for both balls.

The other thing is that the result of the addition is a single vector of a certain magnitude and direction but how doe that apply to new directions and velocity after the collision?

Well that is not an easy answer. Here is a wikipedia article https://en.wikipedia.org/wiki/Elastic_collision. I apologize if that is a cop out answer, but classes are taught on the math involved and I'm no expert on the math, I simply ported the physics code from C++/Java.

Thanks for the question. If you have any other questions let me know.
 

[NOVARSEG]

Lets say 2 point masses collide at 0, 0  both have equal velocity.

The vector sum of the two masses give the  direction / velocity of both masses at the moment of collision.

After the collision, the masses head in new direction / velocity determine by the vector sum.
Ok that is the theory

Object 1  =  x = -2, y = -2   heading towards 0, 0

object 2   =   x =2, y = -2 heading towards 0, 0


Say the vector sum points away from 0, 0  so

Object 1  =  x = 2, y = 2   heading away from 0, 0

object 2   =   x = - 2, y = 2 heading away from 0, 0

vector sum =   (2+ -2 )x,  (2 + 2 )y =  0x, 4y  which seems to make sense as the objects collide at right angles in this case.

Also the new direction  of the objects should be at right angles to the original directions

The directions before collision are

Object 1  =  x = -2, y = -2   heading towards 0, 0

object 2   =   x =2, y = -2 heading towards 0, 0

Find the direction / velocity after collision

vector sum of object  1 with 0x ,4y =  -2x,   2y   heading away from 0, 0
(the new direction is right angle to the original direction.)

vector sum of object  2 with 0x ,4y =  2x,   2y  heading away from 0, 0
(the new direction is right angle to the original direction.)

Might be wrong but it does seem to work for this simple case.
********************************************************

Another one

Object 1  =  x = -2, y = -2   heading towards 0, 0

object 2   =   x =2,  y = 2   heading towards 0, 0

Intuition says the objects reverse direction after collision.  The vector sum is

(-2 + 2)x,   (-2 + 2)y  = 0x,,0y

Vector sum of Object 1  with 0x, 0y =  (-2 + 0)x,   (-2 + 0)y = -2x,  -2y   heading away from 0, 0