Generalized physics engine prototype with arbitrary shapes and collisions

[STxAxTIC]

As the title suggests, this is a generalized physics engine prototype with arbitrary shapes and collisions.

So what does that mean?

1) It's a prototype. If it does something you think is weird, this is still a baby, don't worry. It looks coarse-grained for transparency - when I make all the dots closer to each other, it will be all the smoother looking, and smoother-behaving.

2) The objects in this little 2D universe can have any shape (even open shapes), any mass, rotate about any axis, translate in any direction.

3) The objects collide and properly transfer linear momentum and angular momentum.

4) By "unified" I mean this... most simulations take place in a box, right? Reflect velocity at the wall right? Well, same here, but that's not hard-coded. Instead, the walls are made of the SAME stuff that the objects are made of, I just gave them near-infinite mass so they don't move. This part was worked on the least, so beware the walls (see part 1).

5) If you look at the code, there is a real lot of mathematical mechanism going on, obviously, but I point this out: there are a minimum of nested loops, not a lot of microscopic scanning around for edges, ABSOLUTELY NO TRIG (when it comes to collision mathematics). On that a similar note regarding speed, I point out that this is already passing the large-N test, as the walls are also participating in the loop, so to speak. Doesn't need to stay this way, it's a flex for now.

6) This also supports forces, torques, impulses, all the physics stuff, mostly tested. As a corollary to all this, and the reason I even know it, is during testing I set up a bunch of familiar configurations: pool, newton's cradle, crossfire (kinda) - it all works.

This demo just shows you oddly-shaped pieces crashing into each other while subject to a central "spring" field. Like I said, if you lose a piece, just restart. A few magic numbers will change as I work on this.

SEE BEST ANSWER POST FOR CURRENT CODE

Discussion on this project is continued elsewhere:

https://www.qb64.org/forum/index.php?topic=2295

[TerryRitchie]

I wish I had the chops to develop something like this. Thank you for taking the time to create this. Incorporating actual physics into games I create would be great.

[Qwerkey]

As the title suggests, this is a generalized physics engine prototype with arbitrary shapes and collisions.

2) The objects in this little 2D universe ...

2D?  This seems an unnecessary restriction?  Physical things happen in the 3D world (I suppose that to a mathematician even 3D is an unnecessary restriction!), and _MAPTRIANGLE(3D) - not even OpenGL required - would handle that superbly.  This could be your next iteration?

[STxAxTIC]

Hi Qwerkey,

So going from 2d to 3d is ordinarily a giant pain in the ass when everything is expressed by trig, but with vectors this wouldnt be such a hard leap. If I go into the next dimension with this it wont be for a long time, there is plenty to flesh out in 2d first.

As for plotting the result, whenever it comes, I will be not using maptriangle, I like line and pset.

[STxAxTIC]

New Update / Milestone / Example:

Still playing with magic numbers, but I thought I'd share what happens when pool, air hokey, and crossfire all meet on the street. PRESS SPACE ONCE.

Code: QB64: [Select]

1. SCREEN _NEWIMAGE(800, 600, 32)
2. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
3.  
4. RANDOMIZE TIMER
5.  
6. TYPE Vector
7.     x AS DOUBLE
8.     y AS DOUBLE
9. END TYPE
10.  
11. TYPE Object
12.     CtrMass AS Vector
13.     CtrRot AS Vector
14.     Diameter AS DOUBLE
15.     Mass AS DOUBLE
16.     MOI AS DOUBLE
17.     Length AS INTEGER
18.     Omega AS DOUBLE
19.     Shade AS _UNSIGNED LONG
20.     Velocity AS Vector
21. END TYPE
22.  
23. DIM vtemp AS Vector
24.  
25. DIM SHARED Shape(1000) AS Object
26. DIM SHARED PointChain(1000, 5000) AS Vector
27. DIM SHARED ShapeCount AS INTEGER
28. DIM SHARED CollisionCount AS INTEGER
29. ShapeCount = 0
30. CollisionCount = 0
31.  
32. DIM Gravity AS Vector
33. Gravity.x = 0
34. Gravity.y = -30
35.  
36. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
37. DIM SHARED ProximalPairsCount
38.  
39. ShapeCount = ShapeCount + 1
40. Shape(ShapeCount).CtrRot.x = -220
41. Shape(ShapeCount).CtrRot.y = 0
42. i = 0
43. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
44.     i = i + 1
45.     r = 40 + 25 * COS(1.5 * j) ^ 2
46.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
47.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
48. NEXT
49. Shape(ShapeCount).Length = i
50. Shape(ShapeCount).Mass = i
51. Shape(ShapeCount).Velocity.x = 0
52. Shape(ShapeCount).Velocity.y = 0
53. Shape(ShapeCount).Omega = 0
54. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
55. CALL CalculateCtrMass(ShapeCount)
56. CALL CalculateDiameter(ShapeCount)
57. CALL CalculateMOI(ShapeCount)
58.  
59. ShapeCount = ShapeCount + 1
60. Shape(ShapeCount).CtrRot.x = 170
61. Shape(ShapeCount).CtrRot.y = 0
62. i = 0
63. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
64.     i = i + 1
65.     r = 30
66.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
67.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
68. NEXT
69. Shape(ShapeCount).Length = i
70. Shape(ShapeCount).Mass = i
71. Shape(ShapeCount).Velocity.x = 0
72. Shape(ShapeCount).Velocity.y = 0
73. Shape(ShapeCount).Omega = 0
74. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
75. CALL CalculateCtrMass(ShapeCount)
76. CALL CalculateDiameter(ShapeCount)
77. CALL CalculateMOI(ShapeCount)
78.  
79. ShapeCount = ShapeCount + 1
80. Shape(ShapeCount).CtrRot.x = 170 + 54
81. Shape(ShapeCount).CtrRot.y = -31.25
82. i = 0
83. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
84.     i = i + 1
85.     r = 30
86.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
87.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
88. NEXT
89. Shape(ShapeCount).Length = i
90. Shape(ShapeCount).Mass = i
91. Shape(ShapeCount).Velocity.x = 0
92. Shape(ShapeCount).Velocity.y = 0
93. Shape(ShapeCount).Omega = 0
94. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
95. CALL CalculateCtrMass(ShapeCount)
96. CALL CalculateDiameter(ShapeCount)
97. CALL CalculateMOI(ShapeCount)
98.  
99. ShapeCount = ShapeCount + 1
100. Shape(ShapeCount).CtrRot.x = 170 + 54
101. Shape(ShapeCount).CtrRot.y = 31.25
102. i = 0
103. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
104.     i = i + 1
105.     r = 30
106.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
107.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
108. NEXT
109. Shape(ShapeCount).Length = i
110. Shape(ShapeCount).Mass = i
111. Shape(ShapeCount).Velocity.x = 0
112. Shape(ShapeCount).Velocity.y = 0
113. Shape(ShapeCount).Omega = 0
114. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
115. CALL CalculateCtrMass(ShapeCount)
116. CALL CalculateDiameter(ShapeCount)
117. CALL CalculateMOI(ShapeCount)
118.  
119. ShapeCount = ShapeCount + 1
120. Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
121. Shape(ShapeCount).CtrRot.y = 0
122. i = 0
123. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
124.     i = i + 1
125.     r = 30
126.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
127.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
128. NEXT
129. Shape(ShapeCount).Length = i
130. Shape(ShapeCount).Mass = i
131. Shape(ShapeCount).Velocity.x = 0
132. Shape(ShapeCount).Velocity.y = 0
133. Shape(ShapeCount).Omega = 0
134. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
135. CALL CalculateCtrMass(ShapeCount)
136. CALL CalculateDiameter(ShapeCount)
137. CALL CalculateMOI(ShapeCount)
138.  
139. ShapeCount = ShapeCount + 1
140. Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
141. Shape(ShapeCount).CtrRot.y = -31.25 * 2
142. i = 0
143. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
144.     i = i + 1
145.     r = 30
146.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
147.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
148. NEXT
149. Shape(ShapeCount).Length = i
150. Shape(ShapeCount).Mass = i
151. Shape(ShapeCount).Velocity.x = 0
152. Shape(ShapeCount).Velocity.y = 0
153. Shape(ShapeCount).Omega = 0
154. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
155. CALL CalculateCtrMass(ShapeCount)
156. CALL CalculateDiameter(ShapeCount)
157. CALL CalculateMOI(ShapeCount)
158.  
159. ShapeCount = ShapeCount + 1
160. Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
161. Shape(ShapeCount).CtrRot.y = 31.25 * 2
162. i = 0
163. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
164.     i = i + 1
165.     r = 30
166.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
167.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
168. NEXT
169. Shape(ShapeCount).Length = i
170. Shape(ShapeCount).Mass = i
171. Shape(ShapeCount).Velocity.x = 0
172. Shape(ShapeCount).Velocity.y = 0
173. Shape(ShapeCount).Omega = 0
174. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
175. CALL CalculateCtrMass(ShapeCount)
176. CALL CalculateDiameter(ShapeCount)
177. CALL CalculateMOI(ShapeCount)
178.  
179.  
180. 'ShapeCount = ShapeCount + 1
181. 'Shape(ShapeCount).CtrRot.x = -200
182. 'Shape(ShapeCount).CtrRot.y = 0
183. 'i = 0
184. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
185. '    i = i + 1
186. '    r = 40 + 25 * COS(j) ^ 2
187. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
188. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
189. 'NEXT
190. 'Shape(ShapeCount).Length = i
191. 'Shape(ShapeCount).Mass = i
192. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
193. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
194. 'Shape(ShapeCount).Omega = 0
195. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
196. 'CALL CalculateCtrMass(ShapeCount)
197. 'CALL CalculateDiameter(ShapeCount)
198. 'CALL CalculateMOI(ShapeCount)
199.  
200. 'ShapeCount = ShapeCount + 1
201. 'Shape(ShapeCount).CtrRot.x = 0
202. 'Shape(ShapeCount).CtrRot.y = 0
203. 'i = 0
204. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
205. '    i = i + 1
206. '    r = 40 + 25 * COS(1.5 * j) ^ 2
207. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
208. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
209. 'NEXT
210. 'Shape(ShapeCount).Length = i
211. 'Shape(ShapeCount).Mass = i
212. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
213. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
214. 'Shape(ShapeCount).Omega = 0
215. 'Shape(ShapeCount).Shade = _RGB(255, 0, 255)
216. 'CALL CalculateCtrMass(ShapeCount)
217. 'CALL CalculateDiameter(ShapeCount)
218. 'CALL CalculateMOI(ShapeCount)
219.  
220. 'ShapeCount = ShapeCount + 1
221. 'Shape(ShapeCount).CtrRot.x = 200
222. 'Shape(ShapeCount).CtrRot.y = 0
223. 'i = 0
224. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
225. '    i = i + 1
226. '    r = 50
227. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
228. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
229. 'NEXT
230. 'Shape(ShapeCount).Length = i
231. 'Shape(ShapeCount).Mass = i
232. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
233. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
234. 'Shape(ShapeCount).Omega = 0
235. 'Shape(ShapeCount).Shade = _RGB(255, 255, 0)
236. 'CALL CalculateCtrMass(ShapeCount)
237. 'CALL CalculateDiameter(ShapeCount)
238. 'CALL CalculateMOI(ShapeCount)
239.  
240. 'w = _WIDTH / 2
241. 'h = _HEIGHT / 2
242. 'b = 20
243. 'FOR n = -1 TO 1 STEP 2
244.  
245. '    FOR k = (-w + 2 * 5) TO (w - 2 * 5) STEP b
246. '        ShapeCount = ShapeCount + 1
247. '        Shape(ShapeCount).CtrRot.x = x
248. '        Shape(ShapeCount).CtrRot.y = n * h - n * 5
249. '        i = 0
250. '        FOR j = (Shape(ShapeCount).CtrRot.x - b / 2) TO (Shape(ShapeCount).CtrRot.x + b / 2) STEP 5
251. '            i = i + 1
252. '            PointChain(ShapeCount, i).x = j
253. '            PointChain(ShapeCount, i).y = n * h - n * 5
254. '        NEXT
255. '        Shape(ShapeCount).Length = i
256. '        Shape(ShapeCount).Mass = 999 ^ 999
257. '        Shape(ShapeCount).Velocity.x = 0
258. '        Shape(ShapeCount).Velocity.y = 0
259. '        Shape(ShapeCount).Omega = 0
260. '        Shape(ShapeCount).Shade = _RGB(255, 255, 0)
261. '        CALL CalculateCtrMass(ShapeCount)
262. '        CALL CalculateDiameter(ShapeCount)
263. '        CALL CalculateMOI(ShapeCount)
264. '    NEXT
265.  
266. '    'ShapeCount = ShapeCount + 1
267. '    'Shape(ShapeCount).CtrRot.x = n * w - n * 5
268. '    'Shape(ShapeCount).CtrRot.y = 0
269. '    'i = 0
270. '    'FOR j = (-h + 2 * 5) TO (h - 2 * 5) STEP 3
271. '    '    i = i + 1
272. '    '    PointChain(ShapeCount, i).x = n * w - n * 5
273. '    '    PointChain(ShapeCount, i).y = j
274. '    'NEXT
275. '    'Shape(ShapeCount).Length = i
276. '    'Shape(ShapeCount).Mass = 999 ^ 999
277. '    'Shape(ShapeCount).Velocity.x = 0
278. '    'Shape(ShapeCount).Velocity.y = 0
279. '    'Shape(ShapeCount).Omega = 0
280. '    'Shape(ShapeCount).Shade = _RGB(255, 255, 0)
281. '    'CALL CalculateCtrMass(ShapeCount)
282. '    ''CALL CalculateDiameter(ShapeCount)
283. '    'Shape(ShapeCount).Diameter = 5
284. '    'CALL CalculateMOI(ShapeCount)
285. 'NEXT
286.  
287.  
288.  
289. ' Walls
290. b = 10
291. FOR n = -1 TO 1 STEP 2
292.     FOR k = -(_WIDTH / 2 - b) TO (_WIDTH / 2 - b) STEP 2 * b
293.         ShapeCount = ShapeCount + 1
294.         Shape(ShapeCount).CtrRot.x = k
295.         Shape(ShapeCount).CtrRot.y = n * (_HEIGHT / 2 - b / 2)
296.         i = 0
297.         FOR j = (Shape(ShapeCount).CtrRot.x - b / 2) TO (Shape(ShapeCount).CtrRot.x + b / 2) STEP 3
298.             i = i + 1
299.             PointChain(ShapeCount, i).x = j
300.             PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y
301.         NEXT
302.         Shape(ShapeCount).Length = i
303.         Shape(ShapeCount).Mass = 999 ^ 999
304.         Shape(ShapeCount).Velocity.x = 0
305.         Shape(ShapeCount).Velocity.y = 0
306.         Shape(ShapeCount).Omega = 0
307.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
308.         CALL CalculateCtrMass(ShapeCount)
309.         CALL CalculateDiameter(ShapeCount)
310.         CALL CalculateMOI(ShapeCount)
311.         Shape(ShapeCount).MOI = 999 ^ 999
312.     NEXT
313.  
314.     FOR k = -(_HEIGHT / 2 - b) TO (_HEIGHT / 2 - b) STEP 2 * b
315.         ShapeCount = ShapeCount + 1
316.         Shape(ShapeCount).CtrRot.x = n * (_WIDTH / 2 - b / 2)
317.         Shape(ShapeCount).CtrRot.y = k
318.         i = 0
319.         FOR j = (Shape(ShapeCount).CtrRot.y - b / 2) TO (Shape(ShapeCount).CtrRot.y + b / 2) STEP 3
320.             i = i + 1
321.             PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x
322.             PointChain(ShapeCount, i).y = j
323.         NEXT
324.         Shape(ShapeCount).Length = i
325.         Shape(ShapeCount).Mass = 999 ^ 999
326.         Shape(ShapeCount).Velocity.x = 0
327.         Shape(ShapeCount).Velocity.y = 0
328.         Shape(ShapeCount).Omega = 0
329.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
330.         CALL CalculateCtrMass(ShapeCount)
331.         CALL CalculateDiameter(ShapeCount)
332.         CALL CalculateMOI(ShapeCount)
333.         Shape(ShapeCount).MOI = 999 ^ 999
334.     NEXT
335. NEXT
336.  
337. DO
338.  
339.     'DO WHILE _MOUSEINPUT
340.     '    x = _MOUSEX
341.     '    y = _MOUSEY
342.     '    IF ((x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT)) THEN
343.     '        IF (_MOUSEBUTTON(1)) THEN
344.     '            x = _MOUSEX - _WIDTH / 2
345.     '            y = -_MOUSEY + _HEIGHT / 2
346.     '            Shape(1).CtrRot.x = x
347.     '            Shape(1).CtrRot.y = y
348.     '            CALL CalculateMOI(1)
349.     '            Shape(1).Omega = 0
350.     '        END IF
351.     '        IF (_MOUSEBUTTON(2)) THEN
352.     '            x = _MOUSEX - _WIDTH / 2
353.     '            y = -_MOUSEY + _HEIGHT / 2
354.     '            vtemp.x = x - Shape(1).CtrMass.x
355.     '            vtemp.y = y - Shape(1).CtrMass.y
356.     '            CALL TranslateShape(1, vtemp)
357.     '            CALL CalculateMOI(1)
358.     '            Shape(1).Velocity.x = 0
359.     '            Shape(1).Velocity.y = 0
360.     '        END IF
361.     '        IF _MOUSEWHEEL THEN
362.     '            CALL RotShape(1, Shape(1).CtrRot, .05)
363.     '        END IF
364.     '    END IF
365.     'LOOP
366.  
367.     IF (_KEYHIT = 32) THEN
368.         Shape(1).Velocity.x = Shape(1).Velocity.x + 4
369.         Shape(1).Omega = Omega - .08
370.         Shape(1).Velocity.y = 0
371.         _KEYCLEAR
372.     END IF
373.  
374.     ' Proximity detection
375.     ProximalPairsCount = 0
376.     Shape1 = 0
377.     Shape2 = 0
378.     FOR j = 1 TO ShapeCount
379.         FOR k = j + 1 TO ShapeCount
380.             dx = Shape(j).CtrMass.x - Shape(k).CtrMass.x
381.             dy = Shape(j).CtrMass.y - Shape(k).CtrMass.y
382.             dr = SQR(dx * dx + dy * dy)
383.             IF (dr < 1.10 * (Shape(j).Diameter + Shape(k).Diameter)) THEN
384.                 ProximalPairsCount = ProximalPairsCount + 1
385.                 ProximalPairs(ProximalPairsCount, 1) = j
386.                 ProximalPairs(ProximalPairsCount, 2) = k
387.                 Shape1 = j
388.                 Shape2 = k
389.             END IF
390.         NEXT
391.     NEXT
392.  
393.     IF (ProximalPairsCount > 0) THEN
394.         FOR n = 1 TO ProximalPairsCount
395.             Shape1 = ProximalPairs(n, 1)
396.             Shape2 = ProximalPairs(n, 2)
397.  
398.             ' Collision detection
399.             rmin = 999 ^ 999
400.             ClosestIndex1 = 0
401.             ClosestIndex2 = 0
402.             FOR j = 1 TO Shape(Shape1).Length
403.                 FOR k = 1 TO Shape(Shape2).Length
404.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
405.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
406.                     r2 = dx * dx + dy * dy
407.                     IF (r2 < rmin) THEN
408.                         rmin = r2
409.                         ClosestIndex1 = j
410.                         ClosestIndex2 = k
411.                     END IF
412.                 NEXT
413.             NEXT
414.  
415.             IF (rmin <= 4.5) THEN
416.                 CollisionCount = CollisionCount + 1
417.  
418.                 ' Normal vector 1
419.                 x0 = PointChain(Shape1, ClosestIndex1).x
420.                 y0 = PointChain(Shape1, ClosestIndex1).y
421.                 CALL ccircle(x0, y0, 3, Shape(Shape1).Shade)
422.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
423.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
424.                 norm = SQR(xx * xx + yy * yy)
425.                 xx = xx / norm
426.                 yy = yy / norm
427.                 nx1 = xx
428.                 ny1 = yy
429.                 CALL cline(x0, y0, x0 + nx1 * 15, y0 + ny1 * 15, Shape(Shape1).Shade)
430.  
431.                 ' Normal vector 2
432.                 x0 = PointChain(Shape2, ClosestIndex2).x
433.                 y0 = PointChain(Shape2, ClosestIndex2).y
434.                 CALL ccircle(x0, y0, 3, Shape(Shape2).Shade)
435.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
436.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
437.                 norm = SQR(xx * xx + yy * yy)
438.                 xx = xx / norm
439.                 yy = yy / norm
440.                 nx2 = xx
441.                 ny2 = yy
442.                 CALL cline(x0, y0, x0 + nx2 * 15, y0 + ny2 * 15, Shape(Shape2).Shade)
443.  
444.                 ' Perpendicular vector 1
445.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).CtrRot.x
446.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).CtrRot.y
447.                 px1 = -dy1
448.                 py1 = dx1
449.                 p1 = SQR(px1 * px1 + py1 * py1)
450.                 px1 = px1 / p1
451.                 py1 = py1 / p1
452.                 CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + px1 * 15, PointChain(Shape1, ClosestIndex1).y + py1 * 15, Shape(Shape1).Shade)
453.  
454.                 ' Perpendicular vector 2
455.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).CtrRot.x
456.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).CtrRot.y
457.                 px2 = -dy2
458.                 py2 = dx2
459.                 p2 = SQR(px2 * px2 + py2 * py2)
460.                 px2 = px2 / p2
461.                 py2 = py2 / p2
462.                 CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + px2 * 15, PointChain(Shape2, ClosestIndex2).y + py2 * 15, Shape(Shape2).Shade)
463.  
464.                 ' Angular velocity vector 1
465.                 w1 = Shape(Shape1).Omega
466.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
467.                 vx1 = w1 * r1 * px1
468.                 vy1 = w1 * r1 * py1
469.                 CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + vx1 * 5, PointChain(Shape1, ClosestIndex1).y + vy1 * 5, Shape(Shape1).Shade)
470.  
471.                 ' Angular velocity vector 2
472.                 w2 = Shape(Shape2).Omega
473.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
474.                 vx2 = w2 * r2 * px2
475.                 vy2 = w2 * r2 * py2
476.                 CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + vx2 * 5, PointChain(Shape2, ClosestIndex2).y + vy2 * 5, Shape(Shape2).Shade)
477.  
478.                 ' Mass terms
479.                 m1 = Shape(Shape1).Mass
480.                 i1 = Shape(Shape1).MOI
481.                 m2 = Shape(Shape2).Mass
482.                 i2 = Shape(Shape2).MOI
483.                 mu = 1 / (1 / m1 + 1 / m2)
484.  
485.                 ' Velocity differential 1
486.                 vtx1 = Shape(Shape1).Velocity.x + vx1
487.                 vty1 = Shape(Shape1).Velocity.y + vy1
488.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
489.  
490.                 ' Velocity differential 2
491.                 vtx2 = Shape(Shape2).Velocity.x + vx2
492.                 vty2 = Shape(Shape2).Velocity.y + vy2
493.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
494.  
495.                 ' Velocity differential total
496.                 dvtx = vtx2 - vtx1
497.                 dvty = vty2 - vty1
498.  
499.                 ' Geometry
500.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
501.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
502.  
503.                 ' Momentum exchange
504.                 qx1 = nx1 * 2 * mu * n1dotdvt
505.                 qy1 = ny1 * 2 * mu * n1dotdvt
506.                 qx2 = nx2 * 2 * mu * n2dotdvt
507.                 qy2 = ny2 * 2 * mu * n2dotdvt
508.  
509.                 ' Momentum exchange unit vector
510.                 q1 = SQR(qx1 * qx1 + qy1 * qy1)
511.                 qhatx1 = qx1 / q1
512.                 qhaty1 = qy1 / q1
513.                 q2 = SQR(qx2 * qx2 + qy2 * qy2)
514.                 qhatx2 = qx2 / q2
515.                 qhaty2 = qy2 / q2
516.  
517.                 ' Undo previous motion
518.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -1 * Shape(Shape1).Omega)
519.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -1 * Shape(Shape2).Omega)
520.                 vtemp.x = -1 * Shape(Shape1).Velocity.x
521.                 vtemp.y = -1 * Shape(Shape1).Velocity.y
522.                 CALL TranslateShape(Shape1, vtemp)
523.                 vtemp.x = -1 * Shape(Shape2).Velocity.x
524.                 vtemp.y = -1 * Shape(Shape2).Velocity.y
525.                 CALL TranslateShape(Shape2, vtemp)
526.  
527.                 '' Separate along normal
528.                 'vtemp.x = -nx1 '* vtx1
529.                 'vtemp.y = -ny1 '* vty1
530.                 'CALL TranslateShape(Shape1, vtemp)
531.                 'vtemp.x = -nx2 '* vtx2
532.                 'vtemp.y = -ny2 '* vty2
533.                 'CALL TranslateShape(Shape1, vtemp)
534.  
535.                 ' Translational impulse
536.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
537.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
538.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
539.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
540.                 f1 = -q1dotn1 * n1dotr1hat
541.                 f2 = -q2dotn2 * n2dotr2hat
542.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
543.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
544.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
545.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
546.  
547.                 ' Angular impulse
548.                 q1dotp1 = qx1 * px1 + qy1 * py1
549.                 q2dotp2 = qx2 * px2 + qy2 * py2
550.                 dw1 = r1 * q1dotp1 / i1
551.                 dw2 = -r2 * q2dotp2 / i2
552.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
553.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
554.                 Shape(Shape1).Omega = Shape(Shape1).Omega + dw1
555.                 Shape(Shape2).Omega = Shape(Shape2).Omega + dw2
556.             END IF
557.         NEXT
558.     END IF
559.  
560.     FOR ShapeIndex = 1 TO ShapeCount
561.         dx = Shape(ShapeIndex).CtrMass.x - Shape(ShapeIndex).CtrRot.x
562.         dy = Shape(ShapeIndex).CtrMass.y - Shape(ShapeIndex).CtrRot.y
563.  
564.         cx = Shape(ShapeIndex).CtrMass.x
565.         cy = Shape(ShapeIndex).CtrMass.y
566.         'Gravity.x = 0 '-cx / 10
567.         'Gravity.y = 0 '-cy / 10
568.  
569.         'torque = dx * Gravity.y - dy * Gravity.x
570.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
571.  
572.         ' Rotation update
573.         CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
574.  
575.         ' Velocity update
576.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x '+ Gravity.x
577.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y '+ Gravity.y
578.         CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
579.  
580.         ' Damping
581.         'Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .995
582.         'Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .995
583.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .995
584.     NEXT
585.  
586.     ' Graphics
587.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
588.     FOR ShapeIndex = 1 TO ShapeCount
589.         LOCATE 1, 1: PRINT CollisionCount
590.         FOR i = 1 TO Shape(ShapeIndex).Length
591.             CALL cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
592.         NEXT
593.         CALL ccircle(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, 3, Shape(ShapeIndex).Shade)
594.         CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
595.         CALL cline(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, Shape(ShapeIndex).Shade)
596.     NEXT
597.     CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, Shape(Shape1).CtrRot.x, Shape(Shape1).CtrRot.y, Shape(Shape1).Shade)
598.     CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, Shape(Shape2).CtrRot.x, Shape(Shape2).CtrRot.y, Shape(Shape2).Shade)
599.  
600.     _DISPLAY
601.     _LIMIT 120
602. LOOP
603.  
604. END
605.  
606. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
607.     DIM l AS Vector
608.     DIM r AS Vector
609.     li = i - 1
610.     ri = i + 1
611.     IF (i = 1) THEN li = Shape(k).Length
612.     IF (i = Shape(k).Length) THEN ri = 1
613.     l.x = PointChain(k, li).x
614.     r.x = PointChain(k, ri).x
615.     dx = r.x - l.x
616.     CalculateNormalX = dx
617. END FUNCTION
618.  
619. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
620.     DIM l AS Vector
621.     DIM r AS Vector
622.     li = i - 1
623.     ri = i + 1
624.     IF (i = 1) THEN li = Shape(k).Length
625.     IF (i = Shape(k).Length) THEN ri = 1
626.     l.y = PointChain(k, li).y
627.     r.y = PointChain(k, ri).y
628.     dy = r.y - l.y
629.     CalculateNormalY = dy
630. END FUNCTION
631.  
632. SUB CalculateCtrMass (k AS INTEGER)
633.     xx = 0
634.     yy = 0
635.     FOR i = 1 TO Shape(k).Length
636.         xx = xx + PointChain(k, i).x
637.         yy = yy + PointChain(k, i).y
638.     NEXT
639.     Shape(k).CtrMass.x = xx / Shape(k).Length
640.     Shape(k).CtrMass.y = yy / Shape(k).Length
641. END SUB
642.  
643. SUB CalculateDiameter (k AS INTEGER)
644.     r2max = -1
645.     FOR i = 1 TO Shape(k).Length
646.         xx = Shape(k).CtrMass.x - PointChain(k, i).x
647.         yy = Shape(k).CtrMass.y - PointChain(k, i).y
648.         r2 = xx * xx + yy * yy
649.         IF (r2 > r2max) THEN
650.             r2max = r2
651.         END IF
652.     NEXT
653.     Shape(k).Diameter = SQR(r2max)
654. END SUB
655.  
656. SUB CalculateMOI (k AS INTEGER)
657.     xx = 0
658.     yy = 0
659.     FOR i = 1 TO Shape(k).Length
660.         xx = xx + (Shape(k).CtrRot.x - PointChain(k, i).x) ^ 2
661.         yy = yy + (Shape(k).CtrRot.y - PointChain(k, i).y) ^ 2
662.     NEXT
663.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Length)
664. END SUB
665.  
666. SUB TranslateShape (k AS INTEGER, c AS Vector)
667.     FOR i = 1 TO Shape(k).Length
668.         PointChain(k, i).x = PointChain(k, i).x + c.x
669.         PointChain(k, i).y = PointChain(k, i).y + c.y
670.     NEXT
671.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
672.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
673.     Shape(k).CtrMass.x = Shape(k).CtrMass.x + c.x
674.     Shape(k).CtrMass.y = Shape(k).CtrMass.y + c.y
675. END SUB
676.  
677. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
678.     FOR i = 1 TO Shape(k).Length
679.         xx = PointChain(k, i).x - c.x
680.         yy = PointChain(k, i).y - c.y
681.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
682.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
683.     NEXT
684.     xx = Shape(k).CtrMass.x - c.x
685.     yy = Shape(k).CtrMass.y - c.y
686.     Shape(k).CtrMass.x = c.x + xx * COS(da) - yy * SIN(da)
687.     Shape(k).CtrMass.y = c.y + yy * COS(da) + xx * SIN(da)
688. END SUB
689.  
690. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
691.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
692. END SUB
693.  
694. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
695.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
696. END SUB
697.  
698. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
699.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
700. END SUB

[STxAxTIC]

This one is more fun. We have a gravity test in a low-viscosity fluid. Press space to your heart's content.

Code: QB64: [Select]

1. SCREEN _NEWIMAGE(800, 600, 32)
2. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
3.  
4. RANDOMIZE TIMER
5.  
6. TYPE Vector
7.     x AS DOUBLE
8.     y AS DOUBLE
9. END TYPE
10.  
11. TYPE Object
12.     CtrMass AS Vector
13.     CtrRot AS Vector
14.     Diameter AS DOUBLE
15.     Mass AS DOUBLE
16.     MOI AS DOUBLE
17.     Length AS INTEGER
18.     Omega AS DOUBLE
19.     Shade AS _UNSIGNED LONG
20.     Velocity AS Vector
21. END TYPE
22.  
23. DIM vtemp AS Vector
24.  
25. DIM SHARED Shape(1000) AS Object
26. DIM SHARED PointChain(1000, 5000) AS Vector
27. DIM SHARED ShapeCount AS INTEGER
28. DIM SHARED CollisionCount AS INTEGER
29. ShapeCount = 0
30. CollisionCount = 0
31.  
32. DIM Gravity AS Vector
33. Gravity.x = 0
34. Gravity.y = -2
35.  
36. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
37. DIM SHARED ProximalPairsCount
38.  
39. ShapeCount = ShapeCount + 1
40. Shape(ShapeCount).CtrRot.x = -220
41. Shape(ShapeCount).CtrRot.y = 0
42. i = 0
43. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
44.     i = i + 1
45.     r = 40 + 25 * COS(1.5 * j) ^ 2
46.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
47.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
48. NEXT
49. Shape(ShapeCount).Length = i
50. Shape(ShapeCount).Mass = i
51. Shape(ShapeCount).Velocity.x = 0
52. Shape(ShapeCount).Velocity.y = 0
53. Shape(ShapeCount).Omega = 0
54. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
55. CALL CalculateCtrMass(ShapeCount)
56. CALL CalculateDiameter(ShapeCount)
57. CALL CalculateMOI(ShapeCount)
58.  
59. ShapeCount = ShapeCount + 1
60. Shape(ShapeCount).CtrRot.x = 170
61. Shape(ShapeCount).CtrRot.y = 0
62. i = 0
63. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
64.     i = i + 1
65.     r = 27
66.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
67.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
68. NEXT
69. Shape(ShapeCount).Length = i
70. Shape(ShapeCount).Mass = i
71. Shape(ShapeCount).Velocity.x = 0
72. Shape(ShapeCount).Velocity.y = 0
73. Shape(ShapeCount).Omega = 0
74. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
75. CALL CalculateCtrMass(ShapeCount)
76. CALL CalculateDiameter(ShapeCount)
77. CALL CalculateMOI(ShapeCount)
78.  
79. ShapeCount = ShapeCount + 1
80. Shape(ShapeCount).CtrRot.x = 170 + 54
81. Shape(ShapeCount).CtrRot.y = -31.25
82. i = 0
83. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
84.     i = i + 1
85.     r = 27
86.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
87.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
88. NEXT
89. Shape(ShapeCount).Length = i
90. Shape(ShapeCount).Mass = i
91. Shape(ShapeCount).Velocity.x = 0
92. Shape(ShapeCount).Velocity.y = 0
93. Shape(ShapeCount).Omega = 0
94. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
95. CALL CalculateCtrMass(ShapeCount)
96. CALL CalculateDiameter(ShapeCount)
97. CALL CalculateMOI(ShapeCount)
98.  
99. ShapeCount = ShapeCount + 1
100. Shape(ShapeCount).CtrRot.x = 170 + 54
101. Shape(ShapeCount).CtrRot.y = 31.25
102. i = 0
103. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
104.     i = i + 1
105.     r = 27
106.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
107.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
108. NEXT
109. Shape(ShapeCount).Length = i
110. Shape(ShapeCount).Mass = i
111. Shape(ShapeCount).Velocity.x = 0
112. Shape(ShapeCount).Velocity.y = 0
113. Shape(ShapeCount).Omega = 0
114. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
115. CALL CalculateCtrMass(ShapeCount)
116. CALL CalculateDiameter(ShapeCount)
117. CALL CalculateMOI(ShapeCount)
118.  
119. ShapeCount = ShapeCount + 1
120. Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
121. Shape(ShapeCount).CtrRot.y = 0
122. i = 0
123. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
124.     i = i + 1
125.     r = 27
126.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
127.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
128. NEXT
129. Shape(ShapeCount).Length = i
130. Shape(ShapeCount).Mass = i
131. Shape(ShapeCount).Velocity.x = 0
132. Shape(ShapeCount).Velocity.y = 0
133. Shape(ShapeCount).Omega = 0
134. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
135. CALL CalculateCtrMass(ShapeCount)
136. CALL CalculateDiameter(ShapeCount)
137. CALL CalculateMOI(ShapeCount)
138.  
139. ShapeCount = ShapeCount + 1
140. Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
141. Shape(ShapeCount).CtrRot.y = -31.25 * 2
142. i = 0
143. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
144.     i = i + 1
145.     r = 27
146.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
147.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
148. NEXT
149. Shape(ShapeCount).Length = i
150. Shape(ShapeCount).Mass = i
151. Shape(ShapeCount).Velocity.x = 0
152. Shape(ShapeCount).Velocity.y = 0
153. Shape(ShapeCount).Omega = 0
154. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
155. CALL CalculateCtrMass(ShapeCount)
156. CALL CalculateDiameter(ShapeCount)
157. CALL CalculateMOI(ShapeCount)
158.  
159. ShapeCount = ShapeCount + 1
160. Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
161. Shape(ShapeCount).CtrRot.y = 31.25 * 2
162. i = 0
163. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
164.     i = i + 1
165.     r = 27
166.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
167.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
168. NEXT
169. Shape(ShapeCount).Length = i
170. Shape(ShapeCount).Mass = i
171. Shape(ShapeCount).Velocity.x = 0
172. Shape(ShapeCount).Velocity.y = 0
173. Shape(ShapeCount).Omega = 0
174. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
175. CALL CalculateCtrMass(ShapeCount)
176. CALL CalculateDiameter(ShapeCount)
177. CALL CalculateMOI(ShapeCount)
178.  
179. 'ShapeCount = ShapeCount + 1
180. 'Shape(ShapeCount).CtrRot.x = -200
181. 'Shape(ShapeCount).CtrRot.y = 0
182. 'i = 0
183. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
184. '    i = i + 1
185. '    r = 40 + 25 * COS(j) ^ 2
186. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
187. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
188. 'NEXT
189. 'Shape(ShapeCount).Length = i
190. 'Shape(ShapeCount).Mass = i
191. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
192. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
193. 'Shape(ShapeCount).Omega = 0
194. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
195. 'CALL CalculateCtrMass(ShapeCount)
196. 'CALL CalculateDiameter(ShapeCount)
197. 'CALL CalculateMOI(ShapeCount)
198.  
199. 'ShapeCount = ShapeCount + 1
200. 'Shape(ShapeCount).CtrRot.x = 0
201. 'Shape(ShapeCount).CtrRot.y = 0
202. 'i = 0
203. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
204. '    i = i + 1
205. '    r = 40 + 25 * COS(1.5 * j) ^ 2
206. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
207. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
208. 'NEXT
209. 'Shape(ShapeCount).Length = i
210. 'Shape(ShapeCount).Mass = i
211. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
212. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
213. 'Shape(ShapeCount).Omega = 0
214. 'Shape(ShapeCount).Shade = _RGB(255, 0, 255)
215. 'CALL CalculateCtrMass(ShapeCount)
216. 'CALL CalculateDiameter(ShapeCount)
217. 'CALL CalculateMOI(ShapeCount)
218.  
219. 'ShapeCount = ShapeCount + 1
220. 'Shape(ShapeCount).CtrRot.x = 200
221. 'Shape(ShapeCount).CtrRot.y = 0
222. 'i = 0
223. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
224. '    i = i + 1
225. '    r = 50
226. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
227. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
228. 'NEXT
229. 'Shape(ShapeCount).Length = i
230. 'Shape(ShapeCount).Mass = i
231. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
232. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
233. 'Shape(ShapeCount).Omega = 0
234. 'Shape(ShapeCount).Shade = _RGB(255, 255, 0)
235. 'CALL CalculateCtrMass(ShapeCount)
236. 'CALL CalculateDiameter(ShapeCount)
237. 'CALL CalculateMOI(ShapeCount)
238.  
239. 'w = _WIDTH / 2
240. 'h = _HEIGHT / 2
241. 'b = 20
242. 'FOR n = -1 TO 1 STEP 2
243.  
244. '    FOR k = (-w + 2 * 5) TO (w - 2 * 5) STEP b
245. '        ShapeCount = ShapeCount + 1
246. '        Shape(ShapeCount).CtrRot.x = x
247. '        Shape(ShapeCount).CtrRot.y = n * h - n * 5
248. '        i = 0
249. '        FOR j = (Shape(ShapeCount).CtrRot.x - b / 2) TO (Shape(ShapeCount).CtrRot.x + b / 2) STEP 5
250. '            i = i + 1
251. '            PointChain(ShapeCount, i).x = j
252. '            PointChain(ShapeCount, i).y = n * h - n * 5
253. '        NEXT
254. '        Shape(ShapeCount).Length = i
255. '        Shape(ShapeCount).Mass = 999 ^ 999
256. '        Shape(ShapeCount).Velocity.x = 0
257. '        Shape(ShapeCount).Velocity.y = 0
258. '        Shape(ShapeCount).Omega = 0
259. '        Shape(ShapeCount).Shade = _RGB(255, 255, 0)
260. '        CALL CalculateCtrMass(ShapeCount)
261. '        CALL CalculateDiameter(ShapeCount)
262. '        CALL CalculateMOI(ShapeCount)
263. '    NEXT
264.  
265. '    'ShapeCount = ShapeCount + 1
266. '    'Shape(ShapeCount).CtrRot.x = n * w - n * 5
267. '    'Shape(ShapeCount).CtrRot.y = 0
268. '    'i = 0
269. '    'FOR j = (-h + 2 * 5) TO (h - 2 * 5) STEP 3
270. '    '    i = i + 1
271. '    '    PointChain(ShapeCount, i).x = n * w - n * 5
272. '    '    PointChain(ShapeCount, i).y = j
273. '    'NEXT
274. '    'Shape(ShapeCount).Length = i
275. '    'Shape(ShapeCount).Mass = 999 ^ 999
276. '    'Shape(ShapeCount).Velocity.x = 0
277. '    'Shape(ShapeCount).Velocity.y = 0
278. '    'Shape(ShapeCount).Omega = 0
279. '    'Shape(ShapeCount).Shade = _RGB(255, 255, 0)
280. '    'CALL CalculateCtrMass(ShapeCount)
281. '    ''CALL CalculateDiameter(ShapeCount)
282. '    'Shape(ShapeCount).Diameter = 5
283. '    'CALL CalculateMOI(ShapeCount)
284. 'NEXT
285.  
286. ' Walls
287. b = 10
288. FOR n = -1 TO 1 STEP 2
289.     FOR k = -(_WIDTH / 2 - b) TO (_WIDTH / 2 - b) STEP 2 * b
290.         ShapeCount = ShapeCount + 1
291.         Shape(ShapeCount).CtrRot.x = k
292.         Shape(ShapeCount).CtrRot.y = n * (_HEIGHT / 2 - b / 2)
293.         i = 0
294.         FOR j = (Shape(ShapeCount).CtrRot.x - b / 2) TO (Shape(ShapeCount).CtrRot.x + b / 2) STEP 3
295.             i = i + 1
296.             PointChain(ShapeCount, i).x = j
297.             PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y
298.         NEXT
299.         Shape(ShapeCount).Length = i
300.         Shape(ShapeCount).Mass = 999 ^ 999
301.         Shape(ShapeCount).Velocity.x = 0
302.         Shape(ShapeCount).Velocity.y = 0
303.         Shape(ShapeCount).Omega = 0
304.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
305.         CALL CalculateCtrMass(ShapeCount)
306.         CALL CalculateDiameter(ShapeCount)
307.         CALL CalculateMOI(ShapeCount)
308.         Shape(ShapeCount).MOI = 999 ^ 999
309.     NEXT
310.  
311.     FOR k = -(_HEIGHT / 2 - b) TO (_HEIGHT / 2 - b) STEP 2 * b
312.         ShapeCount = ShapeCount + 1
313.         Shape(ShapeCount).CtrRot.x = n * (_WIDTH / 2 - b / 2)
314.         Shape(ShapeCount).CtrRot.y = k
315.         i = 0
316.         FOR j = (Shape(ShapeCount).CtrRot.y - b / 2) TO (Shape(ShapeCount).CtrRot.y + b / 2) STEP 3
317.             i = i + 1
318.             PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x
319.             PointChain(ShapeCount, i).y = j
320.         NEXT
321.         Shape(ShapeCount).Length = i
322.         Shape(ShapeCount).Mass = 999 ^ 999
323.         Shape(ShapeCount).Velocity.x = 0
324.         Shape(ShapeCount).Velocity.y = 0
325.         Shape(ShapeCount).Omega = 0
326.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
327.         CALL CalculateCtrMass(ShapeCount)
328.         CALL CalculateDiameter(ShapeCount)
329.         CALL CalculateMOI(ShapeCount)
330.         Shape(ShapeCount).MOI = 999 ^ 999
331.     NEXT
332. NEXT
333.  
334. DO
335.  
336.     'DO WHILE _MOUSEINPUT
337.     '    x = _MOUSEX
338.     '    y = _MOUSEY
339.     '    IF ((x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT)) THEN
340.     '        IF (_MOUSEBUTTON(1)) THEN
341.     '            x = _MOUSEX - _WIDTH / 2
342.     '            y = -_MOUSEY + _HEIGHT / 2
343.     '            Shape(1).CtrRot.x = x
344.     '            Shape(1).CtrRot.y = y
345.     '            CALL CalculateMOI(1)
346.     '            Shape(1).Omega = 0
347.     '        END IF
348.     '        IF (_MOUSEBUTTON(2)) THEN
349.     '            x = _MOUSEX - _WIDTH / 2
350.     '            y = -_MOUSEY + _HEIGHT / 2
351.     '            vtemp.x = x - Shape(1).CtrMass.x
352.     '            vtemp.y = y - Shape(1).CtrMass.y
353.     '            CALL TranslateShape(1, vtemp)
354.     '            CALL CalculateMOI(1)
355.     '            Shape(1).Velocity.x = 0
356.     '            Shape(1).Velocity.y = 0
357.     '        END IF
358.     '        IF _MOUSEWHEEL THEN
359.     '            CALL RotShape(1, Shape(1).CtrRot, .05)
360.     '        END IF
361.     '    END IF
362.     'LOOP
363.  
364.     IF (_KEYHIT = 32) THEN
365.         Shape(1).Velocity.x = Shape(1).Velocity.x + 4
366.         Shape(1).Omega = Omega - .08
367.         Shape(1).Velocity.y = 0
368.         _KEYCLEAR
369.     END IF
370.  
371.     ' Proximity detection
372.     ProximalPairsCount = 0
373.     Shape1 = 0
374.     Shape2 = 0
375.     FOR j = 1 TO ShapeCount
376.         FOR k = j + 1 TO ShapeCount
377.             dx = Shape(j).CtrMass.x - Shape(k).CtrMass.x
378.             dy = Shape(j).CtrMass.y - Shape(k).CtrMass.y
379.             dr = SQR(dx * dx + dy * dy)
380.             IF (dr < 1.10 * (Shape(j).Diameter + Shape(k).Diameter)) THEN
381.                 ProximalPairsCount = ProximalPairsCount + 1
382.                 ProximalPairs(ProximalPairsCount, 1) = j
383.                 ProximalPairs(ProximalPairsCount, 2) = k
384.                 Shape1 = j
385.                 Shape2 = k
386.             END IF
387.         NEXT
388.     NEXT
389.  
390.     IF (ProximalPairsCount > 0) THEN
391.         FOR n = 1 TO ProximalPairsCount
392.             Shape1 = ProximalPairs(n, 1)
393.             Shape2 = ProximalPairs(n, 2)
394.  
395.             ' Collision detection
396.             rmin = 999 ^ 999
397.             ClosestIndex1 = 0
398.             ClosestIndex2 = 0
399.             FOR j = 1 TO Shape(Shape1).Length
400.                 FOR k = 1 TO Shape(Shape2).Length
401.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
402.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
403.                     r2 = dx * dx + dy * dy
404.                     IF (r2 < rmin) THEN
405.                         rmin = r2
406.                         ClosestIndex1 = j
407.                         ClosestIndex2 = k
408.                     END IF
409.                 NEXT
410.             NEXT
411.  
412.             IF (rmin <= 2) THEN
413.                 CollisionCount = CollisionCount + 1
414.  
415.                 ' Normal vector 1
416.                 x0 = PointChain(Shape1, ClosestIndex1).x
417.                 y0 = PointChain(Shape1, ClosestIndex1).y
418.                 CALL ccircle(x0, y0, 3, Shape(Shape1).Shade)
419.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
420.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
421.                 norm = SQR(xx * xx + yy * yy)
422.                 xx = xx / norm
423.                 yy = yy / norm
424.                 nx1 = xx
425.                 ny1 = yy
426.                 CALL cline(x0, y0, x0 + nx1 * 15, y0 + ny1 * 15, Shape(Shape1).Shade)
427.  
428.                 ' Normal vector 2
429.                 x0 = PointChain(Shape2, ClosestIndex2).x
430.                 y0 = PointChain(Shape2, ClosestIndex2).y
431.                 CALL ccircle(x0, y0, 3, Shape(Shape2).Shade)
432.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
433.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
434.                 norm = SQR(xx * xx + yy * yy)
435.                 xx = xx / norm
436.                 yy = yy / norm
437.                 nx2 = xx
438.                 ny2 = yy
439.                 CALL cline(x0, y0, x0 + nx2 * 15, y0 + ny2 * 15, Shape(Shape2).Shade)
440.  
441.                 ' Perpendicular vector 1
442.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).CtrRot.x
443.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).CtrRot.y
444.                 px1 = -dy1
445.                 py1 = dx1
446.                 p1 = SQR(px1 * px1 + py1 * py1)
447.                 px1 = px1 / p1
448.                 py1 = py1 / p1
449.                 CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + px1 * 15, PointChain(Shape1, ClosestIndex1).y + py1 * 15, Shape(Shape1).Shade)
450.  
451.                 ' Perpendicular vector 2
452.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).CtrRot.x
453.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).CtrRot.y
454.                 px2 = -dy2
455.                 py2 = dx2
456.                 p2 = SQR(px2 * px2 + py2 * py2)
457.                 px2 = px2 / p2
458.                 py2 = py2 / p2
459.                 CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + px2 * 15, PointChain(Shape2, ClosestIndex2).y + py2 * 15, Shape(Shape2).Shade)
460.  
461.                 ' Angular velocity vector 1
462.                 w1 = Shape(Shape1).Omega
463.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
464.                 vx1 = w1 * r1 * px1
465.                 vy1 = w1 * r1 * py1
466.                 CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + vx1 * 5, PointChain(Shape1, ClosestIndex1).y + vy1 * 5, Shape(Shape1).Shade)
467.  
468.                 ' Angular velocity vector 2
469.                 w2 = Shape(Shape2).Omega
470.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
471.                 vx2 = w2 * r2 * px2
472.                 vy2 = w2 * r2 * py2
473.                 CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + vx2 * 5, PointChain(Shape2, ClosestIndex2).y + vy2 * 5, Shape(Shape2).Shade)
474.  
475.                 ' Mass terms
476.                 m1 = Shape(Shape1).Mass
477.                 i1 = Shape(Shape1).MOI
478.                 m2 = Shape(Shape2).Mass
479.                 i2 = Shape(Shape2).MOI
480.                 mu = 1 / (1 / m1 + 1 / m2)
481.  
482.                 ' Velocity differential 1
483.                 vtx1 = Shape(Shape1).Velocity.x + vx1
484.                 vty1 = Shape(Shape1).Velocity.y + vy1
485.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
486.  
487.                 ' Velocity differential 2
488.                 vtx2 = Shape(Shape2).Velocity.x + vx2
489.                 vty2 = Shape(Shape2).Velocity.y + vy2
490.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
491.  
492.                 ' Velocity differential total
493.                 dvtx = vtx2 - vtx1
494.                 dvty = vty2 - vty1
495.  
496.                 ' Geometry
497.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
498.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
499.  
500.                 ' Momentum exchange
501.                 qx1 = nx1 * 2 * mu * n1dotdvt
502.                 qy1 = ny1 * 2 * mu * n1dotdvt
503.                 qx2 = nx2 * 2 * mu * n2dotdvt
504.                 qy2 = ny2 * 2 * mu * n2dotdvt
505.  
506.                 ' Momentum exchange unit vector
507.                 q1 = SQR(qx1 * qx1 + qy1 * qy1)
508.                 qhatx1 = qx1 / q1
509.                 qhaty1 = qy1 / q1
510.                 q2 = SQR(qx2 * qx2 + qy2 * qy2)
511.                 qhatx2 = qx2 / q2
512.                 qhaty2 = qy2 / q2
513.  
514.                 ' Undo previous motion
515.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -Shape(Shape1).Omega)
516.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -Shape(Shape2).Omega)
517.                 vtemp.x = -Shape(Shape1).Velocity.x
518.                 vtemp.y = -Shape(Shape1).Velocity.y
519.                 CALL TranslateShape(Shape1, vtemp)
520.                 vtemp.x = -Shape(Shape2).Velocity.x
521.                 vtemp.y = -Shape(Shape2).Velocity.y
522.                 CALL TranslateShape(Shape2, vtemp)
523.  
524.                 ' Separate along normal
525.                 'vtemp.x = -nx1 * (1.05)
526.                 'vtemp.y = -ny1 * (1.05)
527.                 'CALL TranslateShape(Shape1, vtemp)
528.                 'vtemp.x = -nx2 * (1.05)
529.                 'vtemp.y = -ny2 * (1.05)
530.                 'CALL TranslateShape(Shape1, vtemp)
531.  
532.                 ' Translational impulse
533.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
534.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
535.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
536.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
537.                 f1 = -q1dotn1 * n1dotr1hat
538.                 f2 = -q2dotn2 * n2dotr2hat
539.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
540.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
541.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
542.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
543.  
544.                 ' Angular impulse
545.                 q1dotp1 = qx1 * px1 + qy1 * py1
546.                 q2dotp2 = qx2 * px2 + qy2 * py2
547.                 dw1 = r1 * q1dotp1 / i1
548.                 dw2 = -r2 * q2dotp2 / i2
549.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
550.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
551.                 Shape(Shape1).Omega = Shape(Shape1).Omega + dw1
552.                 Shape(Shape2).Omega = Shape(Shape2).Omega + dw2
553.  
554.                 ' Static friction
555.                 IF Shape(ShapeIndex).Velocity.x * Shape(ShapeIndex).Velocity.x < .1 THEN Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .01
556.                 IF Shape(ShapeIndex).Velocity.y * Shape(ShapeIndex).Velocity.y < .1 THEN Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .01
557.                 IF Shape(ShapeIndex).Omega * Shape(ShapeIndex).Omega < .03 THEN Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .01
558.  
559.  
560.             END IF
561.         NEXT
562.     END IF
563.  
564.     FOR ShapeIndex = 1 TO ShapeCount
565.         dx = Shape(ShapeIndex).CtrMass.x - Shape(ShapeIndex).CtrRot.x
566.         dy = Shape(ShapeIndex).CtrMass.y - Shape(ShapeIndex).CtrRot.y
567.  
568.         cx = Shape(ShapeIndex).CtrMass.x
569.         cy = Shape(ShapeIndex).CtrMass.y
570.         'Gravity.x = 0 '-cx / 10
571.         'Gravity.y = 0 '-cy / 10
572.  
573.         'torque = dx * Gravity.y - dy * Gravity.x
574.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
575.  
576.         ' Rotation update
577.         CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
578.  
579.         ' Velocity update
580.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Gravity.x / Shape(ShapeIndex).Mass
581.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Gravity.y / Shape(ShapeIndex).Mass
582.         CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
583.  
584.         ' Damping
585.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .995
586.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .995
587.         Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .995
588.     NEXT
589.  
590.     ' Graphics
591.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
592.     FOR ShapeIndex = 1 TO ShapeCount
593.         LOCATE 1, 1: PRINT ProximalPairsCount, CollisionCount
594.         FOR i = 1 TO Shape(ShapeIndex).Length
595.             CALL cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
596.         NEXT
597.         CALL ccircle(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, 3, Shape(ShapeIndex).Shade)
598.         CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
599.         CALL cline(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, Shape(ShapeIndex).Shade)
600.     NEXT
601.     CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, Shape(Shape1).CtrRot.x, Shape(Shape1).CtrRot.y, Shape(Shape1).Shade)
602.     CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, Shape(Shape2).CtrRot.x, Shape(Shape2).CtrRot.y, Shape(Shape2).Shade)
603.  
604.     _DISPLAY
605.     _LIMIT 120
606. LOOP
607.  
608. END
609.  
610. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
611.     DIM l AS Vector
612.     DIM r AS Vector
613.     li = i - 1
614.     ri = i + 1
615.     IF (i = 1) THEN li = Shape(k).Length
616.     IF (i = Shape(k).Length) THEN ri = 1
617.     l.x = PointChain(k, li).x
618.     r.x = PointChain(k, ri).x
619.     dx = r.x - l.x
620.     CalculateNormalX = dx
621. END FUNCTION
622.  
623. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
624.     DIM l AS Vector
625.     DIM r AS Vector
626.     li = i - 1
627.     ri = i + 1
628.     IF (i = 1) THEN li = Shape(k).Length
629.     IF (i = Shape(k).Length) THEN ri = 1
630.     l.y = PointChain(k, li).y
631.     r.y = PointChain(k, ri).y
632.     dy = r.y - l.y
633.     CalculateNormalY = dy
634. END FUNCTION
635.  
636. SUB CalculateCtrMass (k AS INTEGER)
637.     xx = 0
638.     yy = 0
639.     FOR i = 1 TO Shape(k).Length
640.         xx = xx + PointChain(k, i).x
641.         yy = yy + PointChain(k, i).y
642.     NEXT
643.     Shape(k).CtrMass.x = xx / Shape(k).Length
644.     Shape(k).CtrMass.y = yy / Shape(k).Length
645. END SUB
646.  
647. SUB CalculateDiameter (k AS INTEGER)
648.     r2max = -1
649.     FOR i = 1 TO Shape(k).Length
650.         xx = Shape(k).CtrMass.x - PointChain(k, i).x
651.         yy = Shape(k).CtrMass.y - PointChain(k, i).y
652.         r2 = xx * xx + yy * yy
653.         IF (r2 > r2max) THEN
654.             r2max = r2
655.         END IF
656.     NEXT
657.     Shape(k).Diameter = SQR(r2max)
658. END SUB
659.  
660. SUB CalculateMOI (k AS INTEGER)
661.     xx = 0
662.     yy = 0
663.     FOR i = 1 TO Shape(k).Length
664.         xx = xx + (Shape(k).CtrRot.x - PointChain(k, i).x) ^ 2
665.         yy = yy + (Shape(k).CtrRot.y - PointChain(k, i).y) ^ 2
666.     NEXT
667.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Length)
668. END SUB
669.  
670. SUB TranslateShape (k AS INTEGER, c AS Vector)
671.     FOR i = 1 TO Shape(k).Length
672.         PointChain(k, i).x = PointChain(k, i).x + c.x
673.         PointChain(k, i).y = PointChain(k, i).y + c.y
674.     NEXT
675.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
676.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
677.     Shape(k).CtrMass.x = Shape(k).CtrMass.x + c.x
678.     Shape(k).CtrMass.y = Shape(k).CtrMass.y + c.y
679. END SUB
680.  
681. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
682.     FOR i = 1 TO Shape(k).Length
683.         xx = PointChain(k, i).x - c.x
684.         yy = PointChain(k, i).y - c.y
685.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
686.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
687.     NEXT
688.     xx = Shape(k).CtrMass.x - c.x
689.     yy = Shape(k).CtrMass.y - c.y
690.     Shape(k).CtrMass.x = c.x + xx * COS(da) - yy * SIN(da)
691.     Shape(k).CtrMass.y = c.y + yy * COS(da) + xx * SIN(da)
692. END SUB
693.  
694. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
695.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
696. END SUB
697.  
698. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
699.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
700. END SUB
701.  
702. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
703.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
704. END SUB

[STxAxTIC]

And here's an update that lets you crash oddly-shaped potatoes together. Pardon any jitters or explosions, it's not really optimized (too early). It auto-smooths what you draw using code taken shamelessly from the Samples collection.

A curious thing this does *without being directly asked, only indirectly by forces* is to seek the ideal packing of oddly-shaped items in two dimensions.

Code: QB64: [Select]

1. ' Display
2. SCREEN _NEWIMAGE(800, 600, 32)
3. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
4.  
5. ' Meta
6. RANDOMIZE TIMER
7.  
8. ' Data
9. TYPE Vector
10.     x AS DOUBLE
11.     y AS DOUBLE
12. END TYPE
13.  
14. TYPE Object
15.     CtrMass AS Vector
16.     CtrRot AS Vector
17.     Diameter AS DOUBLE
18.     Elements AS INTEGER
19.     Mass AS DOUBLE
20.     MOI AS DOUBLE
21.     Omega AS DOUBLE
22.     Shade AS _UNSIGNED LONG
23.     Velocity AS Vector
24. END TYPE
25.  
26. DIM vtemp AS Vector
27.  
28. ' Statics
29. DIM SHARED Shape(1000) AS Object
30. DIM SHARED PointChain(1000, 5000) AS Vector
31. DIM SHARED TempChain(1000, 5000) AS Vector
32. DIM SHARED ShapeCount AS INTEGER
33. ShapeCount = 0
34.  
35. ' Dynamics
36. DIM SHARED CollisionCount AS INTEGER
37. CollisionCount = 0
38.  
39. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
40. DIM SHARED ProximalPairsCount
41.  
42. DIM Gravity AS Vector
43. Gravity.x = 0
44. Gravity.y = -5
45.  
46. ' Create objects.
47.  
48. ShapeCount = ShapeCount + 1
49. Shape(ShapeCount).CtrRot.x = -220
50. Shape(ShapeCount).CtrRot.y = 0
51. i = 0
52. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
53.     i = i + 1
54.     r = 40 + 25 * COS(1.5 * j) ^ 2
55.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
56.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
57. NEXT
58. Shape(ShapeCount).Elements = i
59. Shape(ShapeCount).Mass = i
60. Shape(ShapeCount).Velocity.x = 0
61. Shape(ShapeCount).Velocity.y = 0
62. Shape(ShapeCount).Omega = 0
63. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
64. CALL CalculateCtrMass(ShapeCount)
65. CALL CalculateDiameter(ShapeCount)
66. CALL CalculateMOI(ShapeCount)
67.  
68. 'ShapeCount = ShapeCount + 1
69. 'Shape(ShapeCount).CtrRot.x = 170
70. 'Shape(ShapeCount).CtrRot.y = 0
71. 'i = 0
72. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
73. '    i = i + 1
74. '    r = 28
75. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
76. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
77. 'NEXT
78. 'Shape(ShapeCount).Elements = i
79. 'Shape(ShapeCount).Mass = i
80. 'Shape(ShapeCount).Velocity.x = 0
81. 'Shape(ShapeCount).Velocity.y = 0
82. 'Shape(ShapeCount).Omega = 0
83. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
84. 'CALL CalculateCtrMass(ShapeCount)
85. 'CALL CalculateDiameter(ShapeCount)
86. 'CALL CalculateMOI(ShapeCount)
87.  
88. 'ShapeCount = ShapeCount + 1
89. 'Shape(ShapeCount).CtrRot.x = 170 + 54
90. 'Shape(ShapeCount).CtrRot.y = -31.25
91. 'i = 0
92. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
93. '    i = i + 1
94. '    r = 28
95. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
96. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
97. 'NEXT
98. 'Shape(ShapeCount).Elements = i
99. 'Shape(ShapeCount).Mass = i
100. 'Shape(ShapeCount).Velocity.x = 0
101. 'Shape(ShapeCount).Velocity.y = 0
102. 'Shape(ShapeCount).Omega = 0
103. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
104. 'CALL CalculateCtrMass(ShapeCount)
105. 'CALL CalculateDiameter(ShapeCount)
106. 'CALL CalculateMOI(ShapeCount)
107.  
108. 'ShapeCount = ShapeCount + 1
109. 'Shape(ShapeCount).CtrRot.x = 170 + 54
110. 'Shape(ShapeCount).CtrRot.y = 31.25
111. 'i = 0
112. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
113. '    i = i + 1
114. '    r = 28
115. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
116. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
117. 'NEXT
118. 'Shape(ShapeCount).Elements = i
119. 'Shape(ShapeCount).Mass = i
120. 'Shape(ShapeCount).Velocity.x = 0
121. 'Shape(ShapeCount).Velocity.y = 0
122. 'Shape(ShapeCount).Omega = 0
123. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
124. 'CALL CalculateCtrMass(ShapeCount)
125. 'CALL CalculateDiameter(ShapeCount)
126. 'CALL CalculateMOI(ShapeCount)
127.  
128. 'ShapeCount = ShapeCount + 1
129. 'Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
130. 'Shape(ShapeCount).CtrRot.y = 0
131. 'i = 0
132. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
133. '    i = i + 1
134. '    r = 28
135. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
136. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
137. 'NEXT
138. 'Shape(ShapeCount).Elements = i
139. 'Shape(ShapeCount).Mass = i
140. 'Shape(ShapeCount).Velocity.x = 0
141. 'Shape(ShapeCount).Velocity.y = 0
142. 'Shape(ShapeCount).Omega = 0
143. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
144. 'CALL CalculateCtrMass(ShapeCount)
145. 'CALL CalculateDiameter(ShapeCount)
146. 'CALL CalculateMOI(ShapeCount)
147.  
148. 'ShapeCount = ShapeCount + 1
149. 'Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
150. 'Shape(ShapeCount).CtrRot.y = -31.25 * 2
151. 'i = 0
152. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
153. '    i = i + 1
154. '    r = 28
155. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
156. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
157. 'NEXT
158. 'Shape(ShapeCount).Elements = i
159. 'Shape(ShapeCount).Mass = i
160. 'Shape(ShapeCount).Velocity.x = 0
161. 'Shape(ShapeCount).Velocity.y = 0
162. 'Shape(ShapeCount).Omega = 0
163. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
164. 'CALL CalculateCtrMass(ShapeCount)
165. 'CALL CalculateDiameter(ShapeCount)
166. 'CALL CalculateMOI(ShapeCount)
167.  
168. 'ShapeCount = ShapeCount + 1
169. 'Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
170. 'Shape(ShapeCount).CtrRot.y = 31.25 * 2
171. 'i = 0
172. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
173. '    i = i + 1
174. '    r = 28
175. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
176. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
177. 'NEXT
178. 'Shape(ShapeCount).Elements = i
179. 'Shape(ShapeCount).Mass = i
180. 'Shape(ShapeCount).Velocity.x = 0
181. 'Shape(ShapeCount).Velocity.y = 0
182. 'Shape(ShapeCount).Omega = 0
183. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
184. 'CALL CalculateCtrMass(ShapeCount)
185. 'CALL CalculateDiameter(ShapeCount)
186. 'CALL CalculateMOI(ShapeCount)
187.  
188. '''
189.  
190. 'ShapeCount = ShapeCount + 1
191. 'Shape(ShapeCount).CtrRot.x = -200
192. 'Shape(ShapeCount).CtrRot.y = 0
193. 'i = 0
194. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
195. '    i = i + 1
196. '    r = 40 + 25 * COS(j) ^ 2
197. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
198. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
199. 'NEXT
200. 'Shape(ShapeCount).Elements = i
201. 'Shape(ShapeCount).Mass = i
202. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
203. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
204. 'Shape(ShapeCount).Omega = 0
205. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
206. 'CALL CalculateCtrMass(ShapeCount)
207. 'CALL CalculateDiameter(ShapeCount)
208. 'CALL CalculateMOI(ShapeCount)
209.  
210. 'ShapeCount = ShapeCount + 1
211. 'Shape(ShapeCount).CtrRot.x = 0
212. 'Shape(ShapeCount).CtrRot.y = 0
213. 'i = 0
214. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
215. '    i = i + 1
216. '    r = 40 + 25 * COS(1.5 * j) ^ 2
217. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
218. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
219. 'NEXT
220. 'Shape(ShapeCount).Elements = i
221. 'Shape(ShapeCount).Mass = i
222. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
223. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
224. 'Shape(ShapeCount).Omega = 0
225. 'Shape(ShapeCount).Shade = _RGB(255, 0, 255)
226. 'CALL CalculateCtrMass(ShapeCount)
227. 'CALL CalculateDiameter(ShapeCount)
228. 'CALL CalculateMOI(ShapeCount)
229.  
230. 'ShapeCount = ShapeCount + 1
231. 'Shape(ShapeCount).CtrRot.x = 200
232. 'Shape(ShapeCount).CtrRot.y = 0
233. 'i = 0
234. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
235. '    i = i + 1
236. '    r = 50
237. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
238. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
239. 'NEXT
240. 'Shape(ShapeCount).Elements = i
241. 'Shape(ShapeCount).Mass = i
242. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
243. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
244. 'Shape(ShapeCount).Omega = 0
245. 'Shape(ShapeCount).Shade = _RGB(255, 255, 0)
246. 'CALL CalculateCtrMass(ShapeCount)
247. 'CALL CalculateDiameter(ShapeCount)
248. 'CALL CalculateMOI(ShapeCount)
249.  
250. 'w = _WIDTH / 2
251. 'h = _HEIGHT / 2
252. 'b = 20
253. 'FOR n = -1 TO 1 STEP 2
254.  
255. '    FOR k = (-w + 2 * 5) TO (w - 2 * 5) STEP b
256. '        ShapeCount = ShapeCount + 1
257. '        Shape(ShapeCount).CtrRot.x = x
258. '        Shape(ShapeCount).CtrRot.y = n * h - n * 5
259. '        i = 0
260. '        FOR j = (Shape(ShapeCount).CtrRot.x - b / 2) TO (Shape(ShapeCount).CtrRot.x + b / 2) STEP 5
261. '            i = i + 1
262. '            PointChain(ShapeCount, i).x = j
263. '            PointChain(ShapeCount, i).y = n * h - n * 5
264. '        NEXT
265. '        Shape(ShapeCount).Elements = i
266. '        Shape(ShapeCount).Mass = 999 ^ 999
267. '        Shape(ShapeCount).Velocity.x = 0
268. '        Shape(ShapeCount).Velocity.y = 0
269. '        Shape(ShapeCount).Omega = 0
270. '        Shape(ShapeCount).Shade = _RGB(255, 255, 0)
271. '        CALL CalculateCtrMass(ShapeCount)
272. '        CALL CalculateDiameter(ShapeCount)
273. '        CALL CalculateMOI(ShapeCount)
274. '    NEXT
275.  
276. '    'ShapeCount = ShapeCount + 1
277. '    'Shape(ShapeCount).CtrRot.x = n * w - n * 5
278. '    'Shape(ShapeCount).CtrRot.y = 0
279. '    'i = 0
280. '    'FOR j = (-h + 2 * 5) TO (h - 2 * 5) STEP 3
281. '    '    i = i + 1
282. '    '    PointChain(ShapeCount, i).x = n * w - n * 5
283. '    '    PointChain(ShapeCount, i).y = j
284. '    'NEXT
285. '    'Shape(ShapeCount).Elements = i
286. '    'Shape(ShapeCount).Mass = 999 ^ 999
287. '    'Shape(ShapeCount).Velocity.x = 0
288. '    'Shape(ShapeCount).Velocity.y = 0
289. '    'Shape(ShapeCount).Omega = 0
290. '    'Shape(ShapeCount).Shade = _RGB(255, 255, 0)
291. '    'CALL CalculateCtrMass(ShapeCount)
292. '    ''CALL CalculateDiameter(ShapeCount)
293. '    'Shape(ShapeCount).Diameter = 5
294. '    'CALL CalculateMOI(ShapeCount)
295. 'NEXT
296.  
297. ' Walls
298. b = 10
299. FOR n = -1 TO 1 STEP 2
300.     FOR k = -(_WIDTH / 2 - b) TO (_WIDTH / 2 - b) STEP 2 * b
301.         ShapeCount = ShapeCount + 1
302.         Shape(ShapeCount).CtrRot.x = k
303.         Shape(ShapeCount).CtrRot.y = n * (_HEIGHT / 2 - b / 2)
304.         i = 0
305.         FOR j = (Shape(ShapeCount).CtrRot.x - b / 2) TO (Shape(ShapeCount).CtrRot.x + b / 2) STEP 3
306.             i = i + 1
307.             PointChain(ShapeCount, i).x = j
308.             PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y
309.         NEXT
310.         Shape(ShapeCount).Elements = i
311.         Shape(ShapeCount).Mass = 999 ^ 999
312.         Shape(ShapeCount).Velocity.x = 0
313.         Shape(ShapeCount).Velocity.y = 0
314.         Shape(ShapeCount).Omega = 0
315.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
316.         CALL CalculateCtrMass(ShapeCount)
317.         CALL CalculateDiameter(ShapeCount)
318.         CALL CalculateMOI(ShapeCount)
319.         Shape(ShapeCount).MOI = 999 ^ 999
320.     NEXT
321.  
322.     FOR k = -(_HEIGHT / 2 - b) TO (_HEIGHT / 2 - b) STEP 2 * b
323.         ShapeCount = ShapeCount + 1
324.         Shape(ShapeCount).CtrRot.x = n * (_WIDTH / 2 - b / 2)
325.         Shape(ShapeCount).CtrRot.y = k
326.         i = 0
327.         FOR j = (Shape(ShapeCount).CtrRot.y - b / 2) TO (Shape(ShapeCount).CtrRot.y + b / 2) STEP 3
328.             i = i + 1
329.             PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x
330.             PointChain(ShapeCount, i).y = j
331.         NEXT
332.         Shape(ShapeCount).Elements = i
333.         Shape(ShapeCount).Mass = 999 ^ 999
334.         Shape(ShapeCount).Velocity.x = 0
335.         Shape(ShapeCount).Velocity.y = 0
336.         Shape(ShapeCount).Omega = 0
337.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
338.         CALL CalculateCtrMass(ShapeCount)
339.         CALL CalculateDiameter(ShapeCount)
340.         CALL CalculateMOI(ShapeCount)
341.         Shape(ShapeCount).MOI = 999 ^ 999
342.     NEXT
343. NEXT
344.  
345. DO
346.  
347.     IF (_KEYHIT = 32) THEN
348.         CLS
349.         CALL Graphics
350.         LOCATE 1, 1: PRINT "Click & Drag to create a shape.    "
351.         CALL CreateShape
352.         _KEYCLEAR
353.     END IF
354.  
355.     ' Proximity detection
356.     ProximalPairsCount = 0
357.     Shape1 = 0
358.     Shape2 = 0
359.     FOR j = 1 TO ShapeCount
360.         FOR k = j + 1 TO ShapeCount
361.             dx = Shape(j).CtrMass.x - Shape(k).CtrMass.x
362.             dy = Shape(j).CtrMass.y - Shape(k).CtrMass.y
363.             dr = SQR(dx * dx + dy * dy)
364.             IF (dr < 1.15 * (Shape(j).Diameter + Shape(k).Diameter)) THEN
365.                 ProximalPairsCount = ProximalPairsCount + 1
366.                 ProximalPairs(ProximalPairsCount, 1) = j
367.                 ProximalPairs(ProximalPairsCount, 2) = k
368.                 Shape1 = j
369.                 Shape2 = k
370.             END IF
371.         NEXT
372.     NEXT
373.  
374.     IF (ProximalPairsCount > 0) THEN
375.         FOR n = 1 TO ProximalPairsCount
376.             Shape1 = ProximalPairs(n, 1)
377.             Shape2 = ProximalPairs(n, 2)
378.  
379.             ' Collision detection
380.             rmin = 999 ^ 999
381.             ClosestIndex1 = 0
382.             ClosestIndex2 = 0
383.             FOR j = 1 TO Shape(Shape1).Elements
384.                 FOR k = 1 TO Shape(Shape2).Elements
385.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
386.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
387.                     r2 = dx * dx + dy * dy
388.                     IF (r2 < rmin) THEN
389.                         rmin = r2
390.                         ClosestIndex1 = j
391.                         ClosestIndex2 = k
392.                     END IF
393.                 NEXT
394.             NEXT
395.  
396.             IF (rmin <= 2) THEN
397.                 CollisionCount = CollisionCount + 1
398.  
399.                 ' Normal vector 1
400.                 x0 = PointChain(Shape1, ClosestIndex1).x
401.                 y0 = PointChain(Shape1, ClosestIndex1).y
402.                 'CALL ccircle(x0, y0, 3, Shape(Shape1).Shade)
403.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
404.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
405.                 norm = SQR(xx * xx + yy * yy)
406.                 xx = xx / norm
407.                 yy = yy / norm
408.                 nx1 = xx
409.                 ny1 = yy
410.                 'CALL cline(x0, y0, x0 + nx1 * 15, y0 + ny1 * 15, Shape(Shape1).Shade)
411.  
412.                 ' Normal vector 2
413.                 x0 = PointChain(Shape2, ClosestIndex2).x
414.                 y0 = PointChain(Shape2, ClosestIndex2).y
415.                 'CALL ccircle(x0, y0, 3, Shape(Shape2).Shade)
416.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
417.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
418.                 norm = SQR(xx * xx + yy * yy)
419.                 xx = xx / norm
420.                 yy = yy / norm
421.                 nx2 = xx
422.                 ny2 = yy
423.                 'CALL cline(x0, y0, x0 + nx2 * 15, y0 + ny2 * 15, Shape(Shape2).Shade)
424.  
425.                 ' Perpendicular vector 1
426.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).CtrRot.x
427.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).CtrRot.y
428.                 px1 = -dy1
429.                 py1 = dx1
430.                 p1 = SQR(px1 * px1 + py1 * py1)
431.                 px1 = px1 / p1
432.                 py1 = py1 / p1
433.                 'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + px1 * 15, PointChain(Shape1, ClosestIndex1).y + py1 * 15, Shape(Shape1).Shade)
434.  
435.                 ' Perpendicular vector 2
436.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).CtrRot.x
437.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).CtrRot.y
438.                 px2 = -dy2
439.                 py2 = dx2
440.                 p2 = SQR(px2 * px2 + py2 * py2)
441.                 px2 = px2 / p2
442.                 py2 = py2 / p2
443.                 'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + px2 * 15, PointChain(Shape2, ClosestIndex2).y + py2 * 15, Shape(Shape2).Shade)
444.  
445.                 ' Angular velocity vector 1
446.                 w1 = Shape(Shape1).Omega
447.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
448.                 vx1 = w1 * r1 * px1
449.                 vy1 = w1 * r1 * py1
450.                 'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + vx1 * 5, PointChain(Shape1, ClosestIndex1).y + vy1 * 5, Shape(Shape1).Shade)
451.  
452.                 ' Angular velocity vector 2
453.                 w2 = Shape(Shape2).Omega
454.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
455.                 vx2 = w2 * r2 * px2
456.                 vy2 = w2 * r2 * py2
457.                 'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + vx2 * 5, PointChain(Shape2, ClosestIndex2).y + vy2 * 5, Shape(Shape2).Shade)
458.  
459.                 ' Mass terms
460.                 m1 = Shape(Shape1).Mass
461.                 i1 = Shape(Shape1).MOI
462.                 m2 = Shape(Shape2).Mass
463.                 i2 = Shape(Shape2).MOI
464.                 mu = 1 / (1 / m1 + 1 / m2)
465.  
466.                 ' Velocity differential 1
467.                 vtx1 = Shape(Shape1).Velocity.x + vx1
468.                 vty1 = Shape(Shape1).Velocity.y + vy1
469.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
470.  
471.                 ' Velocity differential 2
472.                 vtx2 = Shape(Shape2).Velocity.x + vx2
473.                 vty2 = Shape(Shape2).Velocity.y + vy2
474.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
475.  
476.                 ' Velocity differential total
477.                 dvtx = vtx2 - vtx1
478.                 dvty = vty2 - vty1
479.  
480.                 ' Geometry
481.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
482.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
483.  
484.                 ' Momentum exchange
485.                 qx1 = nx1 * 2 * mu * n1dotdvt
486.                 qy1 = ny1 * 2 * mu * n1dotdvt
487.                 qx2 = nx2 * 2 * mu * n2dotdvt
488.                 qy2 = ny2 * 2 * mu * n2dotdvt
489.  
490.                 ' Momentum exchange unit vector
491.                 q1 = SQR(qx1 * qx1 + qy1 * qy1)
492.                 qhatx1 = qx1 / q1
493.                 qhaty1 = qy1 / q1
494.                 q2 = SQR(qx2 * qx2 + qy2 * qy2)
495.                 qhatx2 = qx2 / q2
496.                 qhaty2 = qy2 / q2
497.  
498.                 ' Undo previous motion
499.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -Shape(Shape1).Omega)
500.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -Shape(Shape2).Omega)
501.                 vtemp.x = -Shape(Shape1).Velocity.x
502.                 vtemp.y = -Shape(Shape1).Velocity.y
503.                 CALL TranslateShape(Shape1, vtemp)
504.                 vtemp.x = -Shape(Shape2).Velocity.x
505.                 vtemp.y = -Shape(Shape2).Velocity.y
506.                 CALL TranslateShape(Shape2, vtemp)
507.  
508.                 ' Separate along normal
509.                 vtemp.x = -nx1
510.                 vtemp.y = -ny1
511.                 CALL TranslateShape(Shape1, vtemp)
512.                 vtemp.x = -nx2
513.                 vtemp.y = -ny2
514.                 CALL TranslateShape(Shape1, vtemp)
515.  
516.                 ' Translational impulse
517.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
518.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
519.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
520.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
521.                 f1 = -q1dotn1 * n1dotr1hat
522.                 f2 = -q2dotn2 * n2dotr2hat
523.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
524.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
525.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
526.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
527.  
528.                 ' Angular impulse
529.                 q1dotp1 = qx1 * px1 + qy1 * py1
530.                 q2dotp2 = qx2 * px2 + qy2 * py2
531.                 dw1 = r1 * q1dotp1 / i1
532.                 dw2 = -r2 * q2dotp2 / i2
533.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
534.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
535.                 Shape(Shape1).Omega = Shape(Shape1).Omega + dw1
536.                 Shape(Shape2).Omega = Shape(Shape2).Omega + dw2
537.  
538.                 ' Static friction
539.                 IF Shape(ShapeIndex).Velocity.x * Shape(ShapeIndex).Velocity.x < .25 THEN Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .01
540.                 IF Shape(ShapeIndex).Velocity.y * Shape(ShapeIndex).Velocity.y < .25 THEN Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .01
541.                 IF Shape(ShapeIndex).Omega * Shape(ShapeIndex).Omega < .05 THEN Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .01
542.  
543.             END IF
544.         NEXT
545.     END IF
546.  
547.     FOR ShapeIndex = 1 TO ShapeCount
548.         dx = Shape(ShapeIndex).CtrMass.x - Shape(ShapeIndex).CtrRot.x
549.         dy = Shape(ShapeIndex).CtrMass.y - Shape(ShapeIndex).CtrRot.y
550.  
551.         cx = Shape(ShapeIndex).CtrMass.x
552.         cy = Shape(ShapeIndex).CtrMass.y
553.         Gravity.x = -cx / 20
554.         Gravity.y = -cy / 20
555.  
556.         'torque = dx * Gravity.y - dy * Gravity.x
557.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
558.  
559.         ' Rotation update
560.         CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
561.  
562.         ' Velocity update
563.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Gravity.x / Shape(ShapeIndex).Mass
564.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Gravity.y / Shape(ShapeIndex).Mass
565.         CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
566.  
567.         ' Damping
568.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .975
569.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .975
570.         Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .975
571.     NEXT
572.  
573.     CALL Graphics
574.     _LIMIT 120
575. LOOP
576.  
577. END
578.  
579. SUB Graphics
580.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
581.     FOR ShapeIndex = 1 TO ShapeCount
582.         LOCATE 2, 1: PRINT ProximalPairsCount, CollisionCount
583.         LOCATE 1, 1: PRINT "Press space to enable creative mode."
584.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
585.             x1 = PointChain(ShapeIndex, i).x
586.             y1 = PointChain(ShapeIndex, i).y
587.             x2 = PointChain(ShapeIndex, i + 1).x
588.             y2 = PointChain(ShapeIndex, i + 1).y
589.             CALL cline(x1, y1, x2, y2, Shape(ShapeIndex).Shade)
590.         NEXT
591.         x1 = PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x
592.         y1 = PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y
593.         x2 = PointChain(ShapeIndex, 1).x
594.         y2 = PointChain(ShapeIndex, 1).y
595.         CALL cline(x1, y1, x2, y2, Shape(ShapeIndex).Shade)
596.         'CALL ccircle(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, 3, Shape(ShapeIndex).Shade)
597.         'CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
598.         'CALL cline(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, Shape(ShapeIndex).Shade)
599.         CALL cpaint(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, Shape(ShapeIndex).Shade, Shape(ShapeIndex).Shade)
600.     NEXT
601.     'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, Shape(Shape1).CtrRot.x, Shape(Shape1).CtrRot.y, Shape(Shape1).Shade)
602.     'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, Shape(Shape2).CtrRot.x, Shape(Shape2).CtrRot.y, Shape(Shape2).Shade)
603.     _DISPLAY
604. END SUB
605.  
606. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
607.     DIM l AS Vector
608.     DIM r AS Vector
609.     li = i - 1
610.     ri = i + 1
611.     IF (i = 1) THEN li = Shape(k).Elements
612.     IF (i = Shape(k).Elements) THEN ri = 1
613.     l.x = PointChain(k, li).x
614.     r.x = PointChain(k, ri).x
615.     dx = r.x - l.x
616.     CalculateNormalX = dx
617. END FUNCTION
618.  
619. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
620.     DIM l AS Vector
621.     DIM r AS Vector
622.     li = i - 1
623.     ri = i + 1
624.     IF (i = 1) THEN li = Shape(k).Elements
625.     IF (i = Shape(k).Elements) THEN ri = 1
626.     l.y = PointChain(k, li).y
627.     r.y = PointChain(k, ri).y
628.     dy = r.y - l.y
629.     CalculateNormalY = dy
630. END FUNCTION
631.  
632. SUB CalculateCtrMass (k AS INTEGER)
633.     xx = 0
634.     yy = 0
635.     FOR i = 1 TO Shape(k).Elements
636.         xx = xx + PointChain(k, i).x
637.         yy = yy + PointChain(k, i).y
638.     NEXT
639.     Shape(k).CtrMass.x = xx / Shape(k).Elements
640.     Shape(k).CtrMass.y = yy / Shape(k).Elements
641. END SUB
642.  
643. SUB CalculateDiameter (k AS INTEGER)
644.     r2max = -1
645.     FOR i = 1 TO Shape(k).Elements
646.         xx = Shape(k).CtrMass.x - PointChain(k, i).x
647.         yy = Shape(k).CtrMass.y - PointChain(k, i).y
648.         r2 = xx * xx + yy * yy
649.         IF (r2 > r2max) THEN
650.             r2max = r2
651.         END IF
652.     NEXT
653.     Shape(k).Diameter = SQR(r2max)
654. END SUB
655.  
656. SUB CalculateMOI (k AS INTEGER)
657.     xx = 0
658.     yy = 0
659.     FOR i = 1 TO Shape(k).Elements
660.         xx = xx + (Shape(k).CtrRot.x - PointChain(k, i).x) ^ 2
661.         yy = yy + (Shape(k).CtrRot.y - PointChain(k, i).y) ^ 2
662.     NEXT
663.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Elements)
664. END SUB
665.  
666. SUB TranslateShape (k AS INTEGER, c AS Vector)
667.     FOR i = 1 TO Shape(k).Elements
668.         PointChain(k, i).x = PointChain(k, i).x + c.x
669.         PointChain(k, i).y = PointChain(k, i).y + c.y
670.     NEXT
671.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
672.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
673.     Shape(k).CtrMass.x = Shape(k).CtrMass.x + c.x
674.     Shape(k).CtrMass.y = Shape(k).CtrMass.y + c.y
675. END SUB
676.  
677. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
678.     FOR i = 1 TO Shape(k).Elements
679.         xx = PointChain(k, i).x - c.x
680.         yy = PointChain(k, i).y - c.y
681.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
682.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
683.     NEXT
684.     xx = Shape(k).CtrMass.x - c.x
685.     yy = Shape(k).CtrMass.y - c.y
686.     Shape(k).CtrMass.x = c.x + xx * COS(da) - yy * SIN(da)
687.     Shape(k).CtrMass.y = c.y + yy * COS(da) + xx * SIN(da)
688. END SUB
689.  
690. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
691.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
692. END SUB
693.  
694. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
695.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
696. END SUB
697.  
698. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
699.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
700. END SUB
701.  
702. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
703.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
704. END SUB
705.  
706. SUB CreateShape
707.     rawresolution = 7.5 ' Raw curve resolution.
708.     targetpoints = 100 ' Number of points per curve.
709.     smoothiterations = 10 ' Magnitude of smooth effect.
710.  
711.     ShapeCount = ShapeCount + 1
712.  
713.     numpoints = 0
714.     xold = 999999
715.     yold = 999999
716.  
717.     WHILE _MOUSEINPUT: WEND
718.  
719.     ' Gather raw data for one curve at a time.
720.     ' Click+drag mouse button 1 to trace out a curve.
721.     DO
722.         DO WHILE _MOUSEINPUT
723.             x = _MOUSEX
724.             y = _MOUSEY
725.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
726.                 IF _MOUSEBUTTON(1) THEN
727.                     x = x - (_WIDTH / 2)
728.                     y = -y + (_HEIGHT / 2)
729.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
730.  
731.                     ' Collect data only if the new point is sufficiently far away from the previous point.
732.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
733.                         numpoints = numpoints + 1
734.                         PointChain(ShapeCount, numpoints).x = x
735.                         PointChain(ShapeCount, numpoints).y = y
736.                         CALL cpset(x, y, _RGB(255, 255, 255))
737.                         xold = x
738.                         yold = y
739.                     END IF
740.                 END IF
741.             END IF
742.         LOOP
743.         _DISPLAY
744.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
745.  
746.     ' If the curve contains less than the minimum numer of points, use interpolation to fill in the gaps.
747.     DO WHILE (numpoints < targetpoints)
748.  
749.         ' Determine the pair of neighboring points that have the greatest separation of all pairs.
750.         rad2max = -1
751.         kmax = -1
752.         FOR k = 1 TO numpoints - 1
753.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
754.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
755.             rad2 = xfac ^ 2 + yfac ^ 2
756.             IF rad2 > rad2max THEN
757.                 kmax = k
758.                 rad2max = rad2
759.             END IF
760.         NEXT
761.         '''
762.         cornercase = 0
763.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
764.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
765.         rad2 = xfac ^ 2 + yfac ^ 2
766.         IF rad2 > rad2max THEN
767.             kmax = numpoints
768.             rad2max = rad2
769.             cornercase = 1
770.         END IF
771.         '''
772.         IF (cornercase = 0) THEN
773.  
774.             numpoints = numpoints + 1
775.  
776.             ' Starting next to kmax, create a `gap' by shifting all other points by one index.
777.             FOR j = numpoints TO kmax + 1 STEP -1
778.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
779.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
780.             NEXT
781.  
782.             ' Fill the gap with a new point whose position is determined by the average of its neighbors.
783.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
784.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
785.  
786.         ELSE
787.             numpoints = numpoints + 1
788.             xx = PointChain(ShapeCount, numpoints - 1).x
789.             yy = PointChain(ShapeCount, numpoints - 1).y
790.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
791.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
792.         END IF
793.  
794.     LOOP
795.  
796.     ' At this stage, the curve still has all of its sharp edges. Use a `relaxation method' to smooth.
797.     ' The new position of a point is equal to the average position of its neighboring points.
798.     FOR j = 1 TO smoothiterations
799.         FOR k = 2 TO numpoints - 1
800.             TempChain(ShapeCount, k).x = (1 / 2) * (PointChain(ShapeCount, k - 1).x + PointChain(ShapeCount, k + 1).x)
801.             TempChain(ShapeCount, k).y = (1 / 2) * (PointChain(ShapeCount, k - 1).y + PointChain(ShapeCount, k + 1).y)
802.         NEXT
803.         FOR k = 2 TO numpoints - 1
804.             PointChain(ShapeCount, k).x = TempChain(ShapeCount, k).x
805.             PointChain(ShapeCount, k).y = TempChain(ShapeCount, k).y
806.         NEXT
807.     NEXT
808.  
809.     Shape(ShapeCount).Elements = numpoints
810.     Shape(ShapeCount).Mass = numpoints
811.     Shape(ShapeCount).Velocity.x = 0
812.     Shape(ShapeCount).Velocity.y = 0
813.     Shape(ShapeCount).Omega = 0
814.     Shape(ShapeCount).Shade = _RGB(INT(RND * 255), INT(RND * 255), INT(RND * 255))
815.     CALL CalculateCtrMass(ShapeCount)
816.     Shape(ShapeCount).CtrRot.x = Shape(ShapeCount).CtrMass.x
817.     Shape(ShapeCount).CtrRot.y = Shape(ShapeCount).CtrMass.y
818.     CALL CalculateDiameter(ShapeCount)
819.     CALL CalculateMOI(ShapeCount)
820.  
821. END SUB
822.  

[STxAxTIC]

Okay, in adding a toy feature I realized that the hand-drawn shapes must be drawn counter-clockwise. In this version, the objects erode away like stones when they collide:

Code: QB64: [Select]

1. ' Display
2. SCREEN _NEWIMAGE(800, 600, 32)
3. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
4.  
5. ' Meta
6. RANDOMIZE TIMER
7.  
8. ' Data
9. TYPE Vector
10.     x AS DOUBLE
11.     y AS DOUBLE
12. END TYPE
13.  
14. TYPE Object
15.     CtrMass AS Vector
16.     CtrRot AS Vector
17.     Diameter AS DOUBLE
18.     Elements AS INTEGER
19.     Mass AS DOUBLE
20.     MOI AS DOUBLE
21.     Omega AS DOUBLE
22.     Shade AS _UNSIGNED LONG
23.     Velocity AS Vector
24. END TYPE
25.  
26. DIM vtemp AS Vector
27.  
28. ' Statics
29. DIM SHARED Shape(1000) AS Object
30. DIM SHARED PointChain(1000, 5000) AS Vector
31. DIM SHARED TempChain(1000, 5000) AS Vector
32. DIM SHARED ShapeCount AS INTEGER
33. ShapeCount = 0
34.  
35. ' Dynamics
36. DIM SHARED CollisionCount AS INTEGER
37. CollisionCount = 0
38.  
39. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
40. DIM SHARED ProximalPairsCount
41.  
42. DIM Gravity AS Vector
43. Gravity.x = 0
44. Gravity.y = -5
45.  
46. ' Create objects.
47.  
48. ShapeCount = ShapeCount + 1
49. Shape(ShapeCount).CtrRot.x = -220
50. Shape(ShapeCount).CtrRot.y = 0
51. i = 0
52. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
53.     i = i + 1
54.     r = 40 + 25 * COS(1.5 * j) ^ 2
55.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
56.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
57. NEXT
58. Shape(ShapeCount).Elements = i
59. Shape(ShapeCount).Mass = i
60. Shape(ShapeCount).Velocity.x = 0
61. Shape(ShapeCount).Velocity.y = 0
62. Shape(ShapeCount).Omega = 0
63. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
64. CALL CalculateCtrMass(ShapeCount)
65. CALL CalculateDiameter(ShapeCount)
66. CALL CalculateMOI(ShapeCount)
67.  
68. 'ShapeCount = ShapeCount + 1
69. 'Shape(ShapeCount).CtrRot.x = 170
70. 'Shape(ShapeCount).CtrRot.y = 0
71. 'i = 0
72. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
73. '    i = i + 1
74. '    r = 28
75. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
76. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
77. 'NEXT
78. 'Shape(ShapeCount).Elements = i
79. 'Shape(ShapeCount).Mass = i
80. 'Shape(ShapeCount).Velocity.x = 0
81. 'Shape(ShapeCount).Velocity.y = 0
82. 'Shape(ShapeCount).Omega = 0
83. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
84. 'CALL CalculateCtrMass(ShapeCount)
85. 'CALL CalculateDiameter(ShapeCount)
86. 'CALL CalculateMOI(ShapeCount)
87.  
88. 'ShapeCount = ShapeCount + 1
89. 'Shape(ShapeCount).CtrRot.x = 170 + 54
90. 'Shape(ShapeCount).CtrRot.y = -31.25
91. 'i = 0
92. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
93. '    i = i + 1
94. '    r = 28
95. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
96. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
97. 'NEXT
98. 'Shape(ShapeCount).Elements = i
99. 'Shape(ShapeCount).Mass = i
100. 'Shape(ShapeCount).Velocity.x = 0
101. 'Shape(ShapeCount).Velocity.y = 0
102. 'Shape(ShapeCount).Omega = 0
103. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
104. 'CALL CalculateCtrMass(ShapeCount)
105. 'CALL CalculateDiameter(ShapeCount)
106. 'CALL CalculateMOI(ShapeCount)
107.  
108. 'ShapeCount = ShapeCount + 1
109. 'Shape(ShapeCount).CtrRot.x = 170 + 54
110. 'Shape(ShapeCount).CtrRot.y = 31.25
111. 'i = 0
112. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
113. '    i = i + 1
114. '    r = 28
115. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
116. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
117. 'NEXT
118. 'Shape(ShapeCount).Elements = i
119. 'Shape(ShapeCount).Mass = i
120. 'Shape(ShapeCount).Velocity.x = 0
121. 'Shape(ShapeCount).Velocity.y = 0
122. 'Shape(ShapeCount).Omega = 0
123. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
124. 'CALL CalculateCtrMass(ShapeCount)
125. 'CALL CalculateDiameter(ShapeCount)
126. 'CALL CalculateMOI(ShapeCount)
127.  
128. 'ShapeCount = ShapeCount + 1
129. 'Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
130. 'Shape(ShapeCount).CtrRot.y = 0
131. 'i = 0
132. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
133. '    i = i + 1
134. '    r = 28
135. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
136. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
137. 'NEXT
138. 'Shape(ShapeCount).Elements = i
139. 'Shape(ShapeCount).Mass = i
140. 'Shape(ShapeCount).Velocity.x = 0
141. 'Shape(ShapeCount).Velocity.y = 0
142. 'Shape(ShapeCount).Omega = 0
143. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
144. 'CALL CalculateCtrMass(ShapeCount)
145. 'CALL CalculateDiameter(ShapeCount)
146. 'CALL CalculateMOI(ShapeCount)
147.  
148. 'ShapeCount = ShapeCount + 1
149. 'Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
150. 'Shape(ShapeCount).CtrRot.y = -31.25 * 2
151. 'i = 0
152. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
153. '    i = i + 1
154. '    r = 28
155. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
156. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
157. 'NEXT
158. 'Shape(ShapeCount).Elements = i
159. 'Shape(ShapeCount).Mass = i
160. 'Shape(ShapeCount).Velocity.x = 0
161. 'Shape(ShapeCount).Velocity.y = 0
162. 'Shape(ShapeCount).Omega = 0
163. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
164. 'CALL CalculateCtrMass(ShapeCount)
165. 'CALL CalculateDiameter(ShapeCount)
166. 'CALL CalculateMOI(ShapeCount)
167.  
168. 'ShapeCount = ShapeCount + 1
169. 'Shape(ShapeCount).CtrRot.x = 170 + 54 + 54
170. 'Shape(ShapeCount).CtrRot.y = 31.25 * 2
171. 'i = 0
172. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
173. '    i = i + 1
174. '    r = 28
175. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
176. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
177. 'NEXT
178. 'Shape(ShapeCount).Elements = i
179. 'Shape(ShapeCount).Mass = i
180. 'Shape(ShapeCount).Velocity.x = 0
181. 'Shape(ShapeCount).Velocity.y = 0
182. 'Shape(ShapeCount).Omega = 0
183. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
184. 'CALL CalculateCtrMass(ShapeCount)
185. 'CALL CalculateDiameter(ShapeCount)
186. 'CALL CalculateMOI(ShapeCount)
187.  
188. '''
189.  
190. 'ShapeCount = ShapeCount + 1
191. 'Shape(ShapeCount).CtrRot.x = -200
192. 'Shape(ShapeCount).CtrRot.y = 0
193. 'i = 0
194. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
195. '    i = i + 1
196. '    r = 40 + 25 * COS(j) ^ 2
197. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
198. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
199. 'NEXT
200. 'Shape(ShapeCount).Elements = i
201. 'Shape(ShapeCount).Mass = i
202. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
203. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
204. 'Shape(ShapeCount).Omega = 0
205. 'Shape(ShapeCount).Shade = _RGB(0, 255, 255)
206. 'CALL CalculateCtrMass(ShapeCount)
207. 'CALL CalculateDiameter(ShapeCount)
208. 'CALL CalculateMOI(ShapeCount)
209.  
210. 'ShapeCount = ShapeCount + 1
211. 'Shape(ShapeCount).CtrRot.x = 0
212. 'Shape(ShapeCount).CtrRot.y = 0
213. 'i = 0
214. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
215. '    i = i + 1
216. '    r = 40 + 25 * COS(1.5 * j) ^ 2
217. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
218. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
219. 'NEXT
220. 'Shape(ShapeCount).Elements = i
221. 'Shape(ShapeCount).Mass = i
222. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
223. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
224. 'Shape(ShapeCount).Omega = 0
225. 'Shape(ShapeCount).Shade = _RGB(255, 0, 255)
226. 'CALL CalculateCtrMass(ShapeCount)
227. 'CALL CalculateDiameter(ShapeCount)
228. 'CALL CalculateMOI(ShapeCount)
229.  
230. 'ShapeCount = ShapeCount + 1
231. 'Shape(ShapeCount).CtrRot.x = 200
232. 'Shape(ShapeCount).CtrRot.y = 0
233. 'i = 0
234. 'FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
235. '    i = i + 1
236. '    r = 50
237. '    PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
238. '    PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
239. 'NEXT
240. 'Shape(ShapeCount).Elements = i
241. 'Shape(ShapeCount).Mass = i
242. 'Shape(ShapeCount).Velocity.x = 2 * (RND - .5)
243. 'Shape(ShapeCount).Velocity.y = 2 * (RND - .5)
244. 'Shape(ShapeCount).Omega = 0
245. 'Shape(ShapeCount).Shade = _RGB(255, 255, 0)
246. 'CALL CalculateCtrMass(ShapeCount)
247. 'CALL CalculateDiameter(ShapeCount)
248. 'CALL CalculateMOI(ShapeCount)
249.  
250. 'w = _WIDTH / 2
251. 'h = _HEIGHT / 2
252. 'b = 20
253. 'FOR n = -1 TO 1 STEP 2
254.  
255. '    FOR k = (-w + 2 * 5) TO (w - 2 * 5) STEP b
256. '        ShapeCount = ShapeCount + 1
257. '        Shape(ShapeCount).CtrRot.x = x
258. '        Shape(ShapeCount).CtrRot.y = n * h - n * 5
259. '        i = 0
260. '        FOR j = (Shape(ShapeCount).CtrRot.x - b / 2) TO (Shape(ShapeCount).CtrRot.x + b / 2) STEP 5
261. '            i = i + 1
262. '            PointChain(ShapeCount, i).x = j
263. '            PointChain(ShapeCount, i).y = n * h - n * 5
264. '        NEXT
265. '        Shape(ShapeCount).Elements = i
266. '        Shape(ShapeCount).Mass = 999 ^ 999
267. '        Shape(ShapeCount).Velocity.x = 0
268. '        Shape(ShapeCount).Velocity.y = 0
269. '        Shape(ShapeCount).Omega = 0
270. '        Shape(ShapeCount).Shade = _RGB(255, 255, 0)
271. '        CALL CalculateCtrMass(ShapeCount)
272. '        CALL CalculateDiameter(ShapeCount)
273. '        CALL CalculateMOI(ShapeCount)
274. '    NEXT
275.  
276. '    'ShapeCount = ShapeCount + 1
277. '    'Shape(ShapeCount).CtrRot.x = n * w - n * 5
278. '    'Shape(ShapeCount).CtrRot.y = 0
279. '    'i = 0
280. '    'FOR j = (-h + 2 * 5) TO (h - 2 * 5) STEP 3
281. '    '    i = i + 1
282. '    '    PointChain(ShapeCount, i).x = n * w - n * 5
283. '    '    PointChain(ShapeCount, i).y = j
284. '    'NEXT
285. '    'Shape(ShapeCount).Elements = i
286. '    'Shape(ShapeCount).Mass = 999 ^ 999
287. '    'Shape(ShapeCount).Velocity.x = 0
288. '    'Shape(ShapeCount).Velocity.y = 0
289. '    'Shape(ShapeCount).Omega = 0
290. '    'Shape(ShapeCount).Shade = _RGB(255, 255, 0)
291. '    'CALL CalculateCtrMass(ShapeCount)
292. '    ''CALL CalculateDiameter(ShapeCount)
293. '    'Shape(ShapeCount).Diameter = 5
294. '    'CALL CalculateMOI(ShapeCount)
295. 'NEXT
296.  
297. ' Walls
298. b = 10
299. FOR n = -1 TO 1 STEP 2
300.     FOR k = -(_WIDTH / 2 - b) TO (_WIDTH / 2 - b) STEP 2 * b
301.         ShapeCount = ShapeCount + 1
302.         Shape(ShapeCount).CtrRot.x = k
303.         Shape(ShapeCount).CtrRot.y = n * (_HEIGHT / 2 - b / 2)
304.         i = 0
305.         FOR j = (Shape(ShapeCount).CtrRot.x - b / 2) TO (Shape(ShapeCount).CtrRot.x + b / 2) STEP 3
306.             i = i + 1
307.             PointChain(ShapeCount, i).x = j
308.             PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y
309.         NEXT
310.         Shape(ShapeCount).Elements = i
311.         Shape(ShapeCount).Mass = 999 ^ 999
312.         Shape(ShapeCount).Velocity.x = 0
313.         Shape(ShapeCount).Velocity.y = 0
314.         Shape(ShapeCount).Omega = 0
315.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
316.         CALL CalculateCtrMass(ShapeCount)
317.         CALL CalculateDiameter(ShapeCount)
318.         CALL CalculateMOI(ShapeCount)
319.         Shape(ShapeCount).MOI = 999 ^ 999
320.     NEXT
321.  
322.     FOR k = -(_HEIGHT / 2 - b) TO (_HEIGHT / 2 - b) STEP 2 * b
323.         ShapeCount = ShapeCount + 1
324.         Shape(ShapeCount).CtrRot.x = n * (_WIDTH / 2 - b / 2)
325.         Shape(ShapeCount).CtrRot.y = k
326.         i = 0
327.         FOR j = (Shape(ShapeCount).CtrRot.y - b / 2) TO (Shape(ShapeCount).CtrRot.y + b / 2) STEP 3
328.             i = i + 1
329.             PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x
330.             PointChain(ShapeCount, i).y = j
331.         NEXT
332.         Shape(ShapeCount).Elements = i
333.         Shape(ShapeCount).Mass = 999 ^ 999
334.         Shape(ShapeCount).Velocity.x = 0
335.         Shape(ShapeCount).Velocity.y = 0
336.         Shape(ShapeCount).Omega = 0
337.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
338.         CALL CalculateCtrMass(ShapeCount)
339.         CALL CalculateDiameter(ShapeCount)
340.         CALL CalculateMOI(ShapeCount)
341.         Shape(ShapeCount).MOI = 999 ^ 999
342.     NEXT
343. NEXT
344.  
345. DO
346.  
347.     IF (_KEYHIT = 32) THEN
348.         CLS
349.         CALL Graphics
350.         LOCATE 1, 1: PRINT "Click & Drag counter-clockwise to create a shape."
351.         CALL CreateShape
352.         _KEYCLEAR
353.     END IF
354.  
355.     ' Proximity detection
356.     ProximalPairsCount = 0
357.     Shape1 = 0
358.     Shape2 = 0
359.     FOR j = 1 TO ShapeCount
360.         FOR k = j + 1 TO ShapeCount
361.             dx = Shape(j).CtrMass.x - Shape(k).CtrMass.x
362.             dy = Shape(j).CtrMass.y - Shape(k).CtrMass.y
363.             dr = SQR(dx * dx + dy * dy)
364.             IF (dr < 1.15 * (Shape(j).Diameter + Shape(k).Diameter)) THEN
365.                 ProximalPairsCount = ProximalPairsCount + 1
366.                 ProximalPairs(ProximalPairsCount, 1) = j
367.                 ProximalPairs(ProximalPairsCount, 2) = k
368.                 Shape1 = j
369.                 Shape2 = k
370.             END IF
371.         NEXT
372.     NEXT
373.  
374.     IF (ProximalPairsCount > 0) THEN
375.         FOR n = 1 TO ProximalPairsCount
376.             Shape1 = ProximalPairs(n, 1)
377.             Shape2 = ProximalPairs(n, 2)
378.  
379.             ' Collision detection
380.             rmin = 999 ^ 999
381.             ClosestIndex1 = 0
382.             ClosestIndex2 = 0
383.             FOR j = 1 TO Shape(Shape1).Elements
384.                 FOR k = 1 TO Shape(Shape2).Elements
385.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
386.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
387.                     r2 = dx * dx + dy * dy
388.                     IF (r2 < rmin) THEN
389.                         rmin = r2
390.                         ClosestIndex1 = j
391.                         ClosestIndex2 = k
392.                     END IF
393.                 NEXT
394.             NEXT
395.  
396.             IF (rmin <= 2) THEN
397.                 CollisionCount = CollisionCount + 1
398.  
399.                 ' Normal vector 1
400.                 x0 = PointChain(Shape1, ClosestIndex1).x
401.                 y0 = PointChain(Shape1, ClosestIndex1).y
402.                 'CALL ccircle(x0, y0, 3, Shape(Shape1).Shade)
403.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
404.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
405.                 norm = SQR(xx * xx + yy * yy)
406.                 xx = xx / norm
407.                 yy = yy / norm
408.                 nx1 = xx
409.                 ny1 = yy
410.                 'CALL cline(x0, y0, x0 + nx1 * 15, y0 + ny1 * 15, Shape(Shape1).Shade)
411.  
412.                 ' Normal vector 2
413.                 x0 = PointChain(Shape2, ClosestIndex2).x
414.                 y0 = PointChain(Shape2, ClosestIndex2).y
415.                 'CALL ccircle(x0, y0, 3, Shape(Shape2).Shade)
416.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
417.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
418.                 norm = SQR(xx * xx + yy * yy)
419.                 xx = xx / norm
420.                 yy = yy / norm
421.                 nx2 = xx
422.                 ny2 = yy
423.                 'CALL cline(x0, y0, x0 + nx2 * 15, y0 + ny2 * 15, Shape(Shape2).Shade)
424.  
425.                 ' Perpendicular vector 1
426.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).CtrRot.x
427.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).CtrRot.y
428.                 px1 = -dy1
429.                 py1 = dx1
430.                 p1 = SQR(px1 * px1 + py1 * py1)
431.                 px1 = px1 / p1
432.                 py1 = py1 / p1
433.                 'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + px1 * 15, PointChain(Shape1, ClosestIndex1).y + py1 * 15, Shape(Shape1).Shade)
434.  
435.                 ' Perpendicular vector 2
436.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).CtrRot.x
437.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).CtrRot.y
438.                 px2 = -dy2
439.                 py2 = dx2
440.                 p2 = SQR(px2 * px2 + py2 * py2)
441.                 px2 = px2 / p2
442.                 py2 = py2 / p2
443.                 'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + px2 * 15, PointChain(Shape2, ClosestIndex2).y + py2 * 15, Shape(Shape2).Shade)
444.  
445.                 ' Angular velocity vector 1
446.                 w1 = Shape(Shape1).Omega
447.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
448.                 vx1 = w1 * r1 * px1
449.                 vy1 = w1 * r1 * py1
450.                 'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + vx1 * 5, PointChain(Shape1, ClosestIndex1).y + vy1 * 5, Shape(Shape1).Shade)
451.  
452.                 ' Angular velocity vector 2
453.                 w2 = Shape(Shape2).Omega
454.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
455.                 vx2 = w2 * r2 * px2
456.                 vy2 = w2 * r2 * py2
457.                 'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + vx2 * 5, PointChain(Shape2, ClosestIndex2).y + vy2 * 5, Shape(Shape2).Shade)
458.  
459.                 ' Mass terms
460.                 m1 = Shape(Shape1).Mass
461.                 i1 = Shape(Shape1).MOI
462.                 m2 = Shape(Shape2).Mass
463.                 i2 = Shape(Shape2).MOI
464.                 mu = 1 / (1 / m1 + 1 / m2)
465.  
466.                 ' Velocity differential 1
467.                 vtx1 = Shape(Shape1).Velocity.x + vx1
468.                 vty1 = Shape(Shape1).Velocity.y + vy1
469.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
470.  
471.                 ' Velocity differential 2
472.                 vtx2 = Shape(Shape2).Velocity.x + vx2
473.                 vty2 = Shape(Shape2).Velocity.y + vy2
474.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
475.  
476.                 ' Velocity differential total
477.                 dvtx = vtx2 - vtx1
478.                 dvty = vty2 - vty1
479.  
480.                 ' Geometry
481.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
482.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
483.  
484.                 ' Momentum exchange
485.                 qx1 = nx1 * 2 * mu * n1dotdvt
486.                 qy1 = ny1 * 2 * mu * n1dotdvt
487.                 qx2 = nx2 * 2 * mu * n2dotdvt
488.                 qy2 = ny2 * 2 * mu * n2dotdvt
489.  
490.                 ' Momentum exchange unit vector
491.                 q1 = SQR(qx1 * qx1 + qy1 * qy1)
492.                 qhatx1 = qx1 / q1
493.                 qhaty1 = qy1 / q1
494.                 q2 = SQR(qx2 * qx2 + qy2 * qy2)
495.                 qhatx2 = qx2 / q2
496.                 qhaty2 = qy2 / q2
497.  
498.                 ' Undo previous motion
499.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -Shape(Shape1).Omega)
500.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -Shape(Shape2).Omega)
501.                 vtemp.x = -Shape(Shape1).Velocity.x
502.                 vtemp.y = -Shape(Shape1).Velocity.y
503.                 CALL TranslateShape(Shape1, vtemp)
504.                 vtemp.x = -Shape(Shape2).Velocity.x
505.                 vtemp.y = -Shape(Shape2).Velocity.y
506.                 CALL TranslateShape(Shape2, vtemp)
507.  
508.                 ' Separate along normal
509.                 vtemp.x = -nx1
510.                 vtemp.y = -ny1
511.                 CALL TranslateShape(Shape1, vtemp)
512.                 vtemp.x = -nx2
513.                 vtemp.y = -ny2
514.                 CALL TranslateShape(Shape1, vtemp)
515.  
516.                 ' Translational impulse
517.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
518.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
519.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
520.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
521.                 f1 = -q1dotn1 * n1dotr1hat
522.                 f2 = -q2dotn2 * n2dotr2hat
523.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
524.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
525.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
526.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
527.  
528.                 ' Angular impulse
529.                 q1dotp1 = qx1 * px1 + qy1 * py1
530.                 q2dotp2 = qx2 * px2 + qy2 * py2
531.                 dw1 = r1 * q1dotp1 / i1
532.                 dw2 = -r2 * q2dotp2 / i2
533.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
534.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
535.                 Shape(Shape1).Omega = Shape(Shape1).Omega + dw1
536.                 Shape(Shape2).Omega = Shape(Shape2).Omega + dw2
537.  
538.                 ' Dent along normal
539.                 PointChain(Shape1, ClosestIndex1).x = PointChain(Shape1, ClosestIndex1).x - 1 * nx1
540.                 PointChain(Shape1, ClosestIndex1).y = PointChain(Shape1, ClosestIndex1).y - 1 * ny1
541.                 PointChain(Shape2, ClosestIndex2).x = PointChain(Shape2, ClosestIndex2).x - 1 * nx2
542.                 PointChain(Shape2, ClosestIndex2).y = PointChain(Shape2, ClosestIndex2).y - 1 * ny2
543.                 'CALL SmoothShape(Shape1, Shape(Shape1).Elements, 1)
544.                 'CALL SmoothShape(Shape2, Shape(Shape2).Elements, 1)
545.  
546.                 ' Static friction
547.                 IF Shape(ShapeIndex).Velocity.x * Shape(ShapeIndex).Velocity.x < .25 THEN Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .01
548.                 IF Shape(ShapeIndex).Velocity.y * Shape(ShapeIndex).Velocity.y < .25 THEN Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .01
549.                 IF Shape(ShapeIndex).Omega * Shape(ShapeIndex).Omega < .05 THEN Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .01
550.  
551.             END IF
552.         NEXT
553.     END IF
554.  
555.     FOR ShapeIndex = 1 TO ShapeCount
556.         dx = Shape(ShapeIndex).CtrMass.x - Shape(ShapeIndex).CtrRot.x
557.         dy = Shape(ShapeIndex).CtrMass.y - Shape(ShapeIndex).CtrRot.y
558.  
559.         cx = Shape(ShapeIndex).CtrMass.x
560.         cy = Shape(ShapeIndex).CtrMass.y
561.         Gravity.x = -cx / 20
562.         Gravity.y = -cy / 20
563.  
564.         'torque = dx * Gravity.y - dy * Gravity.x
565.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
566.  
567.         ' Rotation update
568.         CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
569.  
570.         ' Velocity update
571.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Gravity.x / Shape(ShapeIndex).Mass
572.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Gravity.y / Shape(ShapeIndex).Mass
573.         CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
574.  
575.         ' Damping
576.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .975
577.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .975
578.         Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .975
579.     NEXT
580.  
581.     CALL Graphics
582.     _LIMIT 120
583. LOOP
584.  
585. END
586.  
587. SUB Graphics
588.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
589.     FOR ShapeIndex = 1 TO ShapeCount
590.         LOCATE 2, 1: PRINT ProximalPairsCount, CollisionCount
591.         LOCATE 1, 1: PRINT "Press space to enable creative mode."
592.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
593.             x1 = PointChain(ShapeIndex, i).x
594.             y1 = PointChain(ShapeIndex, i).y
595.             x2 = PointChain(ShapeIndex, i + 1).x
596.             y2 = PointChain(ShapeIndex, i + 1).y
597.             CALL cline(x1, y1, x2, y2, Shape(ShapeIndex).Shade)
598.         NEXT
599.         x1 = PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x
600.         y1 = PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y
601.         x2 = PointChain(ShapeIndex, 1).x
602.         y2 = PointChain(ShapeIndex, 1).y
603.         CALL cline(x1, y1, x2, y2, Shape(ShapeIndex).Shade)
604.         'CALL ccircle(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, 3, Shape(ShapeIndex).Shade)
605.         'CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
606.         'CALL cline(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, Shape(ShapeIndex).Shade)
607.         'CALL cpaint(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, Shape(ShapeIndex).Shade, Shape(ShapeIndex).Shade)
608.     NEXT
609.     'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, Shape(Shape1).CtrRot.x, Shape(Shape1).CtrRot.y, Shape(Shape1).Shade)
610.     'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, Shape(Shape2).CtrRot.x, Shape(Shape2).CtrRot.y, Shape(Shape2).Shade)
611.     _DISPLAY
612. END SUB
613.  
614. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
615.     DIM l AS Vector
616.     DIM r AS Vector
617.     li = i - 1
618.     ri = i + 1
619.     IF (i = 1) THEN li = Shape(k).Elements
620.     IF (i = Shape(k).Elements) THEN ri = 1
621.     l.x = PointChain(k, li).x
622.     r.x = PointChain(k, ri).x
623.     dx = r.x - l.x
624.     CalculateNormalX = dx
625. END FUNCTION
626.  
627. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
628.     DIM l AS Vector
629.     DIM r AS Vector
630.     li = i - 1
631.     ri = i + 1
632.     IF (i = 1) THEN li = Shape(k).Elements
633.     IF (i = Shape(k).Elements) THEN ri = 1
634.     l.y = PointChain(k, li).y
635.     r.y = PointChain(k, ri).y
636.     dy = r.y - l.y
637.     CalculateNormalY = dy
638. END FUNCTION
639.  
640. SUB CalculateCtrMass (k AS INTEGER)
641.     xx = 0
642.     yy = 0
643.     FOR i = 1 TO Shape(k).Elements
644.         xx = xx + PointChain(k, i).x
645.         yy = yy + PointChain(k, i).y
646.     NEXT
647.     Shape(k).CtrMass.x = xx / Shape(k).Elements
648.     Shape(k).CtrMass.y = yy / Shape(k).Elements
649. END SUB
650.  
651. SUB CalculateDiameter (k AS INTEGER)
652.     r2max = -1
653.     FOR i = 1 TO Shape(k).Elements
654.         xx = Shape(k).CtrMass.x - PointChain(k, i).x
655.         yy = Shape(k).CtrMass.y - PointChain(k, i).y
656.         r2 = xx * xx + yy * yy
657.         IF (r2 > r2max) THEN
658.             r2max = r2
659.         END IF
660.     NEXT
661.     Shape(k).Diameter = SQR(r2max)
662. END SUB
663.  
664. SUB CalculateMOI (k AS INTEGER)
665.     xx = 0
666.     yy = 0
667.     FOR i = 1 TO Shape(k).Elements
668.         xx = xx + (Shape(k).CtrRot.x - PointChain(k, i).x) ^ 2
669.         yy = yy + (Shape(k).CtrRot.y - PointChain(k, i).y) ^ 2
670.     NEXT
671.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Elements)
672. END SUB
673.  
674. SUB TranslateShape (k AS INTEGER, c AS Vector)
675.     FOR i = 1 TO Shape(k).Elements
676.         PointChain(k, i).x = PointChain(k, i).x + c.x
677.         PointChain(k, i).y = PointChain(k, i).y + c.y
678.     NEXT
679.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
680.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
681.     Shape(k).CtrMass.x = Shape(k).CtrMass.x + c.x
682.     Shape(k).CtrMass.y = Shape(k).CtrMass.y + c.y
683. END SUB
684.  
685. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
686.     FOR i = 1 TO Shape(k).Elements
687.         xx = PointChain(k, i).x - c.x
688.         yy = PointChain(k, i).y - c.y
689.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
690.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
691.     NEXT
692.     xx = Shape(k).CtrMass.x - c.x
693.     yy = Shape(k).CtrMass.y - c.y
694.     Shape(k).CtrMass.x = c.x + xx * COS(da) - yy * SIN(da)
695.     Shape(k).CtrMass.y = c.y + yy * COS(da) + xx * SIN(da)
696. END SUB
697.  
698. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
699.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
700. END SUB
701.  
702. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
703.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
704. END SUB
705.  
706. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
707.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
708. END SUB
709.  
710. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
711.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
712. END SUB
713.  
714. SUB CreateShape
715.     rawresolution = 7.5 ' Raw curve resolution.
716.     targetpoints = 120 ' Number of points per curve.
717.     smoothiterations = 15 ' Magnitude of smooth effect.
718.  
719.     ShapeCount = ShapeCount + 1
720.  
721.     numpoints = 0
722.     xold = 999999
723.     yold = 999999
724.  
725.     WHILE _MOUSEINPUT: WEND
726.  
727.     ' Gather raw data for one curve at a time.
728.     ' Click+drag mouse button 1 to trace out a curve.
729.     DO
730.         DO WHILE _MOUSEINPUT
731.             x = _MOUSEX
732.             y = _MOUSEY
733.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
734.                 IF _MOUSEBUTTON(1) THEN
735.                     x = x - (_WIDTH / 2)
736.                     y = -y + (_HEIGHT / 2)
737.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
738.  
739.                     ' Collect data only if the new point is sufficiently far away from the previous point.
740.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
741.                         numpoints = numpoints + 1
742.                         PointChain(ShapeCount, numpoints).x = x
743.                         PointChain(ShapeCount, numpoints).y = y
744.                         CALL cpset(x, y, _RGB(255, 255, 255))
745.                         xold = x
746.                         yold = y
747.                     END IF
748.                 END IF
749.             END IF
750.         LOOP
751.         _DISPLAY
752.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
753.  
754.     ' If the curve contains less than the minimum numer of points, use interpolation to fill in the gaps.
755.     DO WHILE (numpoints < targetpoints)
756.  
757.         ' Determine the pair of neighboring points that have the greatest separation of all pairs.
758.         rad2max = -1
759.         kmax = -1
760.         FOR k = 1 TO numpoints - 1
761.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
762.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
763.             rad2 = xfac ^ 2 + yfac ^ 2
764.             IF rad2 > rad2max THEN
765.                 kmax = k
766.                 rad2max = rad2
767.             END IF
768.         NEXT
769.         '''
770.         cornercase = 0
771.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
772.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
773.         rad2 = xfac ^ 2 + yfac ^ 2
774.         IF rad2 > rad2max THEN
775.             kmax = numpoints
776.             rad2max = rad2
777.             cornercase = 1
778.         END IF
779.         '''
780.         IF (cornercase = 0) THEN
781.  
782.             numpoints = numpoints + 1
783.  
784.             ' Starting next to kmax, create a `gap' by shifting all other points by one index.
785.             FOR j = numpoints TO kmax + 1 STEP -1
786.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
787.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
788.             NEXT
789.  
790.             ' Fill the gap with a new point whose position is determined by the average of its neighbors.
791.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
792.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
793.  
794.         ELSE
795.             numpoints = numpoints + 1
796.             xx = PointChain(ShapeCount, numpoints - 1).x
797.             yy = PointChain(ShapeCount, numpoints - 1).y
798.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
799.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
800.         END IF
801.  
802.     LOOP
803.  
804.     ' At this stage, the curve still has all of its sharp edges. Use a `relaxation method' to smooth.
805.     ' The new position of a point is equal to the average position of its neighboring points.
806.     CALL SmoothShape(ShapeCount, numpoints, smoothiterations)
807.  
808.     Shape(ShapeCount).Elements = numpoints
809.     Shape(ShapeCount).Mass = numpoints
810.     Shape(ShapeCount).Velocity.x = 0
811.     Shape(ShapeCount).Velocity.y = 0
812.     Shape(ShapeCount).Omega = 0
813.     Shape(ShapeCount).Shade = _RGB(INT(RND * 255), INT(RND * 255), INT(RND * 255))
814.     CALL CalculateCtrMass(ShapeCount)
815.     Shape(ShapeCount).CtrRot.x = Shape(ShapeCount).CtrMass.x
816.     Shape(ShapeCount).CtrRot.y = Shape(ShapeCount).CtrMass.y
817.     CALL CalculateDiameter(ShapeCount)
818.     CALL CalculateMOI(ShapeCount)
819.  
820. END SUB
821.  
822. SUB SmoothShape (i AS INTEGER, n AS INTEGER, s AS INTEGER)
823.     FOR j = 1 TO s
824.         FOR k = 2 TO n - 1
825.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
826.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
827.         NEXT
828.         FOR k = 2 TO n - 1
829.             PointChain(i, k).x = TempChain(i, k).x
830.             PointChain(i, k).y = TempChain(i, k).y
831.         NEXT
832.     NEXT
833. END SUB
834.  
835.  

[STxAxTIC]

Alright, I finally (re-)added friction so this one should be far less jumpy. Hopefully I can go a day without working on this, my other irons are gonna get cold!

Note the center of mass isn't always inside the object, which leads to trouble when PAINTing about the center of mass. It'll stay wireframe for now.

The screenshot below is made from drawing a few odd-shaped potatoes and things that are centrally attracted to the middle of the screen. They self-arrange to find a local energy minimum. I find it amazing that the shapes and contours find each other.

Code: QB64: [Select]

1. ' Display
2. SCREEN _NEWIMAGE(800, 600, 32)
3. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
4.  
5. ' Meta
6. RANDOMIZE TIMER
7.  
8. ' Data
9. TYPE Vector
10.     x AS DOUBLE
11.     y AS DOUBLE
12. END TYPE
13.  
14. TYPE Object
15.     CtrMass AS Vector
16.     CtrRot AS Vector
17.     Diameter AS DOUBLE
18.     Elements AS INTEGER
19.     Mass AS DOUBLE
20.     MOI AS DOUBLE
21.     Omega AS DOUBLE
22.     Shade AS _UNSIGNED LONG
23.     Velocity AS Vector
24. END TYPE
25.  
26. DIM vtemp AS Vector
27.  
28. ' Statics
29. DIM SHARED Shape(1000) AS Object
30. DIM SHARED PointChain(1000, 5000) AS Vector
31. DIM SHARED TempChain(1000, 5000) AS Vector
32. DIM SHARED ShapeCount AS INTEGER
33. ShapeCount = 0
34.  
35. ' Dynamics
36. DIM SHARED CollisionCount AS INTEGER
37. CollisionCount = 0
38.  
39. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
40. DIM SHARED ProximalPairsCount
41.  
42. DIM Gravity AS Vector
43. Gravity.x = 0
44. Gravity.y = 0 '-10
45.  
46. ' Create test object(s)
47.  
48. ShapeCount = ShapeCount + 1
49. Shape(ShapeCount).CtrRot.x = -100
50. Shape(ShapeCount).CtrRot.y = 0
51. i = 0
52. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
53.     i = i + 1
54.     r = 40 + 25 * COS(1.5 * j) ^ 2
55.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
56.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
57. NEXT
58. Shape(ShapeCount).Elements = i
59. Shape(ShapeCount).Mass = i
60. Shape(ShapeCount).Velocity.x = 0
61. Shape(ShapeCount).Velocity.y = 0
62. Shape(ShapeCount).Omega = .1
63. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
64. CALL CalculateCtrMass(ShapeCount)
65. CALL CalculateDiameter(ShapeCount)
66. CALL CalculateMOI(ShapeCount)
67.  
68. ' Walls
69. b = 50
70. FOR n = -1 TO 1 STEP 2
71.     FOR k = -(_WIDTH / 2 - b) + b TO (_WIDTH / 2 - b) - b STEP 2 * b
72.         ShapeCount = ShapeCount + 1
73.         Shape(ShapeCount).CtrRot.x = k
74.         Shape(ShapeCount).CtrRot.y = n * (_HEIGHT / 2 - b * .5)
75.         i = 0
76.         FOR j = (Shape(ShapeCount).CtrRot.x + n * b * .9) TO (Shape(ShapeCount).CtrRot.x - n * b * .9) STEP -n * 2
77.             i = i + 1
78.             PointChain(ShapeCount, i).x = j
79.             PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y
80.         NEXT
81.         Shape(ShapeCount).Elements = i
82.         Shape(ShapeCount).Mass = 999 ^ 999
83.         Shape(ShapeCount).Velocity.x = 0
84.         Shape(ShapeCount).Velocity.y = 0
85.         Shape(ShapeCount).Omega = 0
86.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
87.         CALL CalculateCtrMass(ShapeCount)
88.         CALL CalculateDiameter(ShapeCount)
89.         CALL CalculateMOI(ShapeCount)
90.         Shape(ShapeCount).MOI = 999 ^ 999
91.     NEXT
92.  
93.     FOR k = -(_HEIGHT / 2 - b) + b TO (_HEIGHT / 2 - b) - b STEP 2 * b
94.         ShapeCount = ShapeCount + 1
95.         Shape(ShapeCount).CtrRot.x = n * (_WIDTH / 2 - b * .5)
96.         Shape(ShapeCount).CtrRot.y = k
97.         i = 0
98.         FOR j = (Shape(ShapeCount).CtrRot.y + n * b * .9) TO (Shape(ShapeCount).CtrRot.y - n * b * .9) STEP -n * 2
99.             i = i + 1
100.             PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x
101.             PointChain(ShapeCount, i).y = j
102.         NEXT
103.         Shape(ShapeCount).Elements = i
104.         Shape(ShapeCount).Mass = 999 ^ 999
105.         Shape(ShapeCount).Velocity.x = 0
106.         Shape(ShapeCount).Velocity.y = 0
107.         Shape(ShapeCount).Omega = 0
108.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
109.         CALL CalculateCtrMass(ShapeCount)
110.         CALL CalculateDiameter(ShapeCount)
111.         CALL CalculateMOI(ShapeCount)
112.         Shape(ShapeCount).MOI = 999 ^ 999
113.     NEXT
114. NEXT
115.  
116. DO
117.  
118.     IF (_KEYHIT = 32) THEN
119.         CLS
120.         CALL Graphics
121.         LOCATE 1, 1: PRINT "Click & Drag counter-clockwise to create a shape."
122.         CALL CreateShape
123.         _KEYCLEAR
124.     END IF
125.  
126.     ' Proximity detection
127.     ProximalPairsCount = 0
128.     Shape1 = 0
129.     Shape2 = 0
130.     FOR j = 1 TO ShapeCount
131.         FOR k = j + 1 TO ShapeCount
132.             dx = Shape(j).CtrMass.x - Shape(k).CtrMass.x
133.             dy = Shape(j).CtrMass.y - Shape(k).CtrMass.y
134.             dr = SQR(dx * dx + dy * dy)
135.             IF (dr < 1.15 * (Shape(j).Diameter + Shape(k).Diameter)) THEN
136.                 ProximalPairsCount = ProximalPairsCount + 1
137.                 ProximalPairs(ProximalPairsCount, 1) = j
138.                 ProximalPairs(ProximalPairsCount, 2) = k
139.                 Shape1 = j
140.                 Shape2 = k
141.             END IF
142.         NEXT
143.     NEXT
144.  
145.     IF (ProximalPairsCount > 0) THEN
146.         FOR n = 1 TO ProximalPairsCount
147.             Shape1 = ProximalPairs(n, 1)
148.             Shape2 = ProximalPairs(n, 2)
149.  
150.             ' Collision detection
151.             rmin = 999 ^ 999
152.             ClosestIndex1 = 0
153.             ClosestIndex2 = 0
154.             FOR j = 1 TO Shape(Shape1).Elements
155.                 FOR k = 1 TO Shape(Shape2).Elements
156.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
157.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
158.                     r2 = dx * dx + dy * dy
159.                     IF (r2 < rmin) THEN
160.                         rmin = r2
161.                         ClosestIndex1 = j
162.                         ClosestIndex2 = k
163.                     END IF
164.                 NEXT
165.             NEXT
166.  
167.             IF (rmin <= 2) THEN
168.                 CollisionCount = CollisionCount + 1
169.  
170.                 ' Normal vector 1
171.                 x0 = PointChain(Shape1, ClosestIndex1).x
172.                 y0 = PointChain(Shape1, ClosestIndex1).y
173.                 'CALL ccircle(x0, y0, 3, Shape(Shape1).Shade)
174.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
175.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
176.                 norm = SQR(xx * xx + yy * yy)
177.                 xx = xx / norm
178.                 yy = yy / norm
179.                 nx1 = xx
180.                 ny1 = yy
181.                 'CALL cline(x0, y0, x0 + nx1 * 15, y0 + ny1 * 15, Shape(Shape1).Shade)
182.  
183.                 ' Normal vector 2
184.                 x0 = PointChain(Shape2, ClosestIndex2).x
185.                 y0 = PointChain(Shape2, ClosestIndex2).y
186.                 'CALL ccircle(x0, y0, 3, Shape(Shape2).Shade)
187.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
188.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
189.                 norm = SQR(xx * xx + yy * yy)
190.                 xx = xx / norm
191.                 yy = yy / norm
192.                 nx2 = xx
193.                 ny2 = yy
194.                 'CALL cline(x0, y0, x0 + nx2 * 15, y0 + ny2 * 15, Shape(Shape2).Shade)
195.  
196.                 ' Perpendicular vector 1
197.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).CtrRot.x
198.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).CtrRot.y
199.                 px1 = -dy1
200.                 py1 = dx1
201.                 p1 = SQR(px1 * px1 + py1 * py1)
202.                 px1 = px1 / p1
203.                 py1 = py1 / p1
204.                 'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + px1 * 15, PointChain(Shape1, ClosestIndex1).y + py1 * 15, Shape(Shape1).Shade)
205.  
206.                 ' Perpendicular vector 2
207.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).CtrRot.x
208.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).CtrRot.y
209.                 px2 = -dy2
210.                 py2 = dx2
211.                 p2 = SQR(px2 * px2 + py2 * py2)
212.                 px2 = px2 / p2
213.                 py2 = py2 / p2
214.                 'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + px2 * 15, PointChain(Shape2, ClosestIndex2).y + py2 * 15, Shape(Shape2).Shade)
215.  
216.                 ' Angular velocity vector 1
217.                 w1 = Shape(Shape1).Omega
218.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
219.                 vx1 = w1 * r1 * px1
220.                 vy1 = w1 * r1 * py1
221.                 'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + vx1 * 5, PointChain(Shape1, ClosestIndex1).y + vy1 * 5, Shape(Shape1).Shade)
222.  
223.                 ' Angular velocity vector 2
224.                 w2 = Shape(Shape2).Omega
225.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
226.                 vx2 = w2 * r2 * px2
227.                 vy2 = w2 * r2 * py2
228.                 'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + vx2 * 5, PointChain(Shape2, ClosestIndex2).y + vy2 * 5, Shape(Shape2).Shade)
229.  
230.                 ' Mass terms
231.                 m1 = Shape(Shape1).Mass
232.                 i1 = Shape(Shape1).MOI
233.                 m2 = Shape(Shape2).Mass
234.                 i2 = Shape(Shape2).MOI
235.                 mu = 1 / (1 / m1 + 1 / m2)
236.  
237.                 ' Velocity differential 1
238.                 vtx1 = Shape(Shape1).Velocity.x + vx1
239.                 vty1 = Shape(Shape1).Velocity.y + vy1
240.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
241.  
242.                 ' Velocity differential 2
243.                 vtx2 = Shape(Shape2).Velocity.x + vx2
244.                 vty2 = Shape(Shape2).Velocity.y + vy2
245.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
246.  
247.                 ' Velocity differential total
248.                 dvtx = vtx2 - vtx1
249.                 dvty = vty2 - vty1
250.  
251.                 ' Geometry
252.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
253.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
254.  
255.                 ' Momentum exchange
256.                 qx1 = nx1 * 2 * mu * n1dotdvt
257.                 qy1 = ny1 * 2 * mu * n1dotdvt
258.                 qx2 = nx2 * 2 * mu * n2dotdvt
259.                 qy2 = ny2 * 2 * mu * n2dotdvt
260.  
261.                 ' Momentum exchange unit vector
262.                 q1 = SQR(qx1 * qx1 + qy1 * qy1)
263.                 qhatx1 = qx1 / q1
264.                 qhaty1 = qy1 / q1
265.                 q2 = SQR(qx2 * qx2 + qy2 * qy2)
266.                 qhatx2 = qx2 / q2
267.                 qhaty2 = qy2 / q2
268.  
269.                 ' Undo previous motion
270.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -Shape(Shape1).Omega)
271.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -Shape(Shape2).Omega)
272.                 vtemp.x = -Shape(Shape1).Velocity.x
273.                 vtemp.y = -Shape(Shape1).Velocity.y
274.                 CALL TranslateShape(Shape1, vtemp)
275.                 vtemp.x = -Shape(Shape2).Velocity.x
276.                 vtemp.y = -Shape(Shape2).Velocity.y
277.                 CALL TranslateShape(Shape2, vtemp)
278.  
279.                 ' Separate along normal
280.                 vtemp.x = -nx1 * (v1 + .05)
281.                 vtemp.y = -ny1 * (v1 + .05)
282.                 CALL TranslateShape(Shape1, vtemp)
283.                 vtemp.x = -nx2 * (v2 + .05)
284.                 vtemp.y = -ny2 * (v2 + .05)
285.                 CALL TranslateShape(Shape2, vtemp)
286.  
287.                 ' Translational impulse
288.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
289.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
290.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
291.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
292.                 f1 = -q1dotn1 * n1dotr1hat
293.                 f2 = -q2dotn2 * n2dotr2hat
294.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
295.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
296.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
297.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
298.  
299.                 ' Angular impulse
300.                 q1dotp1 = qx1 * px1 + qy1 * py1
301.                 q2dotp2 = qx2 * px2 + qy2 * py2
302.                 dw1 = r1 * q1dotp1 / i1
303.                 dw2 = -r2 * q2dotp2 / i2
304.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
305.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
306.                 Shape(Shape1).Omega = Shape(Shape1).Omega + dw1
307.                 Shape(Shape2).Omega = Shape(Shape2).Omega + dw2
308.  
309.                 ' Dent along normal
310.                 'PointChain(Shape1, ClosestIndex1).x = PointChain(Shape1, ClosestIndex1).x - v1 * nx1
311.                 'PointChain(Shape1, ClosestIndex1).y = PointChain(Shape1, ClosestIndex1).y - v1 * ny1
312.                 'PointChain(Shape2, ClosestIndex2).x = PointChain(Shape2, ClosestIndex2).x - v2 * nx2
313.                 'PointChain(Shape2, ClosestIndex2).y = PointChain(Shape2, ClosestIndex2).y - v2 * ny2
314.                 'CALL SmoothShape(Shape1, Shape(Shape1).Elements, 1)
315.                 'CALL SmoothShape(Shape2, Shape(Shape2).Elements, 1)
316.  
317.                 ' Static friction
318.                 IF (Shape(Shape1).Velocity.x * Shape(Shape1).Velocity.x < .05) THEN Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * .001
319.                 IF (Shape(Shape1).Velocity.y * Shape(Shape1).Velocity.y < .05) THEN Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * .001
320.                 IF (Shape(Shape2).Velocity.x * Shape(Shape2).Velocity.x < .05) THEN Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * .001
321.                 IF (Shape(Shape2).Velocity.y * Shape(Shape2).Velocity.y < .05) THEN Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * .001
322.                 IF (Shape(Shape1).Omega * Shape(Shape1).Omega < .0001) THEN Shape(Shape1).Omega = Shape(Shape1).Omega * .01
323.                 IF (Shape(Shape2).Omega * Shape(Shape2).Omega < .0001) THEN Shape(Shape2).Omega = Shape(Shape2).Omega * .01
324.             END IF
325.         NEXT
326.     END IF
327.  
328.     FOR ShapeIndex = 1 TO ShapeCount
329.         dx = Shape(ShapeIndex).CtrMass.x - Shape(ShapeIndex).CtrRot.x
330.         dy = Shape(ShapeIndex).CtrMass.y - Shape(ShapeIndex).CtrRot.y
331.  
332.         cx = Shape(ShapeIndex).CtrMass.x
333.         cy = Shape(ShapeIndex).CtrMass.y
334.         Gravity.x = -(cx / Shape(ShapeIndex).Mass) / 20
335.         Gravity.y = -(cy / Shape(ShapeIndex).Mass) / 20
336.  
337.         'torque = dx * Gravity.y - dy * Gravity.x
338.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
339.  
340.         ' Rotation update
341.         CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
342.  
343.         ' Velocity update
344.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Gravity.x
345.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Gravity.y
346.         CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
347.  
348.         ' Damping
349.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .975
350.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .975
351.         Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .975
352.  
353.     NEXT
354.  
355.     CALL Graphics
356.     _LIMIT 60
357. LOOP
358.  
359. END
360.  
361. SUB Graphics
362.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
363.     FOR ShapeIndex = 1 TO ShapeCount
364.         LOCATE 2, 1: PRINT ProximalPairsCount, CollisionCount
365.         LOCATE 1, 1: PRINT "Press space to enable creative mode."
366.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
367.             x1 = PointChain(ShapeIndex, i).x
368.             y1 = PointChain(ShapeIndex, i).y
369.             x2 = PointChain(ShapeIndex, i + 1).x
370.             y2 = PointChain(ShapeIndex, i + 1).y
371.             'CALL cpset(x1, y1, Shape(ShapeIndex).Shade)
372.             CALL cline(x1, y1, x2, y2, Shape(ShapeIndex).Shade)
373.         NEXT
374.         x1 = PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x
375.         y1 = PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y
376.         x2 = PointChain(ShapeIndex, 1).x
377.         y2 = PointChain(ShapeIndex, 1).y
378.         'CALL cpset(x1, y1, Shape(ShapeIndex).Shade)
379.         CALL cline(x1, y1, x2, y2, Shape(ShapeIndex).Shade)
380.         'CALL ccircle(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, 3, Shape(ShapeIndex).Shade)
381.         CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
382.         'CALL cline(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, Shape(ShapeIndex).Shade)
383.         'CALL cpaint(Shape(ShapeIndex).CtrMass.x, Shape(ShapeIndex).CtrMass.y, Shape(ShapeIndex).Shade, Shape(ShapeIndex).Shade)
384.     NEXT
385.     'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, Shape(Shape1).CtrRot.x, Shape(Shape1).CtrRot.y, Shape(Shape1).Shade)
386.     'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, Shape(Shape2).CtrRot.x, Shape(Shape2).CtrRot.y, Shape(Shape2).Shade)
387.     _DISPLAY
388. END SUB
389.  
390. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
391.     DIM l AS Vector
392.     DIM r AS Vector
393.     li = i - 1
394.     ri = i + 1
395.     IF (i = 1) THEN li = Shape(k).Elements
396.     IF (i = Shape(k).Elements) THEN ri = 1
397.     l.x = PointChain(k, li).x
398.     r.x = PointChain(k, ri).x
399.     dx = r.x - l.x
400.     CalculateNormalX = dx
401. END FUNCTION
402.  
403. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
404.     DIM l AS Vector
405.     DIM r AS Vector
406.     li = i - 1
407.     ri = i + 1
408.     IF (i = 1) THEN li = Shape(k).Elements
409.     IF (i = Shape(k).Elements) THEN ri = 1
410.     l.y = PointChain(k, li).y
411.     r.y = PointChain(k, ri).y
412.     dy = r.y - l.y
413.     CalculateNormalY = dy
414. END FUNCTION
415.  
416. SUB CalculateCtrMass (k AS INTEGER)
417.     xx = 0
418.     yy = 0
419.     FOR i = 1 TO Shape(k).Elements
420.         xx = xx + PointChain(k, i).x
421.         yy = yy + PointChain(k, i).y
422.     NEXT
423.     Shape(k).CtrMass.x = xx / Shape(k).Elements
424.     Shape(k).CtrMass.y = yy / Shape(k).Elements
425. END SUB
426.  
427. SUB CalculateDiameter (k AS INTEGER)
428.     r2max = -1
429.     FOR i = 1 TO Shape(k).Elements
430.         xx = Shape(k).CtrMass.x - PointChain(k, i).x
431.         yy = Shape(k).CtrMass.y - PointChain(k, i).y
432.         r2 = xx * xx + yy * yy
433.         IF (r2 > r2max) THEN
434.             r2max = r2
435.         END IF
436.     NEXT
437.     Shape(k).Diameter = SQR(r2max)
438. END SUB
439.  
440. SUB CalculateMOI (k AS INTEGER)
441.     xx = 0
442.     yy = 0
443.     FOR i = 1 TO Shape(k).Elements
444.         xx = xx + (Shape(k).CtrRot.x - PointChain(k, i).x) ^ 2
445.         yy = yy + (Shape(k).CtrRot.y - PointChain(k, i).y) ^ 2
446.     NEXT
447.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Elements)
448. END SUB
449.  
450. SUB TranslateShape (k AS INTEGER, c AS Vector)
451.     FOR i = 1 TO Shape(k).Elements
452.         PointChain(k, i).x = PointChain(k, i).x + c.x
453.         PointChain(k, i).y = PointChain(k, i).y + c.y
454.     NEXT
455.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
456.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
457.     Shape(k).CtrMass.x = Shape(k).CtrMass.x + c.x
458.     Shape(k).CtrMass.y = Shape(k).CtrMass.y + c.y
459. END SUB
460.  
461. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
462.     FOR i = 1 TO Shape(k).Elements
463.         xx = PointChain(k, i).x - c.x
464.         yy = PointChain(k, i).y - c.y
465.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
466.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
467.     NEXT
468.     xx = Shape(k).CtrMass.x - c.x
469.     yy = Shape(k).CtrMass.y - c.y
470.     Shape(k).CtrMass.x = c.x + xx * COS(da) - yy * SIN(da)
471.     Shape(k).CtrMass.y = c.y + yy * COS(da) + xx * SIN(da)
472. END SUB
473.  
474. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
475.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
476. END SUB
477.  
478. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
479.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
480. END SUB
481.  
482. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
483.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
484. END SUB
485.  
486. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
487.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
488. END SUB
489.  
490. SUB CreateShape
491.     rawresolution = 7.5 ' Raw curve resolution.
492.     targetpoints = 120 ' Number of points per curve.
493.     smoothiterations = 15 ' Magnitude of smooth effect.
494.  
495.     ShapeCount = ShapeCount + 1
496.  
497.     numpoints = 0
498.     xold = 999999
499.     yold = 999999
500.  
501.     WHILE _MOUSEINPUT: WEND
502.  
503.     ' Gather raw data for one curve at a time.
504.     ' Click+drag mouse button 1 to trace out a curve.
505.     DO
506.         DO WHILE _MOUSEINPUT
507.             x = _MOUSEX
508.             y = _MOUSEY
509.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
510.                 IF _MOUSEBUTTON(1) THEN
511.                     x = x - (_WIDTH / 2)
512.                     y = -y + (_HEIGHT / 2)
513.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
514.  
515.                     ' Collect data only if the new point is sufficiently far away from the previous point.
516.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
517.                         numpoints = numpoints + 1
518.                         PointChain(ShapeCount, numpoints).x = x
519.                         PointChain(ShapeCount, numpoints).y = y
520.                         CALL cpset(x, y, _RGB(255, 255, 255))
521.                         xold = x
522.                         yold = y
523.                     END IF
524.                 END IF
525.             END IF
526.         LOOP
527.         _DISPLAY
528.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
529.  
530.     ' If the curve contains less than the minimum numer of points, use interpolation to fill in the gaps.
531.     DO WHILE (numpoints < targetpoints)
532.  
533.         ' Determine the pair of neighboring points that have the greatest separation of all pairs.
534.         rad2max = -1
535.         kmax = -1
536.         FOR k = 1 TO numpoints - 1
537.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
538.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
539.             rad2 = xfac ^ 2 + yfac ^ 2
540.             IF rad2 > rad2max THEN
541.                 kmax = k
542.                 rad2max = rad2
543.             END IF
544.         NEXT
545.         '''
546.         cornercase = 0
547.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
548.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
549.         rad2 = xfac ^ 2 + yfac ^ 2
550.         IF rad2 > rad2max THEN
551.             kmax = numpoints
552.             rad2max = rad2
553.             cornercase = 1
554.         END IF
555.         '''
556.         IF (cornercase = 0) THEN
557.  
558.             numpoints = numpoints + 1
559.  
560.             ' Starting next to kmax, create a `gap' by shifting all other points by one index.
561.             FOR j = numpoints TO kmax + 1 STEP -1
562.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
563.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
564.             NEXT
565.  
566.             ' Fill the gap with a new point whose position is determined by the average of its neighbors.
567.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
568.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
569.  
570.         ELSE
571.             numpoints = numpoints + 1
572.             xx = PointChain(ShapeCount, numpoints - 1).x
573.             yy = PointChain(ShapeCount, numpoints - 1).y
574.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
575.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
576.         END IF
577.  
578.     LOOP
579.  
580.     ' At this stage, the curve still has all of its sharp edges. Use a `relaxation method' to smooth.
581.     ' The new position of a point is equal to the average position of its neighboring points.
582.     CALL SmoothShape(ShapeCount, numpoints, smoothiterations)
583.  
584.     Shape(ShapeCount).Elements = numpoints
585.     Shape(ShapeCount).Mass = numpoints
586.     Shape(ShapeCount).Velocity.x = 0
587.     Shape(ShapeCount).Velocity.y = 0
588.     Shape(ShapeCount).Omega = 0
589.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
590.     CALL CalculateCtrMass(ShapeCount)
591.     Shape(ShapeCount).CtrRot.x = Shape(ShapeCount).CtrMass.x
592.     Shape(ShapeCount).CtrRot.y = Shape(ShapeCount).CtrMass.y
593.     CALL CalculateDiameter(ShapeCount)
594.     CALL CalculateMOI(ShapeCount)
595.  
596. END SUB
597.  
598. SUB SmoothShape (i AS INTEGER, n AS INTEGER, s AS INTEGER)
599.     FOR j = 1 TO s
600.         FOR k = 2 TO n - 1
601.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
602.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
603.         NEXT
604.         FOR k = 2 TO n - 1
605.             PointChain(i, k).x = TempChain(i, k).x
606.             PointChain(i, k).y = TempChain(i, k).y
607.         NEXT
608.     NEXT
609. END SUB
610.  

[STxAxTIC]

POOL GAME UPDATE

Kindof. Bear with me: This is a simulation of what happens when you dump a bowl of lucky charms with milk all over the table, and then shove the pieces around with a fidget spinner. Complete with keyboard controls and those early 90's sounds. Have a ball.

Code: QB64: [Select]

1. ' Display
2. SCREEN _NEWIMAGE(800, 600, 32)
3. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
4.  
5. ' Meta
6. RANDOMIZE TIMER
7.  
8. ' Data
9. TYPE Vector
10.     x AS DOUBLE
11.     y AS DOUBLE
12. END TYPE
13.  
14. TYPE Object
15.     CtrMass AS Vector
16.     CtrRot AS Vector
17.     Diameter AS DOUBLE
18.     Elements AS INTEGER
19.     Mass AS DOUBLE
20.     MOI AS DOUBLE
21.     Omega AS DOUBLE
22.     Shade AS _UNSIGNED LONG
23.     Velocity AS Vector
24. END TYPE
25.  
26. DIM vtemp AS Vector
27.  
28. ' Statics
29. DIM SHARED Shape(1000) AS Object
30. DIM SHARED PointChain(1000, 5000) AS Vector
31. DIM SHARED TempChain(1000, 5000) AS Vector
32. DIM SHARED ShapeCount AS INTEGER
33. ShapeCount = 0
34.  
35. ' Dynamics
36. DIM SHARED CollisionCount AS INTEGER
37. CollisionCount = 0
38.  
39. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
40. DIM SHARED ProximalPairsCount
41.  
42. DIM Gravity AS Vector
43. Gravity.x = 0
44. Gravity.y = 0 '-10
45.  
46. ' Create test object(s)
47.  
48. ShapeCount = ShapeCount + 1
49. Shape(ShapeCount).CtrRot.x = -200
50. Shape(ShapeCount).CtrRot.y = 0
51. i = 0
52. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
53.     i = i + 1
54.     r = 40 + 25 * COS(1.5 * j) ^ 2
55.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
56.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
57. NEXT
58. Shape(ShapeCount).Elements = i
59. Shape(ShapeCount).Mass = i
60. Shape(ShapeCount).Velocity.x = 0
61. Shape(ShapeCount).Velocity.y = 0
62. Shape(ShapeCount).Omega = 0
63. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
64. CALL CalculateCtrMass(ShapeCount)
65. CALL CalculateDiameter(ShapeCount)
66. CALL CalculateMOI(ShapeCount)
67.  
68. x0 = 120
69. y0 = 0
70. rr = 22.5
71. gg = 2 * rr + 20
72. xf = COS(30 * 3.14159 / 180)
73. yf = SIN(30 * 3.14159 / 180)
74. gx = gg * xf
75. gy = gg * yf
76.  
77. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
78. ShapeCount = ShapeCount + 1
79. Shape(ShapeCount).CtrRot.x = x0
80. Shape(ShapeCount).CtrRot.y = y0
81. i = 0
82. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
83.     i = i + 1
84.     r = rr + 5 * COS(ss * j) ^ tt
85.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
86.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
87. NEXT
88. Shape(ShapeCount).Elements = i
89. Shape(ShapeCount).Mass = i
90. Shape(ShapeCount).Velocity.x = 0
91. Shape(ShapeCount).Velocity.y = 0
92. Shape(ShapeCount).Omega = 0
93. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
94. CALL CalculateCtrMass(ShapeCount)
95. CALL CalculateDiameter(ShapeCount)
96. CALL CalculateMOI(ShapeCount)
97.  
98. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
99. ShapeCount = ShapeCount + 1
100. Shape(ShapeCount).CtrRot.x = x0 + gx
101. Shape(ShapeCount).CtrRot.y = y0 + gy
102. i = 0
103. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
104.     i = i + 1
105.     r = rr + 5 * COS(ss * j) ^ tt
106.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
107.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
108. NEXT
109. Shape(ShapeCount).Elements = i
110. Shape(ShapeCount).Mass = i
111. Shape(ShapeCount).Velocity.x = 0
112. Shape(ShapeCount).Velocity.y = 0
113. Shape(ShapeCount).Omega = 0
114. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
115. CALL CalculateCtrMass(ShapeCount)
116. CALL CalculateDiameter(ShapeCount)
117. CALL CalculateMOI(ShapeCount)
118.  
119. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
120. ShapeCount = ShapeCount + 1
121. Shape(ShapeCount).CtrRot.x = x0 + gx
122. Shape(ShapeCount).CtrRot.y = y0 - gy
123. i = 0
124. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
125.     i = i + 1
126.     r = rr + 5 * COS(ss * j) ^ tt
127.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
128.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
129. NEXT
130. Shape(ShapeCount).Elements = i
131. Shape(ShapeCount).Mass = i
132. Shape(ShapeCount).Velocity.x = 0
133. Shape(ShapeCount).Velocity.y = 0
134. Shape(ShapeCount).Omega = 0
135. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
136. CALL CalculateCtrMass(ShapeCount)
137. CALL CalculateDiameter(ShapeCount)
138. CALL CalculateMOI(ShapeCount)
139.  
140. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
141. ShapeCount = ShapeCount + 1
142. Shape(ShapeCount).CtrRot.x = x0 + gx + gx
143. Shape(ShapeCount).CtrRot.y = y0
144. i = 0
145. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
146.     i = i + 1
147.     r = rr + 5 * COS(ss * j) ^ tt
148.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
149.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
150. NEXT
151. Shape(ShapeCount).Elements = i
152. Shape(ShapeCount).Mass = i
153. Shape(ShapeCount).Velocity.x = 0
154. Shape(ShapeCount).Velocity.y = 0
155. Shape(ShapeCount).Omega = 0
156. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
157. CALL CalculateCtrMass(ShapeCount)
158. CALL CalculateDiameter(ShapeCount)
159. CALL CalculateMOI(ShapeCount)
160.  
161. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
162. ShapeCount = ShapeCount + 1
163. Shape(ShapeCount).CtrRot.x = x0 + gx + gx
164. Shape(ShapeCount).CtrRot.y = y0 + gy + gy
165. i = 0
166. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
167.     i = i + 1
168.     r = rr + 5 * COS(ss * j) ^ tt
169.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
170.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
171. NEXT
172. Shape(ShapeCount).Elements = i
173. Shape(ShapeCount).Mass = i
174. Shape(ShapeCount).Velocity.x = 0
175. Shape(ShapeCount).Velocity.y = 0
176. Shape(ShapeCount).Omega = 0
177. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
178. CALL CalculateCtrMass(ShapeCount)
179. CALL CalculateDiameter(ShapeCount)
180. CALL CalculateMOI(ShapeCount)
181.  
182. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
183. ShapeCount = ShapeCount + 1
184. Shape(ShapeCount).CtrRot.x = x0 + gx + gx
185. Shape(ShapeCount).CtrRot.y = y0 - gy - gy
186. i = 0
187. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
188.     i = i + 1
189.     r = rr + 5 * COS(ss * j) ^ tt
190.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
191.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
192. NEXT
193. Shape(ShapeCount).Elements = i
194. Shape(ShapeCount).Mass = i
195. Shape(ShapeCount).Velocity.x = 0
196. Shape(ShapeCount).Velocity.y = 0
197. Shape(ShapeCount).Omega = 0
198. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
199. CALL CalculateCtrMass(ShapeCount)
200. CALL CalculateDiameter(ShapeCount)
201. CALL CalculateMOI(ShapeCount)
202.  
203. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
204. ShapeCount = ShapeCount + 1
205. Shape(ShapeCount).CtrRot.x = x0 + gx + gx + gx
206. Shape(ShapeCount).CtrRot.y = y0 + gy
207. i = 0
208. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
209.     i = i + 1
210.     r = rr + 5 * COS(ss * j) ^ tt
211.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
212.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
213. NEXT
214. Shape(ShapeCount).Elements = i
215. Shape(ShapeCount).Mass = i
216. Shape(ShapeCount).Velocity.x = 0
217. Shape(ShapeCount).Velocity.y = 0
218. Shape(ShapeCount).Omega = 0
219. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
220. CALL CalculateCtrMass(ShapeCount)
221. CALL CalculateDiameter(ShapeCount)
222. CALL CalculateMOI(ShapeCount)
223.  
224. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
225. ShapeCount = ShapeCount + 1
226. Shape(ShapeCount).CtrRot.x = x0 + gx + gx + gx
227. Shape(ShapeCount).CtrRot.y = y0 - gy
228. i = 0
229. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
230.     i = i + 1
231.     r = rr + 5 * COS(ss * j) ^ tt
232.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
233.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
234. NEXT
235. Shape(ShapeCount).Elements = i
236. Shape(ShapeCount).Mass = i
237. Shape(ShapeCount).Velocity.x = 0
238. Shape(ShapeCount).Velocity.y = 0
239. Shape(ShapeCount).Omega = 0
240. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
241. CALL CalculateCtrMass(ShapeCount)
242. CALL CalculateDiameter(ShapeCount)
243. CALL CalculateMOI(ShapeCount)
244.  
245. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
246. ShapeCount = ShapeCount + 1
247. Shape(ShapeCount).CtrRot.x = x0 + gx + gx + gx
248. Shape(ShapeCount).CtrRot.y = y0 + gy + gy + gy
249. i = 0
250. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
251.     i = i + 1
252.     r = rr + 5 * COS(ss * j) ^ tt
253.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
254.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
255. NEXT
256. Shape(ShapeCount).Elements = i
257. Shape(ShapeCount).Mass = i
258. Shape(ShapeCount).Velocity.x = 0
259. Shape(ShapeCount).Velocity.y = 0
260. Shape(ShapeCount).Omega = 0
261. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
262. CALL CalculateCtrMass(ShapeCount)
263. CALL CalculateDiameter(ShapeCount)
264. CALL CalculateMOI(ShapeCount)
265.  
266. ss = INT(RND * 3) + 1: tt = INT(RND * 2) + 1
267. ShapeCount = ShapeCount + 1
268. Shape(ShapeCount).CtrRot.x = x0 + gx + gx + gx
269. Shape(ShapeCount).CtrRot.y = y0 - gy - gy - gy
270. i = 0
271. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
272.     i = i + 1
273.     r = rr + 5 * COS(ss * j) ^ tt
274.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
275.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
276. NEXT
277. Shape(ShapeCount).Elements = i
278. Shape(ShapeCount).Mass = i
279. Shape(ShapeCount).Velocity.x = 0
280. Shape(ShapeCount).Velocity.y = 0
281. Shape(ShapeCount).Omega = 0
282. Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
283. CALL CalculateCtrMass(ShapeCount)
284. CALL CalculateDiameter(ShapeCount)
285. CALL CalculateMOI(ShapeCount)
286.  
287. ' Walls
288. FOR n = -1 TO 1 STEP 2
289.     b = _WIDTH / 20
290.     p = (_WIDTH / 2 - b) - b
291.     FOR k = -p TO p STEP 2 * b
292.         ShapeCount = ShapeCount + 1
293.         Shape(ShapeCount).CtrRot.x = k
294.         Shape(ShapeCount).CtrRot.y = n * (_HEIGHT / 2 - b * .25)
295.         i = 0
296.         FOR j = (Shape(ShapeCount).CtrRot.x + n * b * .9) TO (Shape(ShapeCount).CtrRot.x - n * b * .9) STEP -n * 2
297.             i = i + 1
298.             PointChain(ShapeCount, i).x = j
299.             PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y
300.         NEXT
301.         Shape(ShapeCount).Elements = i
302.         Shape(ShapeCount).Mass = 999 ^ 999
303.         Shape(ShapeCount).Velocity.x = 0
304.         Shape(ShapeCount).Velocity.y = 0
305.         Shape(ShapeCount).Omega = 0
306.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
307.         CALL CalculateCtrMass(ShapeCount)
308.         CALL CalculateDiameter(ShapeCount)
309.         CALL CalculateMOI(ShapeCount)
310.         Shape(ShapeCount).MOI = 999 ^ 999
311.     NEXT
312.  
313.     b = _HEIGHT / 20
314.     p = (_HEIGHT / 2 - b) - b
315.     FOR k = -p TO p STEP 2 * b
316.         ShapeCount = ShapeCount + 1
317.         Shape(ShapeCount).CtrRot.x = n * (_WIDTH / 2 - b * .25)
318.         Shape(ShapeCount).CtrRot.y = k
319.         i = 0
320.         FOR j = (Shape(ShapeCount).CtrRot.y + n * b * .9) TO (Shape(ShapeCount).CtrRot.y - n * b * .9) STEP -n * 2
321.             i = i + 1
322.             PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x
323.             PointChain(ShapeCount, i).y = j
324.         NEXT
325.         Shape(ShapeCount).Elements = i
326.         Shape(ShapeCount).Mass = 999 ^ 999
327.         Shape(ShapeCount).Velocity.x = 0
328.         Shape(ShapeCount).Velocity.y = 0
329.         Shape(ShapeCount).Omega = 0
330.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
331.         CALL CalculateCtrMass(ShapeCount)
332.         CALL CalculateDiameter(ShapeCount)
333.         CALL CalculateMOI(ShapeCount)
334.         Shape(ShapeCount).MOI = 999 ^ 999
335.     NEXT
336. NEXT
337.  
338. CALL Graphics
339. LOCATE 10, 15: PRINT "PRESS ANY KEY TO BEGIN"
340. _DISPLAY
341. DO: LOOP UNTIL _KEYHIT
342. Shape(1).Velocity.x = 9
343.  
344. DO
345.  
346.     kk = _KEYHIT
347.     SELECT CASE kk
348.         CASE 32
349.             CLS
350.             CALL Graphics
351.             LOCATE 1, 1: PRINT "Click & Drag counter-clockwise to create a shape."
352.             CALL CreateShape
353.         CASE 18432 ' Up arrow
354.             Shape(1).Velocity.y = Shape(1).Velocity.y + 5
355.         CASE 20480 ' Down arrow
356.             Shape(1).Velocity.y = Shape(1).Velocity.y - 5
357.         CASE 19200 ' Left arrow
358.             Shape(1).Velocity.x = Shape(1).Velocity.x - 5
359.         CASE 19712 ' Right arrow
360.             Shape(1).Velocity.x = Shape(1).Velocity.x + 5
361.     END SELECT
362.     IF (kk) THEN
363.         _KEYCLEAR
364.     END IF
365.  
366.     ' Proximity detection
367.     ProximalPairsCount = 0
368.     Shape1 = 0
369.     Shape2 = 0
370.     FOR j = 1 TO ShapeCount
371.         FOR k = j + 1 TO ShapeCount
372.             dx = Shape(j).CtrMass.x - Shape(k).CtrMass.x
373.             dy = Shape(j).CtrMass.y - Shape(k).CtrMass.y
374.             dr = SQR(dx * dx + dy * dy)
375.             IF (dr < 1.15 * (Shape(j).Diameter + Shape(k).Diameter)) THEN
376.                 ProximalPairsCount = ProximalPairsCount + 1
377.                 ProximalPairs(ProximalPairsCount, 1) = j
378.                 ProximalPairs(ProximalPairsCount, 2) = k
379.                 Shape1 = j
380.                 Shape2 = k
381.             END IF
382.         NEXT
383.     NEXT
384.  
385.     IF (ProximalPairsCount > 0) THEN
386.         FOR n = 1 TO ProximalPairsCount
387.             Shape1 = ProximalPairs(n, 1)
388.             Shape2 = ProximalPairs(n, 2)
389.  
390.             ' Collision detection
391.             rmin = 999 ^ 999
392.             ClosestIndex1 = 0
393.             ClosestIndex2 = 0
394.             FOR j = 1 TO Shape(Shape1).Elements
395.                 FOR k = 1 TO Shape(Shape2).Elements
396.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
397.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
398.                     r2 = dx * dx + dy * dy
399.                     IF (r2 < rmin) THEN
400.                         rmin = r2
401.                         ClosestIndex1 = j
402.                         ClosestIndex2 = k
403.                     END IF
404.                 NEXT
405.             NEXT
406.  
407.             IF (rmin <= 2) THEN
408.                 CollisionCount = CollisionCount + 1
409.  
410.                 ' Normal vector 1
411.                 x0 = PointChain(Shape1, ClosestIndex1).x
412.                 y0 = PointChain(Shape1, ClosestIndex1).y
413.                 'CALL ccircle(x0, y0, 3, Shape(Shape1).Shade)
414.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
415.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
416.                 norm = SQR(xx * xx + yy * yy)
417.                 xx = xx / norm
418.                 yy = yy / norm
419.                 nx1 = xx
420.                 ny1 = yy
421.                 'CALL cline(x0, y0, x0 + nx1 * 15, y0 + ny1 * 15, Shape(Shape1).Shade)
422.  
423.                 ' Normal vector 2
424.                 x0 = PointChain(Shape2, ClosestIndex2).x
425.                 y0 = PointChain(Shape2, ClosestIndex2).y
426.                 'CALL ccircle(x0, y0, 3, Shape(Shape2).Shade)
427.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
428.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
429.                 norm = SQR(xx * xx + yy * yy)
430.                 xx = xx / norm
431.                 yy = yy / norm
432.                 nx2 = xx
433.                 ny2 = yy
434.                 'CALL cline(x0, y0, x0 + nx2 * 15, y0 + ny2 * 15, Shape(Shape2).Shade)
435.  
436.                 ' Perpendicular vector 1
437.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).CtrRot.x
438.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).CtrRot.y
439.                 px1 = -dy1
440.                 py1 = dx1
441.                 p1 = SQR(px1 * px1 + py1 * py1)
442.                 px1 = px1 / p1
443.                 py1 = py1 / p1
444.                 'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + px1 * 15, PointChain(Shape1, ClosestIndex1).y + py1 * 15, Shape(Shape1).Shade)
445.  
446.                 ' Perpendicular vector 2
447.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).CtrRot.x
448.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).CtrRot.y
449.                 px2 = -dy2
450.                 py2 = dx2
451.                 p2 = SQR(px2 * px2 + py2 * py2)
452.                 px2 = px2 / p2
453.                 py2 = py2 / p2
454.                 'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + px2 * 15, PointChain(Shape2, ClosestIndex2).y + py2 * 15, Shape(Shape2).Shade)
455.  
456.                 ' Angular velocity vector 1
457.                 w1 = Shape(Shape1).Omega
458.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
459.                 vx1 = w1 * r1 * px1
460.                 vy1 = w1 * r1 * py1
461.                 'CALL cline(PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, PointChain(Shape1, ClosestIndex1).x + vx1 * 5, PointChain(Shape1, ClosestIndex1).y + vy1 * 5, Shape(Shape1).Shade)
462.  
463.                 ' Angular velocity vector 2
464.                 w2 = Shape(Shape2).Omega
465.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
466.                 vx2 = w2 * r2 * px2
467.                 vy2 = w2 * r2 * py2
468.                 'CALL cline(PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, PointChain(Shape2, ClosestIndex2).x + vx2 * 5, PointChain(Shape2, ClosestIndex2).y + vy2 * 5, Shape(Shape2).Shade)
469.  
470.                 ' Mass terms
471.                 m1 = Shape(Shape1).Mass
472.                 i1 = Shape(Shape1).MOI
473.                 m2 = Shape(Shape2).Mass
474.                 i2 = Shape(Shape2).MOI
475.                 mu = 1 / (1 / m1 + 1 / m2)
476.  
477.                 ' Velocity differential 1
478.                 vtx1 = Shape(Shape1).Velocity.x + vx1
479.                 vty1 = Shape(Shape1).Velocity.y + vy1
480.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
481.  
482.                 ' Velocity differential 2
483.                 vtx2 = Shape(Shape2).Velocity.x + vx2
484.                 vty2 = Shape(Shape2).Velocity.y + vy2
485.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
486.  
487.                 ' Velocity differential total
488.                 dvtx = vtx2 - vtx1
489.                 dvty = vty2 - vty1
490.  
491.                 ' Geometry
492.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
493.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
494.  
495.                 ' Momentum exchange
496.                 qx1 = nx1 * 2 * mu * n1dotdvt
497.                 qy1 = ny1 * 2 * mu * n1dotdvt
498.                 qx2 = nx2 * 2 * mu * n2dotdvt
499.                 qy2 = ny2 * 2 * mu * n2dotdvt
500.  
501.                 ' Momentum exchange unit vector
502.                 q1 = SQR(qx1 * qx1 + qy1 * qy1)
503.                 qhatx1 = qx1 / q1
504.                 qhaty1 = qy1 / q1
505.                 q2 = SQR(qx2 * qx2 + qy2 * qy2)
506.                 qhatx2 = qx2 / q2
507.                 qhaty2 = qy2 / q2
508.  
509.                 ' Undo previous motion
510.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -Shape(Shape1).Omega)
511.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -Shape(Shape2).Omega)
512.                 vtemp.x = -Shape(Shape1).Velocity.x
513.                 vtemp.y = -Shape(Shape1).Velocity.y
514.                 CALL TranslateShape(Shape1, vtemp)
515.                 vtemp.x = -Shape(Shape2).Velocity.x
516.                 vtemp.y = -Shape(Shape2).Velocity.y
517.                 CALL TranslateShape(Shape2, vtemp)
518.  
519.                 ' Separate along normal
520.                 vtemp.x = -nx1 * (v1 + .05)
521.                 vtemp.y = -ny1 * (v1 + .05)
522.                 CALL TranslateShape(Shape1, vtemp)
523.                 vtemp.x = -nx2 * (v2 + .05)
524.                 vtemp.y = -ny2 * (v2 + .05)
525.                 CALL TranslateShape(Shape2, vtemp)
526.  
527.                 ' Translational impulse
528.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
529.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
530.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
531.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
532.                 f1 = -q1dotn1 * n1dotr1hat
533.                 f2 = -q2dotn2 * n2dotr2hat
534.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
535.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
536.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
537.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
538.  
539.                 ' Angular impulse
540.                 q1dotp1 = qx1 * px1 + qy1 * py1
541.                 q2dotp2 = qx2 * px2 + qy2 * py2
542.                 dw1 = r1 * q1dotp1 / i1
543.                 dw2 = -r2 * q2dotp2 / i2
544.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
545.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
546.                 Shape(Shape1).Omega = Shape(Shape1).Omega + dw1
547.                 Shape(Shape2).Omega = Shape(Shape2).Omega + dw2
548.  
549.                 ' Dent along normal
550.                 'PointChain(Shape1, ClosestIndex1).x = PointChain(Shape1, ClosestIndex1).x - v1 * nx1
551.                 'PointChain(Shape1, ClosestIndex1).y = PointChain(Shape1, ClosestIndex1).y - v1 * ny1
552.                 'PointChain(Shape2, ClosestIndex2).x = PointChain(Shape2, ClosestIndex2).x - v2 * nx2
553.                 'PointChain(Shape2, ClosestIndex2).y = PointChain(Shape2, ClosestIndex2).y - v2 * ny2
554.                 'CALL SmoothShape(Shape1, Shape(Shape1).Elements, 1)
555.                 'CALL SmoothShape(Shape2, Shape(Shape2).Elements, 1)
556.  
557.                 ' Static friction
558.                 IF (Shape(Shape1).Velocity.x * Shape(Shape1).Velocity.x < .05) THEN Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * .001
559.                 IF (Shape(Shape1).Velocity.y * Shape(Shape1).Velocity.y < .05) THEN Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * .001
560.                 IF (Shape(Shape2).Velocity.x * Shape(Shape2).Velocity.x < .05) THEN Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * .001
561.                 IF (Shape(Shape2).Velocity.y * Shape(Shape2).Velocity.y < .05) THEN Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * .001
562.                 IF (Shape(Shape1).Omega * Shape(Shape1).Omega < .0001) THEN Shape(Shape1).Omega = Shape(Shape1).Omega * .01
563.                 IF (Shape(Shape2).Omega * Shape(Shape2).Omega < .0001) THEN Shape(Shape2).Omega = Shape(Shape2).Omega * .01
564.  
565.                 CALL snd(100 * (v1 + v2) / 2, 1)
566.  
567.             END IF
568.         NEXT
569.     END IF
570.  
571.     FOR ShapeIndex = 1 TO ShapeCount
572.         dx = Shape(ShapeIndex).CtrMass.x - Shape(ShapeIndex).CtrRot.x
573.         dy = Shape(ShapeIndex).CtrMass.y - Shape(ShapeIndex).CtrRot.y
574.  
575.         cx = Shape(ShapeIndex).CtrMass.x
576.         cy = Shape(ShapeIndex).CtrMass.y
577.         'Gravity.x = -(cx / Shape(ShapeIndex).Mass) / 20
578.         'Gravity.y = -(cy / Shape(ShapeIndex).Mass) / 20
579.  
580.         'torque = dx * Gravity.y - dy * Gravity.x
581.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
582.  
583.         ' Rotation update
584.         CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
585.  
586.         ' Velocity update
587.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Gravity.x
588.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Gravity.y
589.         CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
590.  
591.         ' Damping
592.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .995
593.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .995
594.         Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .995
595.  
596.     NEXT
597.  
598.     CALL Graphics
599.     _LIMIT 60
600. LOOP
601.  
602. END
603.  
604. SUB Graphics
605.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
606.     FOR ShapeIndex = 1 TO ShapeCount
607.         LOCATE 1, 1: PRINT "Tap arrow keys (don't hold)."
608.         'LOCATE 2, 1: PRINT ProximalPairsCount, CollisionCount
609.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
610.             x1 = PointChain(ShapeIndex, i).x
611.             y1 = PointChain(ShapeIndex, i).y
612.             x2 = PointChain(ShapeIndex, i + 1).x
613.             y2 = PointChain(ShapeIndex, i + 1).y
614.             'CALL cpset(x1, y1, Shape(ShapeIndex).Shade)
615.             CALL cline(x1, y1, x2, y2, Shape(ShapeIndex).Shade)
616.         NEXT
617.         x1 = PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x
618.         y1 = PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y
619.         x2 = PointChain(ShapeIndex, 1).x
620.         y2 = PointChain(ShapeIndex, 1).y
621.         'CALL cpset(x1, y1, Shape(ShapeIndex).Shade)
622.         CALL cline(x1, y1, x2, y2, Shape(ShapeIndex).Shade)
623.         CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
624.     NEXT
625.     _DISPLAY
626. END SUB
627.  
628. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
629.     DIM l AS Vector
630.     DIM r AS Vector
631.     li = i - 1
632.     ri = i + 1
633.     IF (i = 1) THEN li = Shape(k).Elements
634.     IF (i = Shape(k).Elements) THEN ri = 1
635.     l.x = PointChain(k, li).x
636.     r.x = PointChain(k, ri).x
637.     dx = r.x - l.x
638.     CalculateNormalX = dx
639. END FUNCTION
640.  
641. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
642.     DIM l AS Vector
643.     DIM r AS Vector
644.     li = i - 1
645.     ri = i + 1
646.     IF (i = 1) THEN li = Shape(k).Elements
647.     IF (i = Shape(k).Elements) THEN ri = 1
648.     l.y = PointChain(k, li).y
649.     r.y = PointChain(k, ri).y
650.     dy = r.y - l.y
651.     CalculateNormalY = dy
652. END FUNCTION
653.  
654. SUB CalculateCtrMass (k AS INTEGER)
655.     xx = 0
656.     yy = 0
657.     FOR i = 1 TO Shape(k).Elements
658.         xx = xx + PointChain(k, i).x
659.         yy = yy + PointChain(k, i).y
660.     NEXT
661.     Shape(k).CtrMass.x = xx / Shape(k).Elements
662.     Shape(k).CtrMass.y = yy / Shape(k).Elements
663. END SUB
664.  
665. SUB CalculateDiameter (k AS INTEGER)
666.     r2max = -1
667.     FOR i = 1 TO Shape(k).Elements
668.         xx = Shape(k).CtrMass.x - PointChain(k, i).x
669.         yy = Shape(k).CtrMass.y - PointChain(k, i).y
670.         r2 = xx * xx + yy * yy
671.         IF (r2 > r2max) THEN
672.             r2max = r2
673.         END IF
674.     NEXT
675.     Shape(k).Diameter = SQR(r2max)
676. END SUB
677.  
678. SUB CalculateMOI (k AS INTEGER)
679.     xx = 0
680.     yy = 0
681.     FOR i = 1 TO Shape(k).Elements
682.         xx = xx + (Shape(k).CtrRot.x - PointChain(k, i).x) ^ 2
683.         yy = yy + (Shape(k).CtrRot.y - PointChain(k, i).y) ^ 2
684.     NEXT
685.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Elements)
686. END SUB
687.  
688. SUB TranslateShape (k AS INTEGER, c AS Vector)
689.     FOR i = 1 TO Shape(k).Elements
690.         PointChain(k, i).x = PointChain(k, i).x + c.x
691.         PointChain(k, i).y = PointChain(k, i).y + c.y
692.     NEXT
693.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
694.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
695.     Shape(k).CtrMass.x = Shape(k).CtrMass.x + c.x
696.     Shape(k).CtrMass.y = Shape(k).CtrMass.y + c.y
697. END SUB
698.  
699. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
700.     FOR i = 1 TO Shape(k).Elements
701.         xx = PointChain(k, i).x - c.x
702.         yy = PointChain(k, i).y - c.y
703.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
704.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
705.     NEXT
706.     xx = Shape(k).CtrMass.x - c.x
707.     yy = Shape(k).CtrMass.y - c.y
708.     Shape(k).CtrMass.x = c.x + xx * COS(da) - yy * SIN(da)
709.     Shape(k).CtrMass.y = c.y + yy * COS(da) + xx * SIN(da)
710. END SUB
711.  
712. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
713.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
714. END SUB
715.  
716. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
717.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
718. END SUB
719.  
720. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
721.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
722. END SUB
723.  
724. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
725.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
726. END SUB
727.  
728. SUB CreateShape
729.     rawresolution = 7.5 ' Raw curve resolution.
730.     targetpoints = 120 ' Number of points per curve.
731.     smoothiterations = 15 ' Magnitude of smooth effect.
732.  
733.     ShapeCount = ShapeCount + 1
734.  
735.     numpoints = 0
736.     xold = 999999
737.     yold = 999999
738.  
739.     WHILE _MOUSEINPUT: WEND
740.  
741.     ' Gather raw data for one curve at a time.
742.     ' Click+drag mouse button 1 to trace out a curve.
743.     DO
744.         DO WHILE _MOUSEINPUT
745.             x = _MOUSEX
746.             y = _MOUSEY
747.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
748.                 IF _MOUSEBUTTON(1) THEN
749.                     x = x - (_WIDTH / 2)
750.                     y = -y + (_HEIGHT / 2)
751.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
752.  
753.                     ' Collect data only if the new point is sufficiently far away from the previous point.
754.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
755.                         numpoints = numpoints + 1
756.                         PointChain(ShapeCount, numpoints).x = x
757.                         PointChain(ShapeCount, numpoints).y = y
758.                         CALL cpset(x, y, _RGB(255, 255, 255))
759.                         xold = x
760.                         yold = y
761.                     END IF
762.                 END IF
763.             END IF
764.         LOOP
765.         _DISPLAY
766.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
767.  
768.     ' If the curve contains less than the minimum numer of points, use interpolation to fill in the gaps.
769.     DO WHILE (numpoints < targetpoints)
770.  
771.         ' Determine the pair of neighboring points that have the greatest separation of all pairs.
772.         rad2max = -1
773.         kmax = -1
774.         FOR k = 1 TO numpoints - 1
775.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
776.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
777.             rad2 = xfac ^ 2 + yfac ^ 2
778.             IF rad2 > rad2max THEN
779.                 kmax = k
780.                 rad2max = rad2
781.             END IF
782.         NEXT
783.         '''
784.         cornercase = 0
785.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
786.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
787.         rad2 = xfac ^ 2 + yfac ^ 2
788.         IF rad2 > rad2max THEN
789.             kmax = numpoints
790.             rad2max = rad2
791.             cornercase = 1
792.         END IF
793.         '''
794.         IF (cornercase = 0) THEN
795.  
796.             numpoints = numpoints + 1
797.  
798.             ' Starting next to kmax, create a `gap' by shifting all other points by one index.
799.             FOR j = numpoints TO kmax + 1 STEP -1
800.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
801.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
802.             NEXT
803.  
804.             ' Fill the gap with a new point whose position is determined by the average of its neighbors.
805.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
806.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
807.  
808.         ELSE
809.             numpoints = numpoints + 1
810.             xx = PointChain(ShapeCount, numpoints - 1).x
811.             yy = PointChain(ShapeCount, numpoints - 1).y
812.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
813.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
814.         END IF
815.  
816.     LOOP
817.  
818.     ' At this stage, the curve still has all of its sharp edges. Use a `relaxation method' to smooth.
819.     ' The new position of a point is equal to the average position of its neighboring points.
820.     CALL SmoothShape(ShapeCount, numpoints, smoothiterations)
821.  
822.     Shape(ShapeCount).Elements = numpoints
823.     Shape(ShapeCount).Mass = numpoints
824.     Shape(ShapeCount).Velocity.x = 0
825.     Shape(ShapeCount).Velocity.y = 0
826.     Shape(ShapeCount).Omega = 0
827.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
828.     CALL CalculateCtrMass(ShapeCount)
829.     Shape(ShapeCount).CtrRot.x = Shape(ShapeCount).CtrMass.x
830.     Shape(ShapeCount).CtrRot.y = Shape(ShapeCount).CtrMass.y
831.     CALL CalculateDiameter(ShapeCount)
832.     CALL CalculateMOI(ShapeCount)
833.  
834. END SUB
835.  
836. SUB SmoothShape (i AS INTEGER, n AS INTEGER, s AS INTEGER)
837.     FOR j = 1 TO s
838.         FOR k = 2 TO n - 1
839.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
840.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
841.         NEXT
842.         FOR k = 2 TO n - 1
843.             PointChain(i, k).x = TempChain(i, k).x
844.             PointChain(i, k).y = TempChain(i, k).y
845.         NEXT
846.     NEXT
847. END SUB
848.  
849. SUB snd (frq, dur)
850.     IF ((frq >= 37) AND (frq <= 32767 - 25000)) THEN
851.         SOUND frq, dur
852.     END IF
853. END SUB
854.  

[STxAxTIC]

Fixed up the walls, and added gravity to the previous situation:

Code: QB64: [Select]

1. ' Display
2. SCREEN _NEWIMAGE(800, 600, 32)
3. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
4.  
5. ' Meta
6. RANDOMIZE TIMER
7.  
8. ' Data
9. TYPE Vector
10.     x AS DOUBLE
11.     y AS DOUBLE
12. END TYPE
13.  
14. TYPE Object
15.     CtrMass AS Vector
16.     CtrRot AS Vector
17.     Diameter AS DOUBLE
18.     Elements AS INTEGER
19.     Mass AS DOUBLE
20.     MOI AS DOUBLE
21.     Omega AS DOUBLE
22.     Shade AS _UNSIGNED LONG
23.     Velocity AS Vector
24. END TYPE
25.  
26. DIM vtemp AS Vector
27.  
28. ' Statics
29. DIM SHARED Shape(1000) AS Object
30. DIM SHARED PointChain(1000, 5000) AS Vector
31. DIM SHARED TempChain(1000, 5000) AS Vector
32. DIM SHARED ShapeCount AS INTEGER
33. ShapeCount = 0
34.  
35. ' Dynamics
36. DIM SHARED CollisionCount AS INTEGER
37. CollisionCount = 0
38.  
39. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
40. DIM SHARED ProximalPairsCount
41.  
42. DIM Gravity AS Vector
43. Gravity.x = 0
44. Gravity.y = -3
45.  
46. ' Main objecct
47.  
48. ShapeCount = ShapeCount + 1
49. Shape(ShapeCount).CtrRot.x = -200
50. Shape(ShapeCount).CtrRot.y = 0
51. i = 0
52. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
53.     i = i + 1
54.     r = 40 + 25 * COS(1.5 * j) ^ 2
55.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
56.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
57. NEXT
58. Shape(ShapeCount).Elements = i
59. Shape(ShapeCount).Mass = i
60. Shape(ShapeCount).Velocity.x = 0
61. Shape(ShapeCount).Velocity.y = 0
62. Shape(ShapeCount).Omega = 0
63. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
64. CALL CalculateCtrMass(ShapeCount)
65. CALL CalculateDiameter(ShapeCount)
66. CALL CalculateMOI(ShapeCount)
67.  
68. ' Balls
69. x0 = 120
70. y0 = 0
71. rr = 22.5
72. gg = 2 * rr + 20
73. xf = COS(30 * 3.14159 / 180)
74. yf = SIN(30 * 3.14159 / 180)
75. gx = gg * xf
76. gy = gg * yf
77. CALL NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, rr)
78. CALL NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, rr)
79. CALL NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, rr)
80. CALL NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, rr)
81. CALL NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, rr)
82. CALL NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, rr)
83. CALL NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, rr)
84. CALL NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, rr)
85. CALL NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, rr)
86. CALL NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, rr)
87.  
88. ' Walls
89. px = 40
90. py = 10
91. x0 = 0
92. y0 = -(_HEIGHT / 2) + 2 * py
93. FOR n = -1 TO 1 STEP 2
94.     FOR k = 0 TO ((_WIDTH / 2) - px) STEP px * 1.1
95.         CALL NewAutoBrick(x0 + k, n * y0, px, py)
96.         IF (k > 0) THEN CALL NewAutoBrick(x0 - k, n * y0, px, py)
97.     NEXT
98. NEXT
99. px = 10
100. py = 40
101. x0 = -(_WIDTH) / 2 + 2 * px
102. y0 = 0
103. FOR n = -1 TO 1 STEP 2
104.     FOR k = 0 TO ((_HEIGHT / 2)) - py STEP py * 1.1
105.         CALL NewAutoBrick(n * x0, y0 + k, px, py)
106.         IF (k > 0) THEN CALL NewAutoBrick(n * x0, y0 - k, px, py)
107.     NEXT
108. NEXT
109.  
110. CALL Graphics
111. LOCATE 10, 15: PRINT "PRESS ANY KEY TO BEGIN"
112. _DISPLAY
113. DO: LOOP UNTIL _KEYHIT
114. Shape(1).Velocity.x = 5
115. Shape(1).Velocity.y = 1
116. Shape(1).Omega = .1
117.  
118. DO
119.  
120.     kk = _KEYHIT
121.     SELECT CASE kk
122.         CASE 32
123.             CLS
124.             CALL Graphics
125.             LOCATE 1, 1: PRINT "Click & Drag counter-clockwise to create a shape."
126.             CALL NewMouseShape
127.         CASE 18432 ' Up arrow
128.             Shape(1).Velocity.y = Shape(1).Velocity.y + 5
129.         CASE 20480 ' Down arrow
130.             Shape(1).Velocity.y = Shape(1).Velocity.y - 5
131.         CASE 19200 ' Left arrow
132.             Shape(1).Velocity.x = Shape(1).Velocity.x - 5
133.         CASE 19712 ' Right arrow
134.             Shape(1).Velocity.x = Shape(1).Velocity.x + 5
135.     END SELECT
136.     IF (kk) THEN
137.         _KEYCLEAR
138.     END IF
139.  
140.     ' Proximity detection
141.     ProximalPairsCount = 0
142.     Shape1 = 0
143.     Shape2 = 0
144.     FOR j = 1 TO ShapeCount
145.         FOR k = j + 1 TO ShapeCount
146.             dx = Shape(j).CtrMass.x - Shape(k).CtrMass.x
147.             dy = Shape(j).CtrMass.y - Shape(k).CtrMass.y
148.             dr = SQR(dx * dx + dy * dy)
149.             IF (dr < 1.15 * (Shape(j).Diameter + Shape(k).Diameter)) THEN
150.                 ProximalPairsCount = ProximalPairsCount + 1
151.                 ProximalPairs(ProximalPairsCount, 1) = j
152.                 ProximalPairs(ProximalPairsCount, 2) = k
153.                 Shape1 = j
154.                 Shape2 = k
155.             END IF
156.         NEXT
157.     NEXT
158.  
159.     IF (ProximalPairsCount > 0) THEN
160.         FOR n = 1 TO ProximalPairsCount
161.             Shape1 = ProximalPairs(n, 1)
162.             Shape2 = ProximalPairs(n, 2)
163.  
164.             ' Collision detection
165.             rmin = 999 ^ 999
166.             ClosestIndex1 = 0
167.             ClosestIndex2 = 0
168.             FOR j = 1 TO Shape(Shape1).Elements
169.                 FOR k = 1 TO Shape(Shape2).Elements
170.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
171.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
172.                     r2 = dx * dx + dy * dy
173.                     IF (r2 < rmin) THEN
174.                         rmin = r2
175.                         ClosestIndex1 = j
176.                         ClosestIndex2 = k
177.                     END IF
178.                 NEXT
179.             NEXT
180.  
181.             IF (rmin <= 2) THEN
182.                 CollisionCount = CollisionCount + 1
183.  
184.                 ' Normal vector 1
185.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
186.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
187.                 norm = SQR(xx * xx + yy * yy)
188.                 xx = xx / norm
189.                 yy = yy / norm
190.                 nx1 = xx
191.                 ny1 = yy
192.  
193.                 ' Normal vector 2
194.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
195.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
196.                 norm = SQR(xx * xx + yy * yy)
197.                 xx = xx / norm
198.                 yy = yy / norm
199.                 nx2 = xx
200.                 ny2 = yy
201.  
202.                 ' Perpendicular vector 1
203.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).CtrRot.x
204.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).CtrRot.y
205.                 px1 = -dy1
206.                 py1 = dx1
207.                 p1 = SQR(px1 * px1 + py1 * py1)
208.                 px1 = px1 / p1
209.                 py1 = py1 / p1
210.  
211.                 ' Perpendicular vector 2
212.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).CtrRot.x
213.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).CtrRot.y
214.                 px2 = -dy2
215.                 py2 = dx2
216.                 p2 = SQR(px2 * px2 + py2 * py2)
217.                 px2 = px2 / p2
218.                 py2 = py2 / p2
219.  
220.                 ' Angular velocity vector 1
221.                 w1 = Shape(Shape1).Omega
222.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
223.                 vx1 = w1 * r1 * px1
224.                 vy1 = w1 * r1 * py1
225.  
226.                 ' Angular velocity vector 2
227.                 w2 = Shape(Shape2).Omega
228.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
229.                 vx2 = w2 * r2 * px2
230.                 vy2 = w2 * r2 * py2
231.  
232.                 ' Mass terms
233.                 m1 = Shape(Shape1).Mass
234.                 i1 = Shape(Shape1).MOI
235.                 m2 = Shape(Shape2).Mass
236.                 i2 = Shape(Shape2).MOI
237.                 mu = 1 / (1 / m1 + 1 / m2)
238.  
239.                 ' Velocity differential 1
240.                 vtx1 = Shape(Shape1).Velocity.x + vx1
241.                 vty1 = Shape(Shape1).Velocity.y + vy1
242.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
243.  
244.                 ' Velocity differential 2
245.                 vtx2 = Shape(Shape2).Velocity.x + vx2
246.                 vty2 = Shape(Shape2).Velocity.y + vy2
247.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
248.  
249.                 ' Velocity differential total
250.                 dvtx = vtx2 - vtx1
251.                 dvty = vty2 - vty1
252.  
253.                 ' Geometry
254.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
255.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
256.  
257.                 ' Momentum exchange
258.                 qx1 = nx1 * 2 * mu * n1dotdvt
259.                 qy1 = ny1 * 2 * mu * n1dotdvt
260.                 qx2 = nx2 * 2 * mu * n2dotdvt
261.                 qy2 = ny2 * 2 * mu * n2dotdvt
262.  
263.                 ' Momentum exchange unit vector
264.                 q1 = SQR(qx1 * qx1 + qy1 * qy1)
265.                 qhatx1 = qx1 / q1
266.                 qhaty1 = qy1 / q1
267.                 q2 = SQR(qx2 * qx2 + qy2 * qy2)
268.                 qhatx2 = qx2 / q2
269.                 qhaty2 = qy2 / q2
270.  
271.                 ' Undo previous motion
272.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -Shape(Shape1).Omega)
273.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -Shape(Shape2).Omega)
274.                 vtemp.x = -Shape(Shape1).Velocity.x
275.                 vtemp.y = -Shape(Shape1).Velocity.y
276.                 CALL TranslateShape(Shape1, vtemp)
277.                 vtemp.x = -Shape(Shape2).Velocity.x
278.                 vtemp.y = -Shape(Shape2).Velocity.y
279.                 CALL TranslateShape(Shape2, vtemp)
280.  
281.                 ' Separate along normal
282.                 vtemp.x = -nx1 * ((v1 + v1 / m1) + .01)
283.                 vtemp.y = -ny1 * ((v1 + v1 / m1) + .01)
284.                 CALL TranslateShape(Shape1, vtemp)
285.                 vtemp.x = -nx2 * ((v2 + v2 / m2) + .01)
286.                 vtemp.y = -ny2 * ((v2 + v2 / m2) + .01)
287.                 CALL TranslateShape(Shape2, vtemp)
288.  
289.                 ' Translational impulse
290.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
291.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
292.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
293.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
294.                 f1 = -q1dotn1 * n1dotr1hat
295.                 f2 = -q2dotn2 * n2dotr2hat
296.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
297.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
298.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
299.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
300.  
301.                 ' Angular impulse
302.                 q1dotp1 = qx1 * px1 + qy1 * py1
303.                 q2dotp2 = qx2 * px2 + qy2 * py2
304.                 dw1 = r1 * q1dotp1 / i1
305.                 dw2 = -r2 * q2dotp2 / i2
306.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
307.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
308.                 Shape(Shape1).Omega = Shape(Shape1).Omega + dw1
309.                 Shape(Shape2).Omega = Shape(Shape2).Omega + dw2
310.  
311.                 ' Dent
312.                 'PointChain(Shape1, ClosestIndex1).x = PointChain(Shape1, ClosestIndex1).x - v1 * nx1
313.                 'PointChain(Shape1, ClosestIndex1).y = PointChain(Shape1, ClosestIndex1).y - v1 * ny1
314.                 'PointChain(Shape2, ClosestIndex2).x = PointChain(Shape2, ClosestIndex2).x - v2 * nx2
315.                 'PointChain(Shape2, ClosestIndex2).y = PointChain(Shape2, ClosestIndex2).y - v2 * ny2
316.                 'CALL SmoothShape(Shape1, Shape(Shape1).Elements, 1)
317.                 'CALL SmoothShape(Shape2, Shape(Shape2).Elements, 1)
318.  
319.                 ' Static friction
320.                 IF (Shape(Shape1).Velocity.x * Shape(Shape1).Velocity.x < .075) THEN Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * .001
321.                 IF (Shape(Shape1).Velocity.y * Shape(Shape1).Velocity.y < .075) THEN Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * .001
322.                 IF (Shape(Shape2).Velocity.x * Shape(Shape2).Velocity.x < .075) THEN Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * .001
323.                 IF (Shape(Shape2).Velocity.y * Shape(Shape2).Velocity.y < .075) THEN Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * .001
324.                 'IF (Shape(Shape1).Omega * Shape(Shape1).Omega < .0001) THEN Shape(Shape1).Omega = Shape(Shape1).Omega * .01
325.                 'IF (Shape(Shape2).Omega * Shape(Shape2).Omega < .0001) THEN Shape(Shape2).Omega = Shape(Shape2).Omega * .01
326.  
327.                 CALL snd(100 * (v1 + v2) / 2, 1)
328.  
329.             END IF
330.         NEXT
331.     END IF
332.  
333.     FOR ShapeIndex = 1 TO ShapeCount
334.         dx = Shape(ShapeIndex).CtrMass.x - Shape(ShapeIndex).CtrRot.x
335.         dy = Shape(ShapeIndex).CtrMass.y - Shape(ShapeIndex).CtrRot.y
336.  
337.         cx = Shape(ShapeIndex).CtrMass.x
338.         cy = Shape(ShapeIndex).CtrMass.y
339.         'Gravity.x = -(cx) / 20
340.         'Gravity.y = -(cy) / 20
341.  
342.         'torque = dx * Gravity.y - dy * Gravity.x
343.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
344.  
345.         ' Rotation update
346.         CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
347.  
348.         ' Velocity update
349.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Gravity.x / Shape(ShapeIndex).Mass
350.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Gravity.y / Shape(ShapeIndex).Mass
351.         CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
352.  
353.         ' Damping
354.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .995
355.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .995
356.         Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .995
357.  
358.     NEXT
359.  
360.     CALL Graphics
361.     _LIMIT 60
362. LOOP
363.  
364. END
365.  
366. SUB Graphics
367.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
368.     FOR ShapeIndex = 1 TO ShapeCount
369.         LOCATE 1, 1: PRINT "Tap arrow keys (don't hold)."
370.         LOCATE 2, 1: PRINT ProximalPairsCount, CollisionCount
371.         CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
372.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
373.             CALL cline(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, PointChain(ShapeIndex, i + 1).x, PointChain(ShapeIndex, i + 1).y, Shape(ShapeIndex).Shade)
374.             'CALL cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
375.         NEXT
376.         CALL cline(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
377.         'CALL cpset(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
378.     NEXT
379.     _DISPLAY
380. END SUB
381.  
382. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
383.     DIM l AS Vector
384.     DIM r AS Vector
385.     li = i - 1
386.     ri = i + 1
387.     IF (i = 1) THEN li = Shape(k).Elements
388.     IF (i = Shape(k).Elements) THEN ri = 1
389.     l.x = PointChain(k, li).x
390.     r.x = PointChain(k, ri).x
391.     dx = r.x - l.x
392.     CalculateNormalX = dx
393. END FUNCTION
394.  
395. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
396.     DIM l AS Vector
397.     DIM r AS Vector
398.     li = i - 1
399.     ri = i + 1
400.     IF (i = 1) THEN li = Shape(k).Elements
401.     IF (i = Shape(k).Elements) THEN ri = 1
402.     l.y = PointChain(k, li).y
403.     r.y = PointChain(k, ri).y
404.     dy = r.y - l.y
405.     CalculateNormalY = dy
406. END FUNCTION
407.  
408. SUB CalculateCtrMass (k AS INTEGER)
409.     xx = 0
410.     yy = 0
411.     FOR i = 1 TO Shape(k).Elements
412.         xx = xx + PointChain(k, i).x
413.         yy = yy + PointChain(k, i).y
414.     NEXT
415.     Shape(k).CtrMass.x = xx / Shape(k).Elements
416.     Shape(k).CtrMass.y = yy / Shape(k).Elements
417. END SUB
418.  
419. SUB CalculateDiameter (k AS INTEGER)
420.     r2max = -1
421.     FOR i = 1 TO Shape(k).Elements
422.         xx = Shape(k).CtrMass.x - PointChain(k, i).x
423.         yy = Shape(k).CtrMass.y - PointChain(k, i).y
424.         r2 = xx * xx + yy * yy
425.         IF (r2 > r2max) THEN
426.             r2max = r2
427.         END IF
428.     NEXT
429.     Shape(k).Diameter = SQR(r2max)
430. END SUB
431.  
432. SUB CalculateMOI (k AS INTEGER)
433.     xx = 0
434.     yy = 0
435.     FOR i = 1 TO Shape(k).Elements
436.         xx = xx + (Shape(k).CtrRot.x - PointChain(k, i).x) ^ 2
437.         yy = yy + (Shape(k).CtrRot.y - PointChain(k, i).y) ^ 2
438.     NEXT
439.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Elements)
440. END SUB
441.  
442. SUB TranslateShape (k AS INTEGER, c AS Vector)
443.     FOR i = 1 TO Shape(k).Elements
444.         PointChain(k, i).x = PointChain(k, i).x + c.x
445.         PointChain(k, i).y = PointChain(k, i).y + c.y
446.     NEXT
447.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
448.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
449.     Shape(k).CtrMass.x = Shape(k).CtrMass.x + c.x
450.     Shape(k).CtrMass.y = Shape(k).CtrMass.y + c.y
451. END SUB
452.  
453. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
454.     FOR i = 1 TO Shape(k).Elements
455.         xx = PointChain(k, i).x - c.x
456.         yy = PointChain(k, i).y - c.y
457.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
458.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
459.     NEXT
460.     xx = Shape(k).CtrMass.x - c.x
461.     yy = Shape(k).CtrMass.y - c.y
462.     Shape(k).CtrMass.x = c.x + xx * COS(da) - yy * SIN(da)
463.     Shape(k).CtrMass.y = c.y + yy * COS(da) + xx * SIN(da)
464. END SUB
465.  
466. SUB NewAutoBall (x1, y1, r1)
467.     pa = INT(RND * 3) + 1
468.     pb = INT(RND * 2) + 1
469.     ShapeCount = ShapeCount + 1
470.     Shape(ShapeCount).CtrRot.x = x1
471.     Shape(ShapeCount).CtrRot.y = y1
472.     i = 0
473.     FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
474.         i = i + 1
475.         r = r1 + 5 * COS(pa * j) ^ pb
476.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
477.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
478.     NEXT
479.     Shape(ShapeCount).Elements = i
480.     Shape(ShapeCount).Mass = i
481.     Shape(ShapeCount).Velocity.x = 0
482.     Shape(ShapeCount).Velocity.y = 0
483.     Shape(ShapeCount).Omega = 0
484.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
485.     CALL CalculateCtrMass(ShapeCount)
486.     CALL CalculateDiameter(ShapeCount)
487.     CALL CalculateMOI(ShapeCount)
488. END SUB
489.  
490. SUB NewAutoBrick (x1, y1, wx, wy)
491.     ShapeCount = ShapeCount + 1
492.     Shape(ShapeCount).CtrRot.x = x1
493.     Shape(ShapeCount).CtrRot.y = y1
494.     i = 0
495.     FOR j = -wy / 2 TO wy / 2 STEP 2
496.         i = i + 1
497.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + wx / 2
498.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + j
499.     NEXT
500.     FOR j = wx / 2 TO -wx / 2 STEP -2
501.         i = i + 1
502.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + j
503.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + wy / 2
504.     NEXT
505.     FOR j = wy / 2 TO -wy / 2 STEP -2
506.         i = i + 1
507.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x - wx / 2
508.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + j
509.     NEXT
510.     FOR j = -wx / 2 TO wx / 2 STEP 2
511.         i = i + 1
512.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + j
513.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y - wy / 2
514.     NEXT
515.     Shape(ShapeCount).Elements = i
516.     Shape(ShapeCount).Mass = 999 ^ 999
517.     Shape(ShapeCount).Velocity.x = 0
518.     Shape(ShapeCount).Velocity.y = 0
519.     Shape(ShapeCount).Omega = 0
520.     Shape(ShapeCount).Shade = _RGB(100, 100, 100)
521.     CALL CalculateCtrMass(ShapeCount)
522.     CALL CalculateDiameter(ShapeCount)
523.     CALL CalculateMOI(ShapeCount)
524.     Shape(ShapeCount).MOI = 999 ^ 999
525. END SUB
526.  
527.  
528. SUB NewMouseShape
529.     rawresolution = 7.5 ' Raw curve resolution.
530.     targetpoints = 120 ' Number of points per curve.
531.     smoothiterations = 15 ' Magnitude of smooth effect.
532.  
533.     ShapeCount = ShapeCount + 1
534.  
535.     numpoints = 0
536.     xold = 999999
537.     yold = 999999
538.  
539.     WHILE _MOUSEINPUT: WEND
540.  
541.     ' Gather raw data for one curve at a time.
542.     ' Click+drag mouse button 1 to trace out a curve.
543.     DO
544.         DO WHILE _MOUSEINPUT
545.             x = _MOUSEX
546.             y = _MOUSEY
547.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
548.                 IF _MOUSEBUTTON(1) THEN
549.                     x = x - (_WIDTH / 2)
550.                     y = -y + (_HEIGHT / 2)
551.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
552.  
553.                     ' Collect data only if the new point is sufficiently far away from the previous point.
554.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
555.                         numpoints = numpoints + 1
556.                         PointChain(ShapeCount, numpoints).x = x
557.                         PointChain(ShapeCount, numpoints).y = y
558.                         CALL cpset(x, y, _RGB(255, 255, 255))
559.                         xold = x
560.                         yold = y
561.                     END IF
562.                 END IF
563.             END IF
564.         LOOP
565.         _DISPLAY
566.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
567.  
568.     ' If the curve contains less than the minimum numer of points, use interpolation to fill in the gaps.
569.     DO WHILE (numpoints < targetpoints)
570.  
571.         ' Determine the pair of neighboring points that have the greatest separation of all pairs.
572.         rad2max = -1
573.         kmax = -1
574.         FOR k = 1 TO numpoints - 1
575.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
576.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
577.             rad2 = xfac ^ 2 + yfac ^ 2
578.             IF rad2 > rad2max THEN
579.                 kmax = k
580.                 rad2max = rad2
581.             END IF
582.         NEXT
583.         '''
584.         cornercase = 0
585.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
586.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
587.         rad2 = xfac ^ 2 + yfac ^ 2
588.         IF rad2 > rad2max THEN
589.             kmax = numpoints
590.             rad2max = rad2
591.             cornercase = 1
592.         END IF
593.         '''
594.         IF (cornercase = 0) THEN
595.  
596.             numpoints = numpoints + 1
597.  
598.             ' Starting next to kmax, create a `gap' by shifting all other points by one index.
599.             FOR j = numpoints TO kmax + 1 STEP -1
600.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
601.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
602.             NEXT
603.  
604.             ' Fill the gap with a new point whose position is determined by the average of its neighbors.
605.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
606.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
607.  
608.         ELSE
609.             numpoints = numpoints + 1
610.             xx = PointChain(ShapeCount, numpoints - 1).x
611.             yy = PointChain(ShapeCount, numpoints - 1).y
612.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
613.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
614.         END IF
615.  
616.     LOOP
617.  
618.     ' At this stage, the curve still has all of its sharp edges. Use a `relaxation method' to smooth.
619.     ' The new position of a point is equal to the average position of its neighboring points.
620.     CALL SmoothShape(ShapeCount, numpoints, smoothiterations)
621.  
622.     Shape(ShapeCount).Elements = numpoints
623.     Shape(ShapeCount).Mass = numpoints
624.     Shape(ShapeCount).Velocity.x = 0
625.     Shape(ShapeCount).Velocity.y = 0
626.     Shape(ShapeCount).Omega = 0
627.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
628.     CALL CalculateCtrMass(ShapeCount)
629.     Shape(ShapeCount).CtrRot.x = Shape(ShapeCount).CtrMass.x
630.     Shape(ShapeCount).CtrRot.y = Shape(ShapeCount).CtrMass.y
631.     CALL CalculateDiameter(ShapeCount)
632.     CALL CalculateMOI(ShapeCount)
633.  
634. END SUB
635.  
636. SUB SmoothShape (i AS INTEGER, n AS INTEGER, s AS INTEGER)
637.     FOR j = 1 TO s
638.         FOR k = 2 TO n - 1
639.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
640.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
641.         NEXT
642.         FOR k = 2 TO n - 1
643.             PointChain(i, k).x = TempChain(i, k).x
644.             PointChain(i, k).y = TempChain(i, k).y
645.         NEXT
646.     NEXT
647. END SUB
648.  
649. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
650.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
651. END SUB
652.  
653. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
654.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
655. END SUB
656.  
657. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
658.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
659. END SUB
660.  
661. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
662.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
663. END SUB
664.  
665. SUB snd (frq, dur)
666.     IF ((frq >= 37) AND (frq <= 32767 - 25000)) THEN
667.         SOUND frq, dur
668.     END IF
669. END SUB

[bplus]

POOL GAME UPDATE
 

LOL Man what a gas! I mean it even works, sorta ;-))

[STxAxTIC]

Thanks for trying it bplus. This is moving so fast, I'm embarrassed by how the code was X-1 hours ago for any given X. This version is the cutting edge:

Code: QB64: [Select]

1. ' Display
2. SCREEN _NEWIMAGE(800, 600, 32)
3. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
4.  
5. ' Meta
6. RANDOMIZE TIMER
7.  
8. ' Data
9. TYPE Vector
10.     x AS DOUBLE
11.     y AS DOUBLE
12. END TYPE
13.  
14. TYPE Object
15.     CtrMass AS Vector
16.     CtrRot AS Vector
17.     Diameter AS DOUBLE
18.     Elements AS INTEGER
19.     Mass AS DOUBLE
20.     MOI AS DOUBLE
21.     Omega AS DOUBLE
22.     Shade AS _UNSIGNED LONG
23.     Velocity AS Vector
24. END TYPE
25.  
26. DIM vtemp AS Vector
27.  
28. ' Statics
29. DIM SHARED Shape(1000) AS Object
30. DIM SHARED PointChain(1000, 5000) AS Vector
31. DIM SHARED TempChain(1000, 5000) AS Vector
32. DIM SHARED ShapeCount AS INTEGER
33. ShapeCount = 0
34.  
35. ' Dynamics
36. DIM SHARED CollisionCount AS INTEGER
37. CollisionCount = 0
38. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
39. DIM SHARED ProximalPairsCount
40.  
41. ' Environment
42. DIM ForceField AS Vector
43. ForceField.x = 0
44. ForceField.y = 0 '-8
45.  
46. ' Main objecct(s)
47. ShapeCount = ShapeCount + 1
48. Shape(ShapeCount).CtrRot.x = -200
49. Shape(ShapeCount).CtrRot.y = 0
50. i = 0
51. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
52.     i = i + 1
53.     r = 40 + 25 * COS(1.5 * j) ^ 2
54.     PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
55.     PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
56. NEXT
57. Shape(ShapeCount).Elements = i
58. Shape(ShapeCount).Mass = i
59. Shape(ShapeCount).Velocity.x = 0
60. Shape(ShapeCount).Velocity.y = 0
61. Shape(ShapeCount).Omega = 0
62. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
63. CALL CalculateCtrMass(ShapeCount)
64. CALL CalculateDiameter(ShapeCount)
65. CALL CalculateMOI(ShapeCount)
66.  
67. ' Balls
68. x0 = 120
69. y0 = 0
70. rr = 22.5
71. gg = 2 * rr + 20
72. xf = COS(30 * 3.14159 / 180)
73. yf = SIN(30 * 3.14159 / 180)
74. gx = gg * xf
75. gy = gg * yf
76. CALL NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, rr)
77. CALL NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, rr)
78. CALL NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, rr)
79. CALL NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, rr)
80. CALL NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, rr)
81. CALL NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, rr)
82. CALL NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, rr)
83. CALL NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, rr)
84. CALL NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, rr)
85. CALL NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, rr)
86.  
87. ' Walls
88. px = 40
89. py = 10
90. x0 = 0
91. y0 = -(_HEIGHT / 2) + 2 * py
92. FOR n = -1 TO 1 STEP 2
93.     FOR k = 0 TO ((_WIDTH / 2) - px) STEP px * 1.1
94.         CALL NewAutoBrick(x0 + k, n * y0, px, py, 0)
95.         IF (k > 0) THEN CALL NewAutoBrick(x0 - k, n * y0, px, py, 0)
96.     NEXT
97. NEXT
98. px = 10
99. py = 40
100. x0 = -(_WIDTH) / 2 + 2 * px
101. y0 = 0
102. FOR n = -1 TO 1 STEP 2
103.     FOR k = 0 TO ((_HEIGHT / 2)) - py STEP py * 1.1
104.         CALL NewAutoBrick(n * x0, y0 + k, px, py, 0)
105.         IF (k > 0) THEN CALL NewAutoBrick(n * x0, y0 - k, px, py, 0)
106.     NEXT
107. NEXT
108.  
109. ' Initial state
110. FOR k = 1 TO ShapeCount
111.     Shape(k).Velocity.x = -500 * RND / Shape(k).Mass
112.     Shape(k).Velocity.y = 0
113.     Shape(k).Omega = 5000 * RND / Shape(k).MOI
114.  
115. NEXT
116. Shape(1).Velocity.x = 4
117. Shape(1).Velocity.y = 0
118. Shape(1).Omega = .1
119. CALL Graphics
120.  
121. ' Prompt
122. LOCATE 10, 15: PRINT "PRESS ANY KEY TO BEGIN"
123. _DISPLAY
124. DO: LOOP UNTIL _KEYHIT
125. WHILE _MOUSEINPUT: WEND
126. _KEYCLEAR
127.  
128. ' Main loop
129. DO
130.  
131.     kk = _KEYHIT
132.     SELECT CASE kk
133.         CASE 32
134.             CLS
135.             CALL Graphics
136.             LOCATE 1, 1: PRINT "Click & Drag counter-clockwise to create a shape.                                 "
137.             LOCATE 2, 1: PRINT "                                                                                  "
138.             CALL NewMouseShape
139.         CASE 18432 ' Up arrow
140.             Shape(1).Velocity.y = Shape(1).Velocity.y + 3
141.         CASE 20480 ' Down arrow
142.             Shape(1).Velocity.y = Shape(1).Velocity.y - 3
143.         CASE 19200 ' Left arrow
144.             Shape(1).Velocity.x = Shape(1).Velocity.x - 3
145.         CASE 19712 ' Right arrow
146.             Shape(1).Velocity.x = Shape(1).Velocity.x + 3
147.     END SELECT
148.     IF (kk) THEN
149.         _KEYCLEAR
150.     END IF
151.  
152.     mb = 0
153.     DO WHILE _MOUSEINPUT
154.         x = _MOUSEX
155.         y = _MOUSEY
156.         IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
157.             IF (_MOUSEBUTTON(1)) THEN
158.                 IF (mb = 0) THEN
159.                     mb = 1
160.                     x = x - (_WIDTH / 2)
161.                     y = -y + (_HEIGHT / 2)
162.                     CALL NewAutoBrick(x, y, 40, 10, 0)
163.                     _DELAY .1
164.                 END IF
165.             END IF
166.             IF (_MOUSEBUTTON(2)) THEN
167.                 IF (mb = 0) THEN
168.                     mb = 1
169.                     x = x - (_WIDTH / 2)
170.                     y = -y + (_HEIGHT / 2)
171.                     CALL NewAutoBrick(x, y, 10, 40, 0)
172.                     _DELAY .1
173.                 END IF
174.             END IF
175.         END IF
176.     LOOP
177.  
178.     ' Proximity detection
179.     ProximalPairsCount = 0
180.     Shape1 = 0
181.     Shape2 = 0
182.     FOR j = 1 TO ShapeCount
183.         FOR k = j + 1 TO ShapeCount
184.             dx = Shape(j).CtrMass.x - Shape(k).CtrMass.x
185.             dy = Shape(j).CtrMass.y - Shape(k).CtrMass.y
186.             dr = SQR(dx * dx + dy * dy)
187.             IF (dr < 1.15 * (Shape(j).Diameter + Shape(k).Diameter)) THEN
188.                 ProximalPairsCount = ProximalPairsCount + 1
189.                 ProximalPairs(ProximalPairsCount, 1) = j
190.                 ProximalPairs(ProximalPairsCount, 2) = k
191.                 Shape1 = j
192.                 Shape2 = k
193.             END IF
194.         NEXT
195.     NEXT
196.  
197.     IF (ProximalPairsCount > 0) THEN
198.         FOR n = 1 TO ProximalPairsCount
199.             Shape1 = ProximalPairs(n, 1)
200.             Shape2 = ProximalPairs(n, 2)
201.  
202.             ' Collision detection
203.             rmin = 999 ^ 999
204.             ClosestIndex1 = 0
205.             ClosestIndex2 = 0
206.             FOR j = 1 TO Shape(Shape1).Elements
207.                 FOR k = 1 TO Shape(Shape2).Elements
208.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
209.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
210.                     r2 = dx * dx + dy * dy
211.                     IF (r2 < rmin) THEN
212.                         rmin = r2
213.                         ClosestIndex1 = j
214.                         ClosestIndex2 = k
215.                     END IF
216.                 NEXT
217.             NEXT
218.  
219.             IF (rmin <= 4) THEN
220.                 CollisionCount = CollisionCount + 1
221.  
222.                 ' Normal vector 1
223.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
224.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
225.                 norm = SQR(xx * xx + yy * yy)
226.                 xx = xx / norm
227.                 yy = yy / norm
228.                 nx1 = xx
229.                 ny1 = yy
230.  
231.                 ' Normal vector 2
232.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
233.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
234.                 norm = SQR(xx * xx + yy * yy)
235.                 xx = xx / norm
236.                 yy = yy / norm
237.                 nx2 = xx
238.                 ny2 = yy
239.  
240.                 ' Perpendicular vector 1
241.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).CtrRot.x
242.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).CtrRot.y
243.                 px1 = -dy1
244.                 py1 = dx1
245.                 p1 = SQR(px1 * px1 + py1 * py1)
246.                 px1 = px1 / p1
247.                 py1 = py1 / p1
248.  
249.                 ' Perpendicular vector 2
250.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).CtrRot.x
251.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).CtrRot.y
252.                 px2 = -dy2
253.                 py2 = dx2
254.                 p2 = SQR(px2 * px2 + py2 * py2)
255.                 px2 = px2 / p2
256.                 py2 = py2 / p2
257.  
258.                 ' Angular velocity vector 1
259.                 w1 = Shape(Shape1).Omega
260.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
261.                 vx1 = w1 * r1 * px1
262.                 vy1 = w1 * r1 * py1
263.  
264.                 ' Angular velocity vector 2
265.                 w2 = Shape(Shape2).Omega
266.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
267.                 vx2 = w2 * r2 * px2
268.                 vy2 = w2 * r2 * py2
269.  
270.                 ' Mass terms
271.                 m1 = Shape(Shape1).Mass
272.                 i1 = Shape(Shape1).MOI
273.                 m2 = Shape(Shape2).Mass
274.                 i2 = Shape(Shape2).MOI
275.                 mu = 1 / (1 / m1 + 1 / m2)
276.  
277.                 ' Velocity differential 1
278.                 vtx1 = Shape(Shape1).Velocity.x + vx1
279.                 vty1 = Shape(Shape1).Velocity.y + vy1
280.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
281.  
282.                 ' Velocity differential 2
283.                 vtx2 = Shape(Shape2).Velocity.x + vx2
284.                 vty2 = Shape(Shape2).Velocity.y + vy2
285.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
286.  
287.                 ' Velocity differential total
288.                 dvtx = vtx2 - vtx1
289.                 dvty = vty2 - vty1
290.  
291.                 ' Geometry
292.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
293.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
294.  
295.                 ' Momentum exchange
296.                 qx1 = nx1 * 2 * mu * n1dotdvt
297.                 qy1 = ny1 * 2 * mu * n1dotdvt
298.                 qx2 = nx2 * 2 * mu * n2dotdvt
299.                 qy2 = ny2 * 2 * mu * n2dotdvt
300.  
301.                 ' Momentum exchange unit vector
302.                 q1 = SQR(qx1 * qx1 + qy1 * qy1)
303.                 qhatx1 = qx1 / q1
304.                 qhaty1 = qy1 / q1
305.                 q2 = SQR(qx2 * qx2 + qy2 * qy2)
306.                 qhatx2 = qx2 / q2
307.                 qhaty2 = qy2 / q2
308.  
309.                 ' Undo previous motion
310.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -Shape(Shape1).Omega)
311.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -Shape(Shape2).Omega)
312.                 vtemp.x = -Shape(Shape1).Velocity.x
313.                 vtemp.y = -Shape(Shape1).Velocity.y
314.                 CALL TranslateShape(Shape1, vtemp)
315.                 vtemp.x = -Shape(Shape2).Velocity.x
316.                 vtemp.y = -Shape(Shape2).Velocity.y
317.                 CALL TranslateShape(Shape2, vtemp)
318.  
319.                 ' Separate along normal
320.                 vtemp.x = -nx1 * (.5 * v1 + .5 / m1)
321.                 vtemp.y = -ny1 * (.5 * v1 + .5 / m1)
322.                 CALL TranslateShape(Shape1, vtemp)
323.                 vtemp.x = -nx2 * (.5 * v2 + .5 / m2)
324.                 vtemp.y = -ny2 * (.5 * v2 + .5 / m2)
325.                 CALL TranslateShape(Shape2, vtemp)
326.  
327.                 ' Translational impulse
328.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
329.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
330.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
331.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
332.                 f1 = -q1dotn1 * n1dotr1hat
333.                 f2 = -q2dotn2 * n2dotr2hat
334.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
335.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
336.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
337.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
338.  
339.                 ' Angular impulse
340.                 q1dotp1 = qx1 * px1 + qy1 * py1
341.                 q2dotp2 = qx2 * px2 + qy2 * py2
342.                 dw1 = r1 * q1dotp1 / i1
343.                 dw2 = -r2 * q2dotp2 / i2
344.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
345.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
346.                 Shape(Shape1).Omega = Shape(Shape1).Omega + dw1
347.                 Shape(Shape2).Omega = Shape(Shape2).Omega + dw2
348.  
349.                 ' Restitution
350.                 Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .9
351.                 Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .9
352.                 Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .9
353.  
354.                 ' Dent
355.                 'PointChain(Shape1, ClosestIndex1).x = PointChain(Shape1, ClosestIndex1).x - v1 * nx1
356.                 'PointChain(Shape1, ClosestIndex1).y = PointChain(Shape1, ClosestIndex1).y - v1 * ny1
357.                 'PointChain(Shape2, ClosestIndex2).x = PointChain(Shape2, ClosestIndex2).x - v2 * nx2
358.                 'PointChain(Shape2, ClosestIndex2).y = PointChain(Shape2, ClosestIndex2).y - v2 * ny2
359.                 'CALL SmoothShape(Shape1, Shape(Shape1).Elements, 1)
360.                 'CALL SmoothShape(Shape2, Shape(Shape2).Elements, 1)
361.  
362.                 ' Static friction
363.                 IF (Shape(Shape1).Velocity.x * Shape(Shape1).Velocity.x < .075) THEN Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * .001
364.                 IF (Shape(Shape1).Velocity.y * Shape(Shape1).Velocity.y < .075) THEN Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * .001
365.                 IF (Shape(Shape2).Velocity.x * Shape(Shape2).Velocity.x < .075) THEN Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * .001
366.                 IF (Shape(Shape2).Velocity.y * Shape(Shape2).Velocity.y < .075) THEN Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * .001
367.                 IF (Shape(Shape1).Omega * Shape(Shape1).Omega < .0001) THEN Shape(Shape1).Omega = Shape(Shape1).Omega * .01
368.                 IF (Shape(Shape2).Omega * Shape(Shape2).Omega < .0001) THEN Shape(Shape2).Omega = Shape(Shape2).Omega * .01
369.  
370.                 CALL snd(100 * (v1 + v2) / 2, 1)
371.  
372.             END IF
373.         NEXT
374.     END IF
375.  
376.     FOR ShapeIndex = 1 TO ShapeCount
377.         dx = Shape(ShapeIndex).CtrMass.x - Shape(ShapeIndex).CtrRot.x
378.         dy = Shape(ShapeIndex).CtrMass.y - Shape(ShapeIndex).CtrRot.y
379.  
380.         cx = Shape(ShapeIndex).CtrMass.x
381.         cy = Shape(ShapeIndex).CtrMass.y
382.         'ForceField.x = -cx / 20
383.         'ForceField.y = -cy / 20
384.  
385.         'torque = dx * ForceField.y - dy * ForceField.x
386.         'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
387.  
388.         ' Rotation update
389.         CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
390.  
391.         ' Velocity update
392.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + ForceField.x / Shape(ShapeIndex).Mass
393.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + ForceField.y / Shape(ShapeIndex).Mass
394.         CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
395.  
396.         ' Damping
397.         Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .985
398.         Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .985
399.         Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .985
400.  
401.     NEXT
402.  
403.     CALL Graphics
404.     _LIMIT 120
405. LOOP
406.  
407. END
408.  
409. SUB Graphics
410.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
411.     FOR ShapeIndex = 1 TO ShapeCount
412.         LOCATE 1, 1: PRINT "Tap arrow keys (don't hold) to move fidget spinner."
413.         PRINT "Press SPACE to enter creative mode. Left or Right click to create bricks."
414.         'LOCATE 3, 1: PRINT ProximalPairsCount, CollisionCount
415.         'CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
416.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
417.             CALL cline(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, PointChain(ShapeIndex, i + 1).x, PointChain(ShapeIndex, i + 1).y, Shape(ShapeIndex).Shade)
418.             'CALL cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
419.         NEXT
420.         CALL cline(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
421.         'CALL cpaint(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, Shape(ShapeIndex).Shade, Shape(ShapeIndex).Shade)
422.         'CALL cpset(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
423.     NEXT
424.     _DISPLAY
425. END SUB
426.  
427. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
428.     DIM l AS Vector
429.     DIM r AS Vector
430.     li = i - 1
431.     ri = i + 1
432.     IF (i = 1) THEN li = Shape(k).Elements
433.     IF (i = Shape(k).Elements) THEN ri = 1
434.     l.x = PointChain(k, li).x
435.     r.x = PointChain(k, ri).x
436.     dx = r.x - l.x
437.     CalculateNormalX = dx
438. END FUNCTION
439.  
440. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
441.     DIM l AS Vector
442.     DIM r AS Vector
443.     li = i - 1
444.     ri = i + 1
445.     IF (i = 1) THEN li = Shape(k).Elements
446.     IF (i = Shape(k).Elements) THEN ri = 1
447.     l.y = PointChain(k, li).y
448.     r.y = PointChain(k, ri).y
449.     dy = r.y - l.y
450.     CalculateNormalY = dy
451. END FUNCTION
452.  
453. SUB CalculateCtrMass (k AS INTEGER)
454.     xx = 0
455.     yy = 0
456.     FOR i = 1 TO Shape(k).Elements
457.         xx = xx + PointChain(k, i).x
458.         yy = yy + PointChain(k, i).y
459.     NEXT
460.     Shape(k).CtrMass.x = xx / Shape(k).Elements
461.     Shape(k).CtrMass.y = yy / Shape(k).Elements
462. END SUB
463.  
464. SUB CalculateDiameter (k AS INTEGER)
465.     r2max = -1
466.     FOR i = 1 TO Shape(k).Elements
467.         xx = Shape(k).CtrMass.x - PointChain(k, i).x
468.         yy = Shape(k).CtrMass.y - PointChain(k, i).y
469.         r2 = xx * xx + yy * yy
470.         IF (r2 > r2max) THEN
471.             r2max = r2
472.         END IF
473.     NEXT
474.     Shape(k).Diameter = SQR(r2max)
475. END SUB
476.  
477. SUB CalculateMOI (k AS INTEGER)
478.     xx = 0
479.     yy = 0
480.     FOR i = 1 TO Shape(k).Elements
481.         xx = xx + (Shape(k).CtrRot.x - PointChain(k, i).x) ^ 2
482.         yy = yy + (Shape(k).CtrRot.y - PointChain(k, i).y) ^ 2
483.     NEXT
484.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Elements)
485. END SUB
486.  
487. SUB TranslateShape (k AS INTEGER, c AS Vector)
488.     FOR i = 1 TO Shape(k).Elements
489.         PointChain(k, i).x = PointChain(k, i).x + c.x
490.         PointChain(k, i).y = PointChain(k, i).y + c.y
491.     NEXT
492.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
493.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
494.     Shape(k).CtrMass.x = Shape(k).CtrMass.x + c.x
495.     Shape(k).CtrMass.y = Shape(k).CtrMass.y + c.y
496. END SUB
497.  
498. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
499.     FOR i = 1 TO Shape(k).Elements
500.         xx = PointChain(k, i).x - c.x
501.         yy = PointChain(k, i).y - c.y
502.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
503.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
504.     NEXT
505.     xx = Shape(k).CtrMass.x - c.x
506.     yy = Shape(k).CtrMass.y - c.y
507.     Shape(k).CtrMass.x = c.x + xx * COS(da) - yy * SIN(da)
508.     Shape(k).CtrMass.y = c.y + yy * COS(da) + xx * SIN(da)
509. END SUB
510.  
511. SUB NewAutoBall (x1, y1, r1)
512.     pa = INT(RND * 4) + 1
513.     pb = INT(RND * 2) + 1
514.     ShapeCount = ShapeCount + 1
515.     Shape(ShapeCount).CtrRot.x = x1
516.     Shape(ShapeCount).CtrRot.y = y1
517.     i = 0
518.     FOR j = 0 TO 2 * 4 * ATN(1) - .05 STEP .05
519.         i = i + 1
520.         r = r1 + 5 * COS(pa * j) ^ pb
521.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + r * COS(j)
522.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + r * SIN(j)
523.     NEXT
524.     Shape(ShapeCount).Elements = i
525.     Shape(ShapeCount).Mass = i
526.     Shape(ShapeCount).Velocity.x = 0
527.     Shape(ShapeCount).Velocity.y = 0
528.     Shape(ShapeCount).Omega = 0
529.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
530.     CALL CalculateCtrMass(ShapeCount)
531.     CALL CalculateDiameter(ShapeCount)
532.     CALL CalculateMOI(ShapeCount)
533. END SUB
534.  
535. SUB NewAutoBrick (x1, y1, wx, wy, ang)
536.     ShapeCount = ShapeCount + 1
537.     Shape(ShapeCount).CtrRot.x = x1
538.     Shape(ShapeCount).CtrRot.y = y1
539.     i = 0
540.     FOR j = -wy / 2 TO wy / 2 STEP 2
541.         i = i + 1
542.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + wx / 2
543.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + j
544.     NEXT
545.     FOR j = wx / 2 TO -wx / 2 STEP -2
546.         i = i + 1
547.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + j
548.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + wy / 2
549.     NEXT
550.     FOR j = wy / 2 TO -wy / 2 STEP -2
551.         i = i + 1
552.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x - wx / 2
553.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y + j
554.     NEXT
555.     FOR j = -wx / 2 TO wx / 2 STEP 2
556.         i = i + 1
557.         PointChain(ShapeCount, i).x = Shape(ShapeCount).CtrRot.x + j
558.         PointChain(ShapeCount, i).y = Shape(ShapeCount).CtrRot.y - wy / 2
559.     NEXT
560.     Shape(ShapeCount).Elements = i
561.     Shape(ShapeCount).Mass = 999 ^ 999
562.     Shape(ShapeCount).Velocity.x = 0
563.     Shape(ShapeCount).Velocity.y = 0
564.     Shape(ShapeCount).Omega = 0
565.     Shape(ShapeCount).Shade = _RGB(100, 100, 100)
566.     CALL CalculateCtrMass(ShapeCount)
567.     CALL CalculateDiameter(ShapeCount)
568.     CALL CalculateMOI(ShapeCount)
569.     Shape(ShapeCount).MOI = 999 ^ 999
570.  
571.     CALL RotShape(ShapeCount, Shape(ShapeCount).CtrMass, ang)
572. END SUB
573.  
574.  
575. SUB NewMouseShape
576.     rawresolution = 7.5 ' Raw curve resolution.
577.     targetpoints = 120 ' Number of points per curve.
578.     smoothiterations = 15 ' Magnitude of smooth effect.
579.  
580.     ShapeCount = ShapeCount + 1
581.     numpoints = 0
582.  
583.     WHILE _MOUSEINPUT: WEND
584.  
585.     ' Gather raw data for one curve at a time.
586.     ' Click+drag mouse button 1 to trace out a curve.
587.     xold = 999999
588.     yold = 999999
589.     DO
590.         DO WHILE _MOUSEINPUT
591.             x = _MOUSEX
592.             y = _MOUSEY
593.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
594.                 IF _MOUSEBUTTON(1) THEN
595.                     x = x - (_WIDTH / 2)
596.                     y = -y + (_HEIGHT / 2)
597.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
598.  
599.                     ' Collect data only if the new point is sufficiently far away from the previous point.
600.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
601.                         numpoints = numpoints + 1
602.                         PointChain(ShapeCount, numpoints).x = x
603.                         PointChain(ShapeCount, numpoints).y = y
604.                         CALL cpset(x, y, _RGB(255, 255, 255))
605.                         xold = x
606.                         yold = y
607.                     END IF
608.                 END IF
609.             END IF
610.         LOOP
611.         _DISPLAY
612.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
613.  
614.     ' If the curve contains less than the minimum numer of points, use interpolation to fill in the gaps.
615.     DO WHILE (numpoints < targetpoints)
616.  
617.         ' Determine the pair of neighboring points that have the greatest separation of all pairs.
618.         rad2max = -1
619.         kmax = -1
620.         FOR k = 1 TO numpoints - 1
621.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
622.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
623.             rad2 = xfac ^ 2 + yfac ^ 2
624.             IF rad2 > rad2max THEN
625.                 kmax = k
626.                 rad2max = rad2
627.             END IF
628.         NEXT
629.         '''
630.         cornercase = 0
631.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
632.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
633.         rad2 = xfac ^ 2 + yfac ^ 2
634.         IF rad2 > rad2max THEN
635.             kmax = numpoints
636.             rad2max = rad2
637.             cornercase = 1
638.         END IF
639.         '''
640.         IF (cornercase = 0) THEN
641.  
642.             numpoints = numpoints + 1
643.  
644.             ' Starting next to kmax, create a `gap' by shifting all other points by one index.
645.             FOR j = numpoints TO kmax + 1 STEP -1
646.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
647.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
648.             NEXT
649.  
650.             ' Fill the gap with a new point whose position is determined by the average of its neighbors.
651.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
652.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
653.  
654.         ELSE
655.             numpoints = numpoints + 1
656.             xx = PointChain(ShapeCount, numpoints - 1).x
657.             yy = PointChain(ShapeCount, numpoints - 1).y
658.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
659.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
660.         END IF
661.  
662.     LOOP
663.  
664.     ' At this stage, the curve still has all of its sharp edges. Use a `relaxation method' to smooth.
665.     ' The new position of a point is equal to the average position of its neighboring points.
666.     CALL SmoothShape(ShapeCount, numpoints, smoothiterations)
667.  
668.     Shape(ShapeCount).Elements = numpoints
669.     Shape(ShapeCount).Mass = numpoints
670.     Shape(ShapeCount).Velocity.x = 0
671.     Shape(ShapeCount).Velocity.y = 0
672.     Shape(ShapeCount).Omega = 0
673.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
674.     CALL CalculateCtrMass(ShapeCount)
675.     Shape(ShapeCount).CtrRot.x = Shape(ShapeCount).CtrMass.x
676.     Shape(ShapeCount).CtrRot.y = Shape(ShapeCount).CtrMass.y
677.     CALL CalculateDiameter(ShapeCount)
678.     CALL CalculateMOI(ShapeCount)
679.  
680. END SUB
681.  
682. SUB SmoothShape (i AS INTEGER, n AS INTEGER, s AS INTEGER)
683.     FOR j = 1 TO s
684.         FOR k = 2 TO n - 1
685.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
686.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
687.         NEXT
688.         FOR k = 2 TO n - 1
689.             PointChain(i, k).x = TempChain(i, k).x
690.             PointChain(i, k).y = TempChain(i, k).y
691.         NEXT
692.     NEXT
693. END SUB
694.  
695. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
696.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
697. END SUB
698.  
699. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
700.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
701. END SUB
702.  
703. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
704.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
705. END SUB
706.  
707. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
708.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
709. END SUB
710.  
711. SUB snd (frq, dur)
712.     IF ((frq >= 37) AND (frq <= 2000)) THEN
713.         SOUND frq, dur
714.     END IF
715. END SUB

[FellippeHeitor]

THIS IS ALL SO COOL.

It's exciting to have this physics engine coming to life as we watch it. This is gonna be even cooler in the long run.

Thanks for the effort, it's a very exciting time.

[STxAxTIC]

Okay, I have *got* to stop working on this so I can make way for other things. Newest code below.

To summarize the last few days' work:

Every one of the points in the top post still stands. This is completely unified - everything is made of the same stuff, even the walls, all obeying the same equations. It's been tested across a wild variety of parameters, not excluding popular games. This code is 80% ready to become any 2D version of (in abc order) bowling, breakout, darts, gorillas, pinball, pong, pool, projectiles, whatever. Any place where the motion needs to look correct, or god willing *be* correct.

There. Now I can let this be for a day.

Code: QB64: [Select]

1. ' Display
2. SCREEN _NEWIMAGE(800, 600, 32)
3. _SCREENMOVE (_DESKTOPWIDTH \ 2 - _WIDTH \ 2) - 3, (_DESKTOPHEIGHT \ 2 - _HEIGHT \ 2) - 29
4.  
5. ' Meta
6. RANDOMIZE TIMER
7.  
8. ' Data
9. TYPE Vector
10.     x AS DOUBLE
11.     y AS DOUBLE
12. END TYPE
13.  
14. TYPE Object
15.     Centroid AS Vector
16.     CtrRot AS Vector
17.     DiameterMax AS DOUBLE
18.     DiameterMin AS DOUBLE
19.     Elements AS INTEGER
20.     Fixed AS INTEGER
21.     Mass AS DOUBLE
22.     MOI AS DOUBLE
23.     Omega AS DOUBLE
24.     Shade AS _UNSIGNED LONG
25.     Velocity AS Vector
26. END TYPE
27.  
28. DIM vtemp AS Vector
29.  
30. ' Statics
31. DIM SHARED Shape(1000) AS Object
32. DIM SHARED PointChain(1000, 5000) AS Vector
33. DIM SHARED TempChain(1000, 5000) AS Vector
34. DIM SHARED ShapeCount AS INTEGER
35.  
36. ' Dynamics
37. DIM SHARED CollisionCount AS INTEGER
38. DIM SHARED CollisionCount2 AS INTEGER
39. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
40. DIM SHARED ProximalPairsCount
41.  
42. ' Environment
43. DIM ForceField AS Vector ' Gravity
44.  
45. start:
46.  
47. ' Initialize
48. ShapeCount = 0
49. CollisionCount = 0
50. CollisionCount2 = 0
51. ForceField.x = 0
52. ForceField.y = -.05
53.  
54. ' Main object(s)
55. ShapeCount = ShapeCount + 1
56. Shape(ShapeCount).Fixed = 0
57. x1 = -200
58. y1 = 0
59. i = 0
60. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
61.     i = i + 1
62.     r = 20 + 15 * COS(1.5 * j) ^ 2
63.     PointChain(ShapeCount, i).x = x1 + r * COS(j)
64.     PointChain(ShapeCount, i).y = y1 + r * SIN(j)
65. NEXT
66. Shape(ShapeCount).Elements = i
67. CALL CalculateMass(ShapeCount, .1)
68. CALL CalculateCentroid(ShapeCount)
69. Shape(ShapeCount).CtrRot.x = x1
70. Shape(ShapeCount).CtrRot.y = y1
71. CALL CalculateMOI(ShapeCount, Shape(ShapeCount).CtrRot)
72. CALL CalculateDiameterMin(ShapeCount)
73. CALL CalculateDiameterMax(ShapeCount)
74. Shape(ShapeCount).Velocity.x = 0
75. Shape(ShapeCount).Velocity.y = 0
76. Shape(ShapeCount).Omega = 0
77. Shape(ShapeCount).Shade = _RGB(0, 255, 255)
78.  
79. ' Balls (billiard setup)
80. x0 = -70
81. y0 = 150
82. r1 = 15.5 '22.5
83. r2 = 2.5 '5
84. gg = 2 * r1 + 20
85. xf = COS(30 * 3.14159 / 180)
86. yf = SIN(30 * 3.14159 / 180)
87. gx = gg * xf
88. gy = gg * yf
89. CALL NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
90. CALL NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
91. CALL NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
92. CALL NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
93. CALL NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
94. CALL NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
95. CALL NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
96. CALL NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
97. CALL NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
98. CALL NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
99.  
100. CALL NewBrickLine(-235, 200, -35, 0, 40, 10)
101. CALL NewBrickLine(235, 200, 35, 0, 40, 10)
102.  
103. ' Rectangular border
104. l = 40
105. w = 10
106. CALL NewBrickLine(-_WIDTH / 2 + 2 * l, _HEIGHT / 2 - 2 * w, _WIDTH / 2, _HEIGHT / 2 - 2 * w, l, w)
107. CALL NewBrickLine(-_WIDTH / 2 + 2 * l, -_HEIGHT / 2 + 2 * w, _WIDTH / 2, -_HEIGHT / 2 + 2 * w, l, w)
108. CALL NewBrickLine(-_WIDTH / 2 + 2 * w, -_HEIGHT / 2 + 2 * l, -_WIDTH / 2 + 2 * w, _HEIGHT / 2 - 2 * l, l, w)
109. CALL NewBrickLine(_WIDTH / 2 - 2 * w, -_HEIGHT / 2 + 2 * l, _WIDTH / 2 - 2 * w, _HEIGHT / 2 - 2 * l, l, w)
110.  
111. ' Initial state
112. FOR k = 1 TO ShapeCount
113.     Shape(k).Velocity.x = -500 * RND / Shape(k).Mass
114.     Shape(k).Velocity.y = 0
115.     Shape(k).Omega = 5000 * RND / Shape(k).MOI
116. NEXT
117. Shape(1).Velocity.x = 4
118. Shape(1).Velocity.y = 0
119. Shape(1).Omega = .1
120.  
121. ' Prompt
122. CLS
123. CALL Graphics
124. CALL cprintstring(0, "PRESS ANY KEY TO BEGIN")
125. CALL cprintstring(-16 * 2, "Arrow keys move spinner, esc halts.")
126. CALL cprintstring(-16 * 3, "Mouse1/2 inserts heavy objects.")
127. CALL cprintstring(-16 * 4, "Space enters creative mode.")
128. CALL cprintstring(-16 * 5, "Press 'r' to restart.")
129. _DISPLAY
130. DO: LOOP UNTIL _KEYHIT > 0
131. WHILE _MOUSEINPUT: WEND
132. _KEYCLEAR
133.  
134. ' Main loop
135. DO
136.  
137.     kk = _KEYHIT
138.     SELECT CASE kk
139.         CASE 32
140.             DO: LOOP UNTIL _KEYHIT
141.             WHILE _MOUSEINPUT: WEND
142.             _KEYCLEAR
143.             CALL Graphics
144.             CALL NewMouseShape
145.             CLS
146.         CASE 18432, ASC("w") ' Up arrow
147.             Shape(1).Velocity.y = Shape(1).Velocity.y * 1.1 + 2
148.         CASE 20480, ASC("s") ' Down arrow
149.             Shape(1).Velocity.y = Shape(1).Velocity.y * 0.9 - 2
150.         CASE 19200, ASC("a") ' Left arrow
151.             Shape(1).Velocity.x = Shape(1).Velocity.x * 0.9 - 2
152.         CASE 19712, ASC("d") ' Right arrow
153.             Shape(1).Velocity.x = Shape(1).Velocity.x * 1.1 + 2
154.         CASE ASC("r")
155.             GOTO start
156.         CASE 27
157.             Shape(1).Velocity.x = 0
158.             Shape(1).Velocity.y = 0
159.     END SELECT
160.     IF (kk) THEN
161.         _KEYCLEAR
162.     END IF
163.  
164.     mb = 0
165.     DO WHILE _MOUSEINPUT
166.         x = _MOUSEX
167.         y = _MOUSEY
168.         IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
169.             'IF (_MOUSEBUTTON(1)) THEN
170.             '    IF (mb = 0) THEN
171.             '        mb = 1
172.             '        x = x - (_WIDTH / 2)
173.             '        y = -y + (_HEIGHT / 2)
174.             '        CALL NewAutoBrick(x, y, 20, 20, 0)
175.             '        _DELAY .1
176.             '    END IF
177.             'END IF
178.             IF (_MOUSEBUTTON(1)) THEN
179.                 x = _MOUSEX - _WIDTH / 2
180.                 y = -_MOUSEY + _HEIGHT / 2
181.                 Shape(1).CtrRot.x = x
182.                 Shape(1).CtrRot.y = y
183.                 CALL CalculateMOI(1, Shape(1).CtrRot)
184.                 'Shape(1).Omega = 0
185.             END IF
186.             IF (_MOUSEBUTTON(2)) THEN
187.                 IF (mb = 0) THEN
188.                     mb = 1
189.                     x = x - (_WIDTH / 2)
190.                     y = -y + (_HEIGHT / 2)
191.                     CALL NewAutoBall(x, y, 20, 0, 1, 1, 1)
192.                     _DELAY .1
193.                 END IF
194.             END IF
195.         END IF
196.     LOOP
197.  
198.     ' Proximity detection
199.     ProximalPairsCount = 0
200.     Shape1 = 0
201.     Shape2 = 0
202.     FOR j = 1 TO ShapeCount
203.         FOR k = j + 1 TO ShapeCount
204.             dx = Shape(j).Centroid.x - Shape(k).Centroid.x
205.             dy = Shape(j).Centroid.y - Shape(k).Centroid.y
206.             dr = SQR(dx * dx + dy * dy)
207.             IF (dr < 1.15 * (Shape(j).DiameterMax + Shape(k).DiameterMax)) THEN
208.                 ProximalPairsCount = ProximalPairsCount + 1
209.                 ProximalPairs(ProximalPairsCount, 1) = j
210.                 ProximalPairs(ProximalPairsCount, 2) = k
211.                 Shape1 = j
212.                 Shape2 = k
213.             END IF
214.         NEXT
215.     NEXT
216.  
217.     IF (ProximalPairsCount > 0) THEN
218.         FOR n = 1 TO ProximalPairsCount
219.             Shape1 = ProximalPairs(n, 1)
220.             Shape2 = ProximalPairs(n, 2)
221.  
222.             ' Collision detection
223.             rmin = 999 ^ 999
224.             ClosestIndex1 = 0
225.             ClosestIndex2 = 0
226.             FOR j = 1 TO Shape(Shape1).Elements
227.                 FOR k = 1 TO Shape(Shape2).Elements
228.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
229.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
230.                     r2 = dx * dx + dy * dy
231.                     IF (r2 < rmin) THEN
232.                         rmin = r2
233.                         ClosestIndex1 = j
234.                         ClosestIndex2 = k
235.                     END IF
236.                 NEXT
237.             NEXT
238.  
239.             '''
240.             ''' NEW ROTATION AXIS FOR SUSTAINED CONTACT, CENTROID FOR GLANCING BLOW
241.             '''
242.  
243.             IF (rmin <= 4) THEN
244.                 CollisionCount = CollisionCount + 1
245.  
246.                 ' Normal vector 1 (nx1, ny1)
247.                 xx = CalculateNormalY(Shape1, ClosestIndex1)
248.                 yy = -CalculateNormalX(Shape1, ClosestIndex1)
249.                 nn = SQR(xx * xx + yy * yy)
250.                 xx = xx / nn
251.                 yy = yy / nn
252.                 nx1 = xx
253.                 ny1 = yy
254.  
255.                 ' Normal vector 2 (nx2, ny2)
256.                 xx = CalculateNormalY(Shape2, ClosestIndex2)
257.                 yy = -CalculateNormalX(Shape2, ClosestIndex2)
258.                 nn = SQR(xx * xx + yy * yy)
259.                 xx = xx / nn
260.                 yy = yy / nn
261.                 nx2 = xx
262.                 ny2 = yy
263.  
264.                 ' Main differentials 1 (dx1, dy1)
265.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).Centroid.x
266.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).Centroid.y
267.  
268.                 ' Main differentials 2 (dx2, dy2)
269.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).Centroid.x
270.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).Centroid.y
271.  
272.                 ' Perpendicular vector 1 (px1, py1)
273.                 px1 = -dy1
274.                 py1 = dx1
275.                 pp = SQR(px1 * px1 + py1 * py1)
276.                 px1 = px1 / pp
277.                 py1 = py1 / pp
278.  
279.                 ' Perpendicular vector 2 (px2, py2)
280.                 px2 = -dy2
281.                 py2 = dx2
282.                 pp = SQR(px2 * px2 + py2 * py2)
283.                 px2 = px2 / pp
284.                 py2 = py2 / pp
285.  
286.                 ' Angular velocity vector 1 (w1, r1, vx1, vy1)
287.                 w1 = Shape(Shape1).Omega
288.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
289.                 vx1 = w1 * r1 * px1
290.                 vy1 = w1 * r1 * py1
291.  
292.                 ' Angular velocity vector 2 (w2, r2, vx2, vy2)
293.                 w2 = Shape(Shape2).Omega
294.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
295.                 vx2 = w2 * r2 * px2
296.                 vy2 = w2 * r2 * py2
297.  
298.                 ' Mass terms (m1, m2, mu)
299.                 m1 = Shape(Shape1).Mass
300.                 m2 = Shape(Shape2).Mass
301.                 mu = 1 / (1 / m1 + 1 / m2)
302.  
303.                 ' Re-Calculate moment of inertia (i1, i2)
304.                 vtemp.x = PointChain(Shape1, ClosestIndex1).x
305.                 vtemp.y = PointChain(Shape1, ClosestIndex1).y
306.                 CALL CalculateMOI(Shape1, vtemp)
307.                 vtemp.x = PointChain(Shape2, ClosestIndex2).x
308.                 vtemp.y = PointChain(Shape2, ClosestIndex2).y
309.                 CALL CalculateMOI(Shape2, vtemp)
310.                 i1 = Shape(Shape1).MOI
311.                 i2 = Shape(Shape2).MOI
312.  
313.                 ' Use the parallel axis theorem working instead?
314.                 'x1 = Shape(Shape1).Centroid.x - PointChain(Shape1, ClosestIndex1).x
315.                 'y1 = Shape(Shape1).Centroid.y - PointChain(Shape1, ClosestIndex1).y
316.                 'x2 = Shape(Shape2).Centroid.x - PointChain(Shape2, ClosestIndex2).x
317.                 'y2 = Shape(Shape2).Centroid.y - PointChain(Shape2, ClosestIndex2).y
318.                 'r1 = x1 * x1 + y1 * y1
319.                 'r2 = x2 * x2 + y2 * y2
320.                 'i1 = Shape(Shape1).MOI + Shape(Shape1).Elements * r1
321.                 'i2 = Shape(Shape2).MOI + Shape(Shape2).Elements * r2
322.  
323.                 ' Velocity differentials (v1, v2, dvtx, dvty)
324.                 vtx1 = Shape(Shape1).Velocity.x + vx1
325.                 vty1 = Shape(Shape1).Velocity.y + vy1
326.                 vtx2 = Shape(Shape2).Velocity.x + vx2
327.                 vty2 = Shape(Shape2).Velocity.y + vy2
328.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
329.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
330.                 dvtx = vtx2 - vtx1
331.                 dvty = vty2 - vty1
332.  
333.                 IF (v1 + v2 > 0.001) THEN CollisionCount2 = CollisionCount2 + 1
334.  
335.                 ' Geometry (n1dotdvt, n2dotdvt)
336.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
337.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
338.  
339.                 ' Momentum exchange (qx1, qy1, qx2, qy2)
340.                 qx1 = nx1 * 2 * mu * n1dotdvt
341.                 qy1 = ny1 * 2 * mu * n1dotdvt
342.                 qx2 = nx2 * 2 * mu * n2dotdvt
343.                 qy2 = ny2 * 2 * mu * n2dotdvt
344.  
345.                 ' Momentum exchange unit vector
346.                 qq = SQR(qx1 * qx1 + qy1 * qy1)
347.                 qhatx1 = qx1 / qq
348.                 qhaty1 = qy1 / qq
349.                 qq = SQR(qx2 * qx2 + qy2 * qy2)
350.                 qhatx2 = qx2 / qq
351.                 qhaty2 = qy2 / qq
352.  
353.                 ' Undo previous motion
354.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, -Shape(Shape1).Omega)
355.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, -Shape(Shape2).Omega)
356.                 vtemp.x = -Shape(Shape1).Velocity.x
357.                 vtemp.y = -Shape(Shape1).Velocity.y
358.                 CALL TranslateShape(Shape1, vtemp)
359.                 vtemp.x = -Shape(Shape2).Velocity.x
360.                 vtemp.y = -Shape(Shape2).Velocity.y
361.                 CALL TranslateShape(Shape2, vtemp)
362.  
363.                 ' Separate along normal
364.                 vtemp.x = -nx1 * (.25 * v1 + .25 / m1 + .25 * .5 * (Shape(Shape1).DiameterMin + Shape(Shape1).DiameterMax) / m1)
365.                 vtemp.y = -ny1 * (.25 * v1 + .25 / m1 + .25 * .5 * (Shape(Shape1).DiameterMin + Shape(Shape1).DiameterMax) / m1)
366.                 CALL TranslateShape(Shape1, vtemp)
367.                 vtemp.x = -nx2 * (.25 * v2 + .25 / m2 + .25 * .5 * (Shape(Shape2).DiameterMin + Shape(Shape2).DiameterMax) / m2)
368.                 vtemp.y = -ny2 * (.25 * v2 + .25 / m2 + .25 * .5 * (Shape(Shape2).DiameterMin + Shape(Shape2).DiameterMax) / m2)
369.                 CALL TranslateShape(Shape2, vtemp)
370.  
371.                 ' Translational impulse
372.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
373.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
374.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
375.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
376.                 f1 = -q1dotn1 * n1dotr1hat
377.                 f2 = -q2dotn2 * n2dotr2hat
378.                 Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x + f1 * qx1 / m1
379.                 Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y + f1 * qy1 / m1
380.                 Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x + f2 * qx2 / m2
381.                 Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y + f2 * qy2 / m2
382.  
383.                 ' Angular impulse
384.                 q1dotp1 = qx1 * px1 + qy1 * py1
385.                 q2dotp2 = qx2 * px2 + qy2 * py2
386.                 dw1 = r1 * q1dotp1 / i1
387.                 dw2 = -r2 * q2dotp2 / i2
388.                 CALL RotShape(Shape1, Shape(Shape1).CtrRot, dw1)
389.                 CALL RotShape(Shape2, Shape(Shape2).CtrRot, dw2)
390.                 Shape(Shape1).Omega = w1 + dw1
391.                 Shape(Shape2).Omega = w2 + dw2
392.  
393.                 ' Restitution
394.                 Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .955
395.                 Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .955
396.                 'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .995
397.  
398.                 ' Static friction
399.                 IF (Shape(Shape1).Velocity.x * Shape(Shape1).Velocity.x < .075) THEN Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * .001
400.                 IF (Shape(Shape1).Velocity.y * Shape(Shape1).Velocity.y < .075) THEN Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * .001
401.                 IF (Shape(Shape2).Velocity.x * Shape(Shape2).Velocity.x < .075) THEN Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * .001
402.                 IF (Shape(Shape2).Velocity.y * Shape(Shape2).Velocity.y < .075) THEN Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * .001
403.                 'IF (Shape(Shape1).Omega * Shape(Shape1).Omega < .0001) THEN Shape(Shape1).Omega = Shape(Shape1).Omega * .01
404.                 'IF (Shape(Shape2).Omega * Shape(Shape2).Omega < .0001) THEN Shape(Shape2).Omega = Shape(Shape2).Omega * .01
405.  
406.                 ' Feedback
407.                 CALL cline(Shape(Shape1).Centroid.x, Shape(Shape1).Centroid.y, PointChain(Shape1, ClosestIndex1).x, PointChain(Shape1, ClosestIndex1).y, Shape(Shape1).Shade)
408.                 CALL cline(Shape(Shape2).Centroid.x, Shape(Shape2).Centroid.y, PointChain(Shape2, ClosestIndex2).x, PointChain(Shape2, ClosestIndex2).y, Shape(Shape2).Shade)
409.                 _DISPLAY
410.                 CALL snd(100 * (v1 + v2) / 2, 1)
411.  
412.             END IF
413.         NEXT
414.     END IF
415.  
416.     FOR ShapeIndex = 1 TO ShapeCount
417.         IF Shape(ShapeIndex).Fixed = 0 THEN
418.             dx = Shape(ShapeIndex).Centroid.x - Shape(ShapeIndex).CtrRot.x
419.             dy = Shape(ShapeIndex).Centroid.y - Shape(ShapeIndex).CtrRot.y
420.  
421.             torque = dx * ForceField.y - dy * ForceField.x
422.             Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + torque / Shape(ShapeIndex).MOI
423.  
424.             ' Rotation update
425.             CALL RotShape(ShapeIndex, Shape(ShapeIndex).CtrRot, Shape(ShapeIndex).Omega)
426.  
427.             ' Velocity update
428.             ax = ForceField.x
429.             ay = ForceField.y
430.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + ax
431.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + ay
432.             CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
433.  
434.             ' Damping
435.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .985
436.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .985
437.             'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .998 * (1 - .025 * (Shape(ShapeIndex).DiameterMin / Shape(ShapeIndex).DiameterMax))
438.  
439.         END IF
440.     NEXT
441.  
442.     CALL Graphics
443.     _LIMIT 60
444. LOOP
445.  
446. END
447.  
448. SUB Graphics
449.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
450.     FOR ShapeIndex = 1 TO ShapeCount
451.         LOCATE 1, 1: PRINT ProximalPairsCount, CollisionCount, CollisionCount2
452.         CALL ccircle(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, 3, Shape(ShapeIndex).Shade)
453.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
454.             CALL cline(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, PointChain(ShapeIndex, i + 1).x, PointChain(ShapeIndex, i + 1).y, Shape(ShapeIndex).Shade)
455.             'CALL cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
456.         NEXT
457.         CALL cline(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
458.         CALL cline(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
459.         'CALL cpaint(Shape(ShapeIndex).CtrRot.x, Shape(ShapeIndex).CtrRot.y, Shape(ShapeIndex).Shade, Shape(ShapeIndex).Shade)
460.         'CALL cpset(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
461.     NEXT
462.     _DISPLAY
463. END SUB
464.  
465. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
466.     DIM l AS Vector
467.     DIM r AS Vector
468.     li = i - 1
469.     ri = i + 1
470.     IF (i = 1) THEN li = Shape(k).Elements
471.     IF (i = Shape(k).Elements) THEN ri = 1
472.     l.x = PointChain(k, li).x
473.     r.x = PointChain(k, ri).x
474.     dx = r.x - l.x
475.     CalculateNormalX = dx
476. END FUNCTION
477.  
478. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
479.     DIM l AS Vector
480.     DIM r AS Vector
481.     li = i - 1
482.     ri = i + 1
483.     IF (i = 1) THEN li = Shape(k).Elements
484.     IF (i = Shape(k).Elements) THEN ri = 1
485.     l.y = PointChain(k, li).y
486.     r.y = PointChain(k, ri).y
487.     dy = r.y - l.y
488.     CalculateNormalY = dy
489. END FUNCTION
490.  
491. SUB CalculateCentroid (k AS INTEGER)
492.     xx = 0
493.     yy = 0
494.     FOR i = 1 TO Shape(k).Elements
495.         xx = xx + PointChain(k, i).x
496.         yy = yy + PointChain(k, i).y
497.     NEXT
498.     Shape(k).Centroid.x = xx / Shape(k).Elements
499.     Shape(k).Centroid.y = yy / Shape(k).Elements
500. END SUB
501.  
502. SUB CalculateDiameterMin (k AS INTEGER)
503.     r2min = 999 ^ 999
504.     FOR i = 1 TO Shape(k).Elements
505.         xx = Shape(k).Centroid.x - PointChain(k, i).x
506.         yy = Shape(k).Centroid.y - PointChain(k, i).y
507.         r2 = xx * xx + yy * yy
508.         IF (r2 < r2min) THEN
509.             r2min = r2
510.         END IF
511.     NEXT
512.     Shape(k).DiameterMin = SQR(r2min)
513. END SUB
514.  
515. SUB CalculateDiameterMax (k AS INTEGER)
516.     r2max = -1
517.     FOR i = 1 TO Shape(k).Elements
518.         xx = Shape(k).Centroid.x - PointChain(k, i).x
519.         yy = Shape(k).Centroid.y - PointChain(k, i).y
520.         r2 = xx * xx + yy * yy
521.         IF (r2 > r2max) THEN
522.             r2max = r2
523.         END IF
524.     NEXT
525.     Shape(k).DiameterMax = SQR(r2max)
526. END SUB
527.  
528. SUB CalculateMass (k AS INTEGER, factor AS DOUBLE)
529.     aa = 0
530.     FOR i = 1 TO Shape(k).Elements - 1
531.         x = (Shape(k).Centroid.x - PointChain(k, i).x)
532.         y = (Shape(k).Centroid.y - PointChain(k, i).y)
533.         dx = (Shape(k).Centroid.x - PointChain(k, i + 1).x) - x
534.         dy = (Shape(k).Centroid.y - PointChain(k, i + 1).y) - y
535.         da = .5 * (x * dy - y * dx)
536.         aa = aa + da
537.     NEXT
538.     Shape(k).Mass = factor * aa
539. END SUB
540.  
541. SUB CalculateMOI (k AS INTEGER, ctrvec AS Vector)
542.     xx = 0
543.     yy = 0
544.     FOR i = 1 TO Shape(k).Elements
545.         xx = xx + (ctrvec.x - PointChain(k, i).x) ^ 2
546.         yy = yy + (ctrvec.y - PointChain(k, i).y) ^ 2
547.     NEXT
548.     Shape(k).MOI = (xx + yy) * (Shape(k).Mass / Shape(k).Elements)
549. END SUB
550.  
551. SUB TranslateShape (k AS INTEGER, c AS Vector)
552.     FOR i = 1 TO Shape(k).Elements
553.         PointChain(k, i).x = PointChain(k, i).x + c.x
554.         PointChain(k, i).y = PointChain(k, i).y + c.y
555.     NEXT
556.     Shape(k).CtrRot.x = Shape(k).CtrRot.x + c.x
557.     Shape(k).CtrRot.y = Shape(k).CtrRot.y + c.y
558.     Shape(k).Centroid.x = Shape(k).Centroid.x + c.x
559.     Shape(k).Centroid.y = Shape(k).Centroid.y + c.y
560. END SUB
561.  
562. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
563.     FOR i = 1 TO Shape(k).Elements
564.         xx = PointChain(k, i).x - c.x
565.         yy = PointChain(k, i).y - c.y
566.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
567.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
568.     NEXT
569.     xx = Shape(k).Centroid.x - c.x
570.     yy = Shape(k).Centroid.y - c.y
571.     Shape(k).Centroid.x = c.x + xx * COS(da) - yy * SIN(da)
572.     Shape(k).Centroid.y = c.y + yy * COS(da) + xx * SIN(da)
573. END SUB
574.  
575. SUB NewAutoBall (x1, y1, r1, r2, pa, pb, fx)
576.     ShapeCount = ShapeCount + 1
577.     Shape(ShapeCount).Fixed = fx
578.     i = 0
579.     FOR j = 0 TO 2 * 4 * ATN(1) - .05 STEP .05
580.         i = i + 1
581.         r = r1 + r2 * COS(pa * j) ^ pb
582.         PointChain(ShapeCount, i).x = x1 + r * COS(j)
583.         PointChain(ShapeCount, i).y = y1 + r * SIN(j)
584.     NEXT
585.     Shape(ShapeCount).Elements = i
586.     IF (fx = 0) THEN
587.         CALL CalculateMass(ShapeCount, .1)
588.     ELSE
589.         CALL CalculateMass(ShapeCount, 999)
590.     END IF
591.     CALL CalculateCentroid(ShapeCount)
592.     Shape(ShapeCount).CtrRot.x = x1
593.     Shape(ShapeCount).CtrRot.y = y1
594.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).CtrRot)
595.     CALL CalculateDiameterMin(ShapeCount)
596.     CALL CalculateDiameterMax(ShapeCount)
597.     Shape(ShapeCount).Velocity.x = 0
598.     Shape(ShapeCount).Velocity.y = 0
599.     Shape(ShapeCount).Omega = 0
600.     IF (fx = 0) THEN
601.         Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
602.     ELSE
603.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
604.     END IF
605. END SUB
606.  
607. SUB NewAutoBrick (x1, y1, wx, wy, ang)
608.     ShapeCount = ShapeCount + 1
609.     Shape(ShapeCount).Fixed = 1
610.     i = 0
611.     FOR j = -wy / 2 TO wy / 2 STEP 2
612.         i = i + 1
613.         PointChain(ShapeCount, i).x = x1 + wx / 2
614.         PointChain(ShapeCount, i).y = y1 + j
615.     NEXT
616.     FOR j = wx / 2 TO -wx / 2 STEP -2
617.         i = i + 1
618.         PointChain(ShapeCount, i).x = x1 + j
619.         PointChain(ShapeCount, i).y = y1 + wy / 2
620.     NEXT
621.     FOR j = wy / 2 TO -wy / 2 STEP -2
622.         i = i + 1
623.         PointChain(ShapeCount, i).x = x1 - wx / 2
624.         PointChain(ShapeCount, i).y = y1 + j
625.     NEXT
626.     FOR j = -wx / 2 TO wx / 2 STEP 2
627.         i = i + 1
628.         PointChain(ShapeCount, i).x = x1 + j
629.         PointChain(ShapeCount, i).y = y1 - wy / 2
630.     NEXT
631.     Shape(ShapeCount).Elements = i
632.     CALL CalculateMass(ShapeCount, 9999)
633.     CALL CalculateCentroid(ShapeCount)
634.     Shape(ShapeCount).CtrRot.x = x1
635.     Shape(ShapeCount).CtrRot.y = y1
636.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).CtrRot)
637.     CALL CalculateDiameterMin(ShapeCount)
638.     CALL CalculateDiameterMax(ShapeCount)
639.     Shape(ShapeCount).MOI = 999 ^ 999
640.     Shape(ShapeCount).Velocity.x = 0
641.     Shape(ShapeCount).Velocity.y = 0
642.     Shape(ShapeCount).Omega = 0
643.     Shape(ShapeCount).Shade = _RGB(100, 100, 100)
644.     CALL RotShape(ShapeCount, Shape(ShapeCount).Centroid, ang)
645. END SUB
646.  
647. SUB NewBrickLine (xi, yi, xf, yf, l, w)
648.     d1 = SQR((xf - xi) ^ 2 + (yf - yi) ^ 2)
649.     d2 = SQR(l ^ 2 + w ^ 2)
650.     ang = ATN((yf - yi) / (xf - xi))
651.     FOR t = 0 TO 1 STEP 1.25 * d2 / d1
652.         CALL NewAutoBrick(xi * (1 - t) + xf * t, yi * (1 - t) + yf * t, l, w, ang)
653.     NEXT
654. END SUB
655.  
656. SUB NewMouseShape
657.     rawresolution = 7.5 ' Raw curve resolution.
658.     targetpoints = 150 ' Number of points per curve.
659.     smoothiterations = 25 ' Magnitude of smooth effect.
660.  
661.     ShapeCount = ShapeCount + 1
662.     Shape(ShapeCount).Fixed = 0
663.  
664.     numpoints = 0
665.  
666.     ' Click+drag mouse button 1 to trace out a curve.
667.     xold = 999999
668.     yold = 999999
669.     DO
670.         DO WHILE _MOUSEINPUT
671.             x = _MOUSEX
672.             y = _MOUSEY
673.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
674.                 IF _MOUSEBUTTON(1) THEN
675.                     x = x - (_WIDTH / 2)
676.                     y = -y + (_HEIGHT / 2)
677.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
678.  
679.                     ' Collect data only if the new point is sufficiently far away from the previous point.
680.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
681.                         numpoints = numpoints + 1
682.                         PointChain(ShapeCount, numpoints).x = x
683.                         PointChain(ShapeCount, numpoints).y = y
684.                         CALL cpset(x, y, _RGB(255, 255, 255))
685.                         xold = x
686.                         yold = y
687.                     END IF
688.                 END IF
689.             END IF
690.         LOOP
691.         _DISPLAY
692.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
693.  
694.     ' If the curve contains less than the minimum numer of points, use interpolation to fill in the gaps.
695.     DO WHILE (numpoints < targetpoints)
696.  
697.         ' Determine the pair of neighboring points that have the greatest separation of all pairs.
698.         rad2max = -1
699.         kmax = -1
700.         FOR k = 1 TO numpoints - 1
701.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
702.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
703.             rad2 = xfac ^ 2 + yfac ^ 2
704.             IF rad2 > rad2max THEN
705.                 kmax = k
706.                 rad2max = rad2
707.             END IF
708.         NEXT
709.         '''
710.         cornercase = 0
711.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
712.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
713.         rad2 = xfac ^ 2 + yfac ^ 2
714.         IF rad2 > rad2max THEN
715.             kmax = numpoints
716.             rad2max = rad2
717.             cornercase = 1
718.         END IF
719.         '''
720.         IF (cornercase = 0) THEN
721.  
722.             numpoints = numpoints + 1
723.  
724.             ' Starting next to kmax, create a gap by shifting all other points by one index.
725.             FOR j = numpoints TO kmax + 1 STEP -1
726.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
727.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
728.             NEXT
729.  
730.             ' Fill the gap with a new point whose position is determined by the average of its neighbors.
731.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
732.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
733.  
734.         ELSE
735.             numpoints = numpoints + 1
736.             xx = PointChain(ShapeCount, numpoints - 1).x
737.             yy = PointChain(ShapeCount, numpoints - 1).y
738.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
739.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
740.         END IF
741.  
742.     LOOP
743.  
744.     ' At this stage, the curve still has all of its sharp edges. Use a relaxation method to smooth.
745.     ' The new position of a point is equal to the average position of its neighboring points.
746.     CALL SmoothShape(ShapeCount, numpoints, smoothiterations)
747.  
748.     Shape(ShapeCount).Elements = numpoints
749.     CALL CalculateMass(ShapeCount, .1)
750.     CALL CalculateCentroid(ShapeCount)
751.     Shape(ShapeCount).CtrRot.x = Shape(ShapeCount).Centroid.x
752.     Shape(ShapeCount).CtrRot.y = Shape(ShapeCount).Centroid.y
753.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).CtrRot)
754.     CALL CalculateDiameterMin(ShapeCount)
755.     CALL CalculateDiameterMax(ShapeCount)
756.     Shape(ShapeCount).Velocity.x = 0
757.     Shape(ShapeCount).Velocity.y = 0
758.     Shape(ShapeCount).Omega = 0
759.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
760.  
761. END SUB
762.  
763. SUB SmoothShape (i AS INTEGER, n AS INTEGER, s AS INTEGER)
764.     FOR j = 1 TO s
765.         FOR k = 2 TO n - 1
766.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
767.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
768.         NEXT
769.         FOR k = 2 TO n - 1
770.             PointChain(i, k).x = TempChain(i, k).x
771.             PointChain(i, k).y = TempChain(i, k).y
772.         NEXT
773.     NEXT
774. END SUB
775.  
776. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
777.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
778. END SUB
779.  
780. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
781.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
782. END SUB
783.  
784. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
785.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
786. END SUB
787.  
788. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
789.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
790. END SUB
791.  
792. SUB cprintstring (y, a AS STRING)
793.     _PRINTSTRING (_WIDTH / 2 - (LEN(a) * 8) / 2, -y + _HEIGHT / 2), a
794. END SUB
795.  
796. SUB snd (frq, dur)
797.     IF ((frq >= 37) AND (frq <= 2000)) THEN
798.         SOUND frq, dur
799.     END IF
800. END SUB