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Author Topic: Generalized physics engine prototype with arbitrary shapes and collisions  (Read 6762 times)

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FellippeHeitor

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #15 on: February 23, 2020, 03:37:02 pm »
Potatoes!
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Offline STxAxTIC

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #16 on: February 29, 2020, 07:04:04 pm »
A quick update below. Still deciding what the end-game for this will be.

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. start:
  8.  
  10.  
  11. ' Data
  12. TYPE Vector
  13.     x AS DOUBLE
  14.     y AS DOUBLE
  16.  
  17. TYPE Object
  18.     Centroid AS Vector
  19.     Collisions AS LONG
  20.     CollisionSwitch AS INTEGER
  21.     DeltaO AS DOUBLE
  22.     DeltaV AS Vector
  23.     DiameterMax AS DOUBLE
  24.     DiameterMin AS DOUBLE
  25.     Elements AS INTEGER
  26.     Fixed AS INTEGER
  27.     Mass AS DOUBLE
  28.     MOI AS DOUBLE
  29.     PartialNormal AS Vector
  30.     Omega AS DOUBLE
  31.     Shade AS _UNSIGNED LONG
  32.     Velocity AS Vector
  34.  
  35. DIM vtemp AS Vector
  36.  
  37. ' Statics
  38. DIM SHARED Shape(1000) AS Object
  39. DIM SHARED PointChain(1000, 5000) AS Vector
  40. DIM SHARED TempChain(1000, 5000) AS Vector
  41. DIM SHARED ShapeCount AS INTEGER
  42.  
  43. ' Dynamics
  44. DIM SHARED CollisionCount AS INTEGER
  45. DIM SHARED ProximalPairs(1000 / 2, 1 TO 2)
  46. DIM SHARED ProximalPairsCount
  47.  
  48. ' Environment
  49. DIM ForceField AS Vector ' Gravity
  50. ForceField.x = 0
  51. ForceField.y = -.08
  52.  
  53. ' Initialize
  54. ShapeCount = 0
  55. CollisionCount = 0
  56.  
  57. ' Balls (billiard setup)
  58. x0 = -70
  59. y0 = 120
  60. r1 = 15.5
  61. r2 = 2.5
  62. gg = 2 * r1 + 20
  63. xf = COS(30 * 3.14159 / 180)
  64. yf = SIN(30 * 3.14159 / 180)
  65. gx = gg * xf
  66. gy = gg * yf
  67. CALL NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  68. CALL NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  69. CALL NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  70. CALL NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  71. CALL NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  72. 'CALL NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  73. 'CALL NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  74. 'CALL NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  75. 'CALL NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  76. 'CALL NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  77.  
  78. ' Rectangular border
  79. l = 40
  80. w = 10
  81. CALL NewBrickLine(-_WIDTH / 2 + 2 * l, _HEIGHT / 2 - 2 * w, _WIDTH / 2, _HEIGHT / 2 - 2 * w, l, w)
  82. CALL NewBrickLine(-_WIDTH / 2 + 2 * l, -_HEIGHT / 2 + 2 * w, _WIDTH / 2, -_HEIGHT / 2 + 2 * w, l, w)
  83. CALL NewBrickLine(-_WIDTH / 2 + 2 * w, -_HEIGHT / 2 + 2 * l, -_WIDTH / 2 + 2 * w, _HEIGHT / 2 - 2 * l, l, w)
  84. CALL NewBrickLine(_WIDTH / 2 - 2 * w, -_HEIGHT / 2 + 2 * l, _WIDTH / 2 - 2 * w, _HEIGHT / 2 - 2 * l, l, w)
  85.  
  86. ' Misc. bricks
  87. CALL NewBrickLine(-100 + 4, 100, 0 + 4, 0, 60, 10)
  88. CALL NewBrickLine(100 - 4, 100, 0 - 4, 0, 60, 10)
  89.  
  90. 'CALL NewAutoBrick(0, -100, 200, 100, 0)
  91.  
  92. ' Main object(s)
  93. ShapeCount = ShapeCount + 1
  94. Shape(ShapeCount).Fixed = 0
  95. Shape(ShapeCount).Collisions = 0
  96. x1 = 0
  97. y1 = -150
  98. i = 0
  99. FOR j = 0 TO 2 * 4 * ATN(1) STEP .05
  100.     i = i + 1
  101.     r = 20 + 15 * COS(1.5 * j) ^ 2
  102.     PointChain(ShapeCount, i).x = x1 + r * COS(j)
  103.     PointChain(ShapeCount, i).y = y1 + r * SIN(j)
  105. Shape(ShapeCount).Elements = i
  106. CALL CalculateMass(ShapeCount, 1)
  107. CALL CalculateCentroid(ShapeCount)
  108. CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  109. CALL CalculateDiameterMin(ShapeCount)
  110. CALL CalculateDiameterMax(ShapeCount)
  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.  
  116. ' Prompt
  118. CALL Graphics
  119. CALL cprintstring(0, "PRESS ANY KEY TO BEGIN")
  120. CALL cprintstring(-16 * 2, "Arrow keys boost most recently-created object.")
  121. CALL cprintstring(-16 * 3, "Space enters creative mode.")
  122. CALL cprintstring(-16 * 4, "Press 'r' to restart.")
  127.  
  128. ' Main loop
  130.  
  131.     ' Keyboard input
  132.     kk = _KEYHIT
  133.     SELECT CASE kk
  134.         CASE 32
  135.             DO: LOOP UNTIL _KEYHIT
  136.             WHILE _MOUSEINPUT: WEND
  137.             _KEYCLEAR
  138.             CALL cprintstring(16 * 17, "Drag mouse counter-clockwise to draw a new shape.")
  139.             CALL cprintstring(16 * 16, "Make sure centroid is inside body.")
  140.             'CALL Graphics
  141.             CALL NewMouseShape(7.5, 75, 25)
  142.             CLS
  143.         CASE 18432, ASC("w") ' Up arrow
  144.             Shape(ShapeCount).Velocity.y = Shape(ShapeCount).Velocity.y * 1.1 + 2
  145.         CASE 20480, ASC("s") ' Down arrow
  146.             Shape(ShapeCount).Velocity.y = Shape(ShapeCount).Velocity.y * 0.9 - 2
  147.         CASE 19200, ASC("a") ' Left arrow
  148.             Shape(ShapeCount).Velocity.x = Shape(ShapeCount).Velocity.x * 0.9 - 2
  149.         CASE 19712, ASC("d") ' Right arrow
  150.             Shape(ShapeCount).Velocity.x = Shape(ShapeCount).Velocity.x * 1.1 + 2
  151.         CASE ASC("r")
  152.             GOTO start
  153.         CASE 27
  154.             FOR k = 1 TO ShapeCount
  155.                 Shape(k).Velocity.x = .000001
  156.                 Shape(k).Velocity.y = .000001
  157.                 Shape(k).Omega = .000001
  158.             NEXT
  159.     END SELECT
  160.     IF (kk) THEN
  161.         _KEYCLEAR
  162.     END IF
  163.  
  164.     ' Mouse input
  165.     mb = 0
  167.         x = _MOUSEX
  168.         y = _MOUSEY
  169.         IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
  170.             IF (_MOUSEBUTTON(1)) THEN
  171.                 IF (mb = 0) THEN
  172.                     mb = 1
  173.                     x = x - (_WIDTH / 2)
  174.                     y = -y + (_HEIGHT / 2)
  175.                     vtemp.x = x - Shape(ShapeCount).Centroid.x
  176.                     vtemp.y = y - Shape(ShapeCount).Centroid.y
  177.                     CALL TranslateShape(ShapeCount, vtemp)
  178.                     Shape(ShapeCount).Velocity.x = 0
  179.                     Shape(ShapeCount).Velocity.y = 0
  180.                     Shape(ShapeCount).Omega = 0
  181.                 END IF
  182.             END IF
  183.             IF (_MOUSEBUTTON(2)) THEN
  184.                 IF (mb = 0) THEN
  185.                     mb = 1
  186.                     x = x - (_WIDTH / 2)
  187.                     y = -y + (_HEIGHT / 2)
  188.                     CALL NewAutoBall(x, y, 20, 0, 1, 1, 1)
  189.                     _DELAY .1
  190.                 END IF
  191.             END IF
  192.         END IF
  193.     LOOP
  194.  
  195.     ' Proximity detection
  196.     ProximalPairsCount = 0
  197.     Shape1 = 0
  198.     Shape2 = 0
  199.     FOR j = 1 TO ShapeCount
  200.         Shape(j).CollisionSwitch = 0
  201.         Shape(j).DeltaO = 0
  202.         Shape(j).DeltaV.x = 0
  203.         Shape(j).DeltaV.y = 0
  204.         Shape(j).PartialNormal.x = 0
  205.         Shape(j).PartialNormal.y = 0
  206.         FOR k = j + 1 TO ShapeCount
  207.             dx = Shape(j).Centroid.x - Shape(k).Centroid.x
  208.             dy = Shape(j).Centroid.y - Shape(k).Centroid.y
  209.             dr = SQR(dx * dx + dy * dy)
  210.             IF (dr < (1.15) * (Shape(j).DiameterMax + Shape(k).DiameterMax)) THEN
  211.                 ProximalPairsCount = ProximalPairsCount + 1
  212.                 ProximalPairs(ProximalPairsCount, 1) = j
  213.                 ProximalPairs(ProximalPairsCount, 2) = k
  214.                 Shape1 = j
  215.                 Shape2 = k
  216.             END IF
  217.         NEXT
  218.     NEXT
  219.  
  220.     IF (ProximalPairsCount > 0) THEN
  221.         FOR n = 1 TO ProximalPairsCount
  222.             Shape1 = ProximalPairs(n, 1)
  223.             Shape2 = ProximalPairs(n, 2)
  224.  
  225.             ' Collision detection
  226.             rmin = 999999999
  227.             ClosestIndex1 = 0
  228.             ClosestIndex2 = 0
  229.             FOR j = 1 TO Shape(Shape1).Elements
  230.                 FOR k = 1 TO Shape(Shape2).Elements
  231.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
  232.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
  233.                     r2 = dx * dx + dy * dy
  234.  
  235.                     IF (r2 <= 8) THEN
  236.  
  237.                         ' Normal vector 1
  238.                         nx1 = CalculateNormalY(Shape1, j)
  239.                         ny1 = -CalculateNormalX(Shape1, j)
  240.                         nn = SQR(nx1 * nx1 + ny1 * ny1)
  241.                         nx1 = nx1 / nn
  242.                         ny1 = ny1 / nn
  243.                         Shape(Shape1).PartialNormal.x = Shape(Shape1).PartialNormal.x + nx1
  244.                         Shape(Shape1).PartialNormal.y = Shape(Shape1).PartialNormal.y + ny1
  245.  
  246.                         ' Normal vector 2
  247.                         nx2 = CalculateNormalY(Shape2, k)
  248.                         ny2 = -CalculateNormalX(Shape2, k)
  249.                         nn = SQR(nx2 * nx2 + ny2 * ny2)
  250.                         nx2 = nx2 / nn
  251.                         ny2 = ny2 / nn
  252.                         Shape(Shape2).PartialNormal.x = Shape(Shape2).PartialNormal.x + nx2
  253.                         Shape(Shape2).PartialNormal.y = Shape(Shape2).PartialNormal.y + ny2
  254.  
  255.                     END IF
  256.                     IF (r2 < rmin) THEN
  257.                         rmin = r2
  258.                         ClosestIndex1 = j
  259.                         ClosestIndex2 = k
  260.                     END IF
  261.                 NEXT
  262.             NEXT
  263.  
  264.             IF (rmin <= 8) THEN
  265.  
  266.                 ' Undo previous motion
  267.                 IF (Shape(Shape1).Collisions = 0) THEN
  268.                     CALL RotShape(Shape1, Shape(Shape1).Centroid, -Shape(Shape1).Omega)
  269.                     vtemp.x = -(Shape(Shape1).Velocity.x)
  270.                     vtemp.y = -(Shape(Shape1).Velocity.y)
  271.                     CALL TranslateShape(Shape1, vtemp)
  272.                 END IF
  273.                 IF (Shape(Shape2).Collisions = 0) THEN
  274.                     CALL RotShape(Shape2, Shape(Shape2).Centroid, -Shape(Shape2).Omega)
  275.                     vtemp.x = -(Shape(Shape2).Velocity.x)
  276.                     vtemp.y = -(Shape(Shape2).Velocity.y)
  277.                     CALL TranslateShape(Shape2, vtemp)
  278.                 END IF
  279.  
  280.                 IF (Shape(Shape1).Collisions = 0) THEN
  281.                     Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * .75
  282.                     Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * .75
  283.                 END IF
  284.                 IF (Shape(Shape2).Collisions = 0) THEN
  285.                     Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * .75
  286.                     Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * .75
  287.                 END IF
  288.  
  289.                 CollisionCount = CollisionCount + 1
  290.                 Shape(Shape1).CollisionSwitch = 1
  291.                 Shape(Shape2).CollisionSwitch = 1
  292.  
  293.                 ' Normal vector 1 (nx1, ny1)
  294.                 nn = SQR(Shape(Shape1).PartialNormal.x * Shape(Shape1).PartialNormal.x + Shape(Shape1).PartialNormal.y * Shape(Shape1).PartialNormal.y)
  295.                 nx1 = Shape(Shape1).PartialNormal.x / nn
  296.                 ny1 = Shape(Shape1).PartialNormal.y / nn
  297.                 Shape(Shape1).PartialNormal.x = nx1
  298.                 Shape(Shape1).PartialNormal.y = ny1
  299.  
  300.                 ' Normal vector 2 (nx2, ny2)
  301.                 nn = SQR(Shape(Shape2).PartialNormal.x * Shape(Shape2).PartialNormal.x + Shape(Shape2).PartialNormal.y * Shape(Shape2).PartialNormal.y)
  302.                 nx2 = Shape(Shape2).PartialNormal.x / nn
  303.                 ny2 = Shape(Shape2).PartialNormal.y / nn
  304.                 Shape(Shape2).PartialNormal.x = nx2
  305.                 Shape(Shape2).PartialNormal.y = ny2
  306.  
  307.                 ' Contact-centroid differentials 1 (dx1, dy1)
  308.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).Centroid.x
  309.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).Centroid.y
  310.  
  311.                 ' Contact-centroid differentials 2 (dx2, dy2)
  312.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).Centroid.x
  313.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).Centroid.y
  314.  
  315.                 ' Perpendicular vector 1 (px1, py1)
  316.                 px1 = -dy1
  317.                 py1 = dx1
  318.                 pp = SQR(px1 * px1 + py1 * py1)
  319.                 px1 = px1 / pp
  320.                 py1 = py1 / pp
  321.  
  322.                 ' Perpendicular vector 2 (px2, py2)
  323.                 px2 = -dy2
  324.                 py2 = dx2
  325.                 pp = SQR(px2 * px2 + py2 * py2)
  326.                 px2 = px2 / pp
  327.                 py2 = py2 / pp
  328.  
  329.                 ' Angular velocity vector 1 (w1, r1, vx1, vy1)
  330.                 w1 = Shape(Shape1).Omega
  331.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
  332.                 vx1 = w1 * r1 * px1
  333.                 vy1 = w1 * r1 * py1
  334.  
  335.                 ' Angular velocity vector 2 (w2, r2, vx2, vy2)
  336.                 w2 = Shape(Shape2).Omega
  337.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
  338.                 vx2 = w2 * r2 * px2
  339.                 vy2 = w2 * r2 * py2
  340.  
  341.                 ' Mass terms (m1, m2, mu)
  342.                 m1 = Shape(Shape1).Mass
  343.                 m2 = Shape(Shape2).Mass
  344.                 mu = 1 / (1 / m1 + 1 / m2)
  345.  
  346.                 ' Re-Calculate moment of inertia (i1, i2)
  347.                 vtemp.x = PointChain(Shape1, ClosestIndex1).x
  348.                 vtemp.y = PointChain(Shape1, ClosestIndex1).y
  349.                 CALL CalculateMOI(Shape1, vtemp)
  350.                 vtemp.x = PointChain(Shape2, ClosestIndex2).x
  351.                 vtemp.y = PointChain(Shape2, ClosestIndex2).y
  352.                 CALL CalculateMOI(Shape2, vtemp)
  353.                 i1 = Shape(Shape1).MOI
  354.                 i2 = Shape(Shape2).MOI
  355.  
  356.                 ' Velocity differentials (v1, v2, dvtx, dvty)
  357.                 vcx1 = Shape(Shape1).Velocity.x
  358.                 vcy1 = Shape(Shape1).Velocity.y
  359.                 vcx2 = Shape(Shape2).Velocity.x
  360.                 vcy2 = Shape(Shape2).Velocity.y
  361.                 vtx1 = vcx1 + vx1
  362.                 vty1 = vcy1 + vy1
  363.                 vtx2 = vcx2 + vx2
  364.                 vty2 = vcy2 + vy2
  365.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
  366.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
  367.                 dvtx = vtx2 - vtx1
  368.                 dvty = vty2 - vty1
  369.  
  370.                 ' Geometry (n1dotdvt, n2dotdvt)
  371.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
  372.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
  373.  
  374.                 ' Momentum exchange (qx1, qy1, qx2, qy2)
  375.                 qx1 = nx1 * 2 * mu * n1dotdvt
  376.                 qy1 = ny1 * 2 * mu * n1dotdvt
  377.                 qx2 = nx2 * 2 * mu * n2dotdvt
  378.                 qy2 = ny2 * 2 * mu * n2dotdvt
  379.  
  380.                 ' Momentum exchange unit vector
  381.                 qq = SQR(qx1 * qx1 + qy1 * qy1)
  382.                 qhatx1 = qx1 / qq
  383.                 qhaty1 = qy1 / qq
  384.                 qq = SQR(qx2 * qx2 + qy2 * qy2)
  385.                 qhatx2 = qx2 / qq
  386.                 qhaty2 = qy2 / qq
  387.  
  388.                 ' Translational impulse
  389.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
  390.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
  391.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
  392.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
  393.                 f1 = -q1dotn1 * n1dotr1hat
  394.                 f2 = -q2dotn2 * n2dotr2hat
  395.                 Shape(Shape1).DeltaV.x = Shape(Shape1).DeltaV.x + f1 * qx1 / m1
  396.                 Shape(Shape1).DeltaV.y = Shape(Shape1).DeltaV.y + f1 * qy1 / m1
  397.                 Shape(Shape2).DeltaV.x = Shape(Shape2).DeltaV.x + f2 * qx2 / m2
  398.                 Shape(Shape2).DeltaV.y = Shape(Shape2).DeltaV.y + f2 * qy2 / m2
  399.  
  400.                 ' Angular impulse
  401.                 q1dotp1 = qx1 * px1 + qy1 * py1
  402.                 q2dotp2 = qx2 * px2 + qy2 * py2
  403.                 dw1 = r1 * q1dotp1 / i1
  404.                 dw2 = -r2 * q2dotp2 / i2
  405.                 Shape(Shape1).DeltaO = Shape(Shape1).DeltaO + dw1
  406.                 Shape(Shape2).DeltaO = Shape(Shape2).DeltaO + dw2
  407.  
  408.                 ' Separate along normal
  409.                 'IF (Shape(Shape1).Collisions = 0) THEN
  410.                 vtemp.x = -nx1 * 1 * ((v1 + 0) / m1)
  411.                 vtemp.y = -ny1 * 1 * ((v1 + 0) / m1)
  412.                 CALL TranslateShape(Shape1, vtemp)
  413.                 'END IF
  414.                 'IF (Shape(Shape2).Collisions = 0) THEN
  415.                 vtemp.x = -nx2 * 1 * ((v2 + 0) / m2)
  416.                 vtemp.y = -ny2 * 1 * ((v2 + 0) / m2)
  417.                 CALL TranslateShape(Shape2, vtemp)
  418.                 'END IF
  419.  
  420.                 ' External torque
  421.                 'IF (Shape(Shape1).Collisions > 0) THEN
  422.                 torque1 = dx1 * ForceField.y - dy1 * ForceField.x
  423.                 Shape(Shape1).DeltaO = Shape(Shape1).DeltaO - m1 * torque1 / i1
  424.                 'END IF
  425.                 'IF (Shape(Shape2).Collisions > 0) THEN
  426.                 torque2 = dx2 * ForceField.y - dy2 * ForceField.x
  427.                 Shape(Shape2).DeltaO = Shape(Shape2).DeltaO - m2 * torque2 / i2
  428.                 'END IF
  429.  
  430.                 ' Feedback
  431.                 CALL snd(100 * (v1 + v2) / 2, .5)
  432.  
  433.                 'END IF
  434.             END IF
  435.         NEXT
  436.     END IF
  437.  
  438.     FOR ShapeIndex = 1 TO ShapeCount
  439.  
  440.         ' Contact update
  441.         IF (Shape(ShapeIndex).CollisionSwitch = 1) THEN
  442.             Shape(ShapeIndex).Collisions = Shape(ShapeIndex).Collisions + 1
  443.         ELSE
  444.             Shape(ShapeIndex).Collisions = 0
  445.         END IF
  446.  
  447.         IF ((Shape(ShapeIndex).Fixed = 0)) THEN
  448.  
  449.             ' Angular velocity update
  450.             Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + Shape(ShapeIndex).DeltaO
  451.  
  452.             ' Linear velocity update
  453.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Shape(ShapeIndex).DeltaV.x
  454.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Shape(ShapeIndex).DeltaV.y
  455.  
  456.             IF (Shape(ShapeIndex).Collisions = 0) THEN
  457.                 ' Freefall (if airborne)
  458.                 Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + ForceField.x
  459.                 Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + ForceField.y
  460.             ELSE
  461.                 ' Friction
  462.                 IF (Shape(ShapeIndex).Velocity.x * Shape(ShapeIndex).Velocity.x) < .05 THEN Shape(ShapeIndex).Velocity.x = 0
  463.                 IF (Shape(ShapeIndex).Velocity.y * Shape(ShapeIndex).Velocity.y) < .05 THEN Shape(ShapeIndex).Velocity.y = 0
  464.                 'IF (Shape(ShapeIndex).Omega * Shape(ShapeIndex).Omega) < .001 THEN Shape(ShapeIndex).Omega = 0
  465.             END IF
  466.  
  467.             ' Rotation update
  468.             CALL RotShape(ShapeIndex, Shape(ShapeIndex).Centroid, Shape(ShapeIndex).Omega)
  469.  
  470.             ' Position update
  471.             CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
  472.  
  473.             ' Damping
  474.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .995
  475.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .995
  476.             'Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * (1 - .25 * (Shape(ShapeIndex).DiameterMin / Shape(ShapeIndex).DiameterMax))
  477.  
  478.         END IF
  479.     NEXT
  480.  
  481.     CALL Graphics
  482.     _LIMIT 120
  484.  
  486.  
  487. SUB Graphics
  488.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
  489.     FOR ShapeIndex = 1 TO ShapeCount
  490.         'LOCATE 1, 1: PRINT ProximalPairsCount, CollisionCount ', Shape(ShapeCount).Collisions, Shape(ShapeCount - 1).Collisions
  491.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
  492.             CALL cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
  493.             CALL cline(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, PointChain(ShapeIndex, i + 1).x, PointChain(ShapeIndex, i + 1).y, Shape(ShapeIndex).Shade)
  494.         NEXT
  495.         CALL cpset(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, Shape(ShapeIndex).Shade)
  496.         CALL cline(PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, Shape(ShapeIndex).Shade)
  497.         'CALL cline(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, Shape(ShapeIndex).Shade)
  498.         'CALL ccircle(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, 3, _RGB(255, 255, 255))
  499.     NEXT
  500.     CALL cpaint(Shape(ShapeCount).Centroid.x, Shape(ShapeCount).Centroid.y, Shape(ShapeCount).Shade, Shape(ShapeCount).Shade)
  501.     _DISPLAY
  503.  
  504. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
  505.     DIM l AS Vector
  506.     DIM r AS Vector
  507.     li = i - 1
  508.     ri = i + 1
  509.     IF (i = 1) THEN li = Shape(k).Elements
  510.     IF (i = Shape(k).Elements) THEN ri = 1
  511.     l.x = PointChain(k, li).x
  512.     r.x = PointChain(k, ri).x
  513.     dx = r.x - l.x
  514.     CalculateNormalX = dx
  516.  
  517. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
  518.     DIM l AS Vector
  519.     DIM r AS Vector
  520.     li = i - 1
  521.     ri = i + 1
  522.     IF (i = 1) THEN li = Shape(k).Elements
  523.     IF (i = Shape(k).Elements) THEN ri = 1
  524.     l.y = PointChain(k, li).y
  525.     r.y = PointChain(k, ri).y
  526.     dy = r.y - l.y
  527.     CalculateNormalY = dy
  529.  
  530. SUB CalculateCentroid (k AS INTEGER)
  531.     xx = 0
  532.     yy = 0
  533.     FOR i = 1 TO Shape(k).Elements
  534.         xx = xx + PointChain(k, i).x
  535.         yy = yy + PointChain(k, i).y
  536.     NEXT
  537.     Shape(k).Centroid.x = xx / Shape(k).Elements
  538.     Shape(k).Centroid.y = yy / Shape(k).Elements
  540.  
  541. SUB CalculateDiameterMin (k AS INTEGER)
  542.     r2min = 999 ^ 999
  543.     FOR i = 1 TO Shape(k).Elements
  544.         xx = Shape(k).Centroid.x - PointChain(k, i).x
  545.         yy = Shape(k).Centroid.y - PointChain(k, i).y
  546.         r2 = xx * xx + yy * yy
  547.         IF (r2 < r2min) THEN
  548.             r2min = r2
  549.         END IF
  550.     NEXT
  551.     Shape(k).DiameterMin = SQR(r2min)
  553.  
  554. SUB CalculateDiameterMax (k AS INTEGER)
  555.     r2max = -1
  556.     FOR i = 1 TO Shape(k).Elements
  557.         xx = Shape(k).Centroid.x - PointChain(k, i).x
  558.         yy = Shape(k).Centroid.y - PointChain(k, i).y
  559.         r2 = xx * xx + yy * yy
  560.         IF (r2 > r2max) THEN
  561.             r2max = r2
  562.         END IF
  563.     NEXT
  564.     Shape(k).DiameterMax = SQR(r2max)
  566.  
  567. SUB CalculateMass (k AS INTEGER, factor AS DOUBLE)
  568.     aa = 0
  569.     FOR i = 1 TO Shape(k).Elements - 1
  570.         x = (Shape(k).Centroid.x - PointChain(k, i).x)
  571.         y = (Shape(k).Centroid.y - PointChain(k, i).y)
  572.         dx = (Shape(k).Centroid.x - PointChain(k, i + 1).x) - x
  573.         dy = (Shape(k).Centroid.y - PointChain(k, i + 1).y) - y
  574.         da = .5 * (x * dy - y * dx)
  575.         aa = aa + da
  576.     NEXT
  577.     Shape(k).Mass = factor * SQR(aa * aa)
  579.  
  580. SUB CalculateMOI (k AS INTEGER, ctrvec AS Vector)
  581.     xx = 0
  582.     yy = 0
  583.     FOR i = 1 TO Shape(k).Elements
  584.         a = ctrvec.x - PointChain(k, i).x
  585.         b = ctrvec.y - PointChain(k, i).y
  586.         xx = xx + a * a
  587.         yy = yy + b * b
  588.     NEXT
  589.     Shape(k).MOI = SQR((xx + yy) * (xx + yy)) * (Shape(k).Mass / Shape(k).Elements)
  591.  
  592. SUB TranslateShape (k AS INTEGER, c AS Vector)
  593.     FOR i = 1 TO Shape(k).Elements
  594.         PointChain(k, i).x = PointChain(k, i).x + c.x
  595.         PointChain(k, i).y = PointChain(k, i).y + c.y
  596.     NEXT
  597.     Shape(k).Centroid.x = Shape(k).Centroid.x + c.x
  598.     Shape(k).Centroid.y = Shape(k).Centroid.y + c.y
  600.  
  601. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
  602.     FOR i = 1 TO Shape(k).Elements
  603.         xx = PointChain(k, i).x - c.x
  604.         yy = PointChain(k, i).y - c.y
  605.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
  606.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
  607.     NEXT
  608.     xx = Shape(k).Centroid.x - c.x
  609.     yy = Shape(k).Centroid.y - c.y
  610.     Shape(k).Centroid.x = c.x + xx * COS(da) - yy * SIN(da)
  611.     Shape(k).Centroid.y = c.y + yy * COS(da) + xx * SIN(da)
  613.  
  614. SUB NewAutoBall (x1, y1, r1, r2, pa, pb, fx)
  615.     ShapeCount = ShapeCount + 1
  616.     Shape(ShapeCount).Fixed = fx
  617.     Shape(ShapeCount).Collisions = 0
  618.     i = 0
  619.     FOR j = 0 TO 2 * 4 * ATN(1) - .15 STEP .15
  620.         i = i + 1
  621.         r = r1 + r2 * COS(pa * j) ^ pb
  622.         PointChain(ShapeCount, i).x = x1 + r * COS(j)
  623.         PointChain(ShapeCount, i).y = y1 + r * SIN(j)
  624.     NEXT
  625.     Shape(ShapeCount).Elements = i
  626.     IF (fx = 0) THEN
  627.         CALL CalculateMass(ShapeCount, 1)
  628.     ELSE
  629.         CALL CalculateMass(ShapeCount, 999999)
  630.     END IF
  631.     CALL CalculateCentroid(ShapeCount)
  632.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  633.     CALL CalculateDiameterMin(ShapeCount)
  634.     CALL CalculateDiameterMax(ShapeCount)
  635.     Shape(ShapeCount).Velocity.x = 0
  636.     Shape(ShapeCount).Velocity.y = 0
  637.     Shape(ShapeCount).Omega = 0
  638.     IF (fx = 0) THEN
  639.         Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
  640.     ELSE
  641.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
  642.     END IF
  644.  
  645. SUB NewAutoBrick (x1, y1, wx, wy, ang)
  646.     ShapeCount = ShapeCount + 1
  647.     Shape(ShapeCount).Fixed = 1
  648.     Shape(ShapeCount).Collisions = 0
  649.     i = 0
  650.     FOR j = -wy / 2 TO wy / 2 STEP 5
  651.         i = i + 1
  652.         PointChain(ShapeCount, i).x = x1 + wx / 2
  653.         PointChain(ShapeCount, i).y = y1 + j
  654.     NEXT
  655.     FOR j = wx / 2 TO -wx / 2 STEP -5
  656.         i = i + 1
  657.         PointChain(ShapeCount, i).x = x1 + j
  658.         PointChain(ShapeCount, i).y = y1 + wy / 2
  659.     NEXT
  660.     FOR j = wy / 2 TO -wy / 2 STEP -5
  661.         i = i + 1
  662.         PointChain(ShapeCount, i).x = x1 - wx / 2
  663.         PointChain(ShapeCount, i).y = y1 + j
  664.     NEXT
  665.     FOR j = -wx / 2 TO wx / 2 STEP 5
  666.         i = i + 1
  667.         PointChain(ShapeCount, i).x = x1 + j
  668.         PointChain(ShapeCount, i).y = y1 - wy / 2
  669.     NEXT
  670.     Shape(ShapeCount).Elements = i
  671.     CALL CalculateMass(ShapeCount, 99999)
  672.     CALL CalculateCentroid(ShapeCount)
  673.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  674.     CALL CalculateDiameterMin(ShapeCount)
  675.     CALL CalculateDiameterMax(ShapeCount)
  676.     Shape(ShapeCount).MOI = 999 ^ 999
  677.     Shape(ShapeCount).Velocity.x = 0
  678.     Shape(ShapeCount).Velocity.y = 0
  679.     Shape(ShapeCount).Omega = 0
  680.     Shape(ShapeCount).Shade = _RGB(100, 100, 100)
  681.     CALL RotShape(ShapeCount, Shape(ShapeCount).Centroid, ang)
  683.  
  684. SUB NewBrickLine (xi, yi, xf, yf, l, w)
  685.     d1 = SQR((xf - xi) ^ 2 + (yf - yi) ^ 2)
  686.     d2 = SQR(l ^ 2 + w ^ 2)
  687.     ang = ATN((yf - yi) / (xf - xi))
  688.     FOR t = 0 TO 1 STEP 1.175 * d2 / d1
  689.         CALL NewAutoBrick(xi * (1 - t) + xf * t, yi * (1 - t) + yf * t, l, w, ang)
  690.     NEXT
  692.  
  693. SUB NewMouseShape (rawresolution AS DOUBLE, targetpoints AS INTEGER, smoothiterations AS INTEGER)
  694.     'rawresolution = Raw curve resolution.
  695.     'targetpoints = Number of points per curve.
  696.     'smoothiterations = Magnitude of smooth effect.
  697.  
  698.     ShapeCount = ShapeCount + 1
  699.     Shape(ShapeCount).Fixed = 0
  700.     Shape(ShapeCount).Collisions = 0
  701.  
  702.     numpoints = 0
  703.  
  704.     ' Click+drag mouse button 1 to trace out a curve.
  705.     xold = 999999
  706.     yold = 999999
  707.     DO
  708.         DO WHILE _MOUSEINPUT
  709.             x = _MOUSEX
  710.             y = _MOUSEY
  711.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
  712.                 IF _MOUSEBUTTON(1) THEN
  713.                     x = x - (_WIDTH / 2)
  714.                     y = -y + (_HEIGHT / 2)
  715.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
  716.  
  717.                     ' Collect data only if the new point is sufficiently far away from the previous point.
  718.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
  719.                         numpoints = numpoints + 1
  720.                         PointChain(ShapeCount, numpoints).x = x
  721.                         PointChain(ShapeCount, numpoints).y = y
  722.                         CALL cpset(x, y, _RGB(0, 255, 255))
  723.                         xold = x
  724.                         yold = y
  725.                     END IF
  726.                 END IF
  727.             END IF
  728.         LOOP
  729.         _DISPLAY
  730.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
  731.  
  732.     ' If the curve contains less than the minimum numer of points, use interpolation to fill in the gaps.
  733.     DO WHILE (numpoints < targetpoints)
  734.  
  735.         ' Determine the pair of neighboring points that have the greatest separation of all pairs.
  736.         rad2max = -1
  737.         kmax = -1
  738.         FOR k = 1 TO numpoints - 1
  739.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
  740.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
  741.             rad2 = xfac ^ 2 + yfac ^ 2
  742.             IF rad2 > rad2max THEN
  743.                 kmax = k
  744.                 rad2max = rad2
  745.             END IF
  746.         NEXT
  747.         '''
  748.         edgecase = 0
  749.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
  750.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
  751.         rad2 = xfac ^ 2 + yfac ^ 2
  752.         IF rad2 > rad2max THEN
  753.             kmax = numpoints
  754.             rad2max = rad2
  755.             edgecase = 1
  756.         END IF
  757.         '''
  758.         IF (edgecase = 0) THEN
  759.  
  760.             numpoints = numpoints + 1
  761.  
  762.             ' Starting next to kmax, create a gap by shifting all other points by one index.
  763.             FOR j = numpoints TO kmax + 1 STEP -1
  764.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
  765.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
  766.             NEXT
  767.  
  768.             ' Fill the gap with a new point whose position is determined by the average of its neighbors.
  769.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
  770.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
  771.  
  772.         ELSE
  773.             numpoints = numpoints + 1
  774.             xx = PointChain(ShapeCount, numpoints - 1).x
  775.             yy = PointChain(ShapeCount, numpoints - 1).y
  776.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
  777.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
  778.         END IF
  779.  
  780.     LOOP
  781.  
  782.     ' At this stage, the curve still has all of its sharp edges. Use a relaxation method to smooth.
  783.     ' The new position of a point is equal to the average position of its neighboring points.
  784.     CALL SmoothShape(ShapeCount, numpoints, smoothiterations)
  785.  
  786.     Shape(ShapeCount).Elements = numpoints
  787.     CALL CalculateMass(ShapeCount, 1)
  788.     CALL CalculateCentroid(ShapeCount)
  789.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  790.     CALL CalculateDiameterMin(ShapeCount)
  791.     CALL CalculateDiameterMax(ShapeCount)
  792.     Shape(ShapeCount).Velocity.x = 0
  793.     Shape(ShapeCount).Velocity.y = 0
  794.     Shape(ShapeCount).Omega = 0
  795.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
  796.  
  798.  
  799. SUB SmoothShape (i AS INTEGER, n AS INTEGER, s AS INTEGER)
  800.     FOR j = 1 TO s
  801.         FOR k = 2 TO n - 1
  802.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
  803.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
  804.         NEXT
  805.         FOR k = 2 TO n - 1
  806.             PointChain(i, k).x = TempChain(i, k).x
  807.             PointChain(i, k).y = TempChain(i, k).y
  808.         NEXT
  809.     NEXT
  811.  
  812. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
  813.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
  815.  
  816. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
  817.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
  819.  
  820. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
  821.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
  823.  
  824. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
  825.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
  827.  
  828. SUB cprintstring (y, a AS STRING)
  829.     _PRINTSTRING (_WIDTH / 2 - (LEN(a) * 8) / 2, -y + _HEIGHT / 2), a
  831.  
  832. SUB snd (frq, dur)
  833.     IF ((frq >= 37) AND (frq <= 2000)) THEN
  834.         SOUND frq, dur
  835.     END IF
« Last Edit: February 29, 2020, 08:08:47 pm by STxAxTIC »
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Offline TerryRitchie

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #17 on: February 29, 2020, 07:18:01 pm »
Quote from: STxAxTIC on February 29, 2020, 07:04:04 pm
A quick update below. Still deciding what the end-game for this will be.

Something like Box2D for QB64 would be awesome! :-)))

https://box2d.org/
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FellippeHeitor

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #18 on: February 29, 2020, 07:21:57 pm »
A very interesting update! Objects seem heavier and more easily controllable. I bounced an object against one of the primary eggs so hard that it ended up inside a potato I'd drawn before.

This is so cool, man.

 
Captura de Tela 2020-02-29 às 21.17.48.png
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Offline STxAxTIC

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #19 on: February 29, 2020, 07:34:46 pm »
@TerryRitchie

Yeah, there are a handful of nice examples of 2D physics libraries out there, box2d seems cool, I like matter.js quite a bit too. I'm finding that JS and C++ are a bit faster than QB64 for a variety of reasons, and the more complexity I add, the more complicated the loop gets and things bog down. I'm trying to walk that fine edge between capturing real physics and being just simply efficient. It's an incredibly slow process given my schedule. I can only wrap my head properly around this like one day a week, haha. So there's that effect too.

@FellippeHeitor

Thanks for noting that behavior! I undoubtedly noticed, and oh man - there is some wacky stuff you can do. It turns out that objects being drawn clockwise turned out to have *negative* mass, which is surely a bug I fixed - but now the centroid has to always be inside the object. You can intentionally draw objects within objects, but of course they exchange momentum backwards, haha. If I decide to keep that I'll have to put in a line that reverses a normal vector somewhere.

Since I'm not sure I want this code dominating my life and I'm only one guy, I may let this round off right where it is: doing collisions more-or-less perfectly, but avoid doing rag-doll physics, meshes, membranes, or whatever would be next.
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Offline STxAxTIC

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #20 on: March 01, 2020, 02:55:01 am »
Made the code far tighter, and to celebrate, here's the best pool break I've made to date. It's not the real game of course, but if anyone in that department wants to start thinking about graphics, you've got the motion part already.

By "tighter", I mean everything that specifies the game, including physics constants, takes place before line, I think 115 in this edition, and that can be made even sooner.

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. start:
  9.  
  11.  
  12. ' Data structures
  13. TYPE Vector
  14.     x AS DOUBLE
  15.     y AS DOUBLE
  17.  
  18. DIM SHARED vtemp AS Vector
  19.  
  20. ' Object type
  21. TYPE Object
  22.     Centroid AS Vector
  23.     Collisions AS LONG
  24.     CollisionSwitch AS INTEGER
  25.     DeltaO AS DOUBLE
  26.     DeltaV AS Vector
  27.     DiameterMax AS DOUBLE
  28.     DiameterMin AS DOUBLE
  29.     Elements AS INTEGER
  30.     Fixed AS INTEGER
  31.     Mass AS DOUBLE
  32.     MOI AS DOUBLE
  33.     PartialNormal AS Vector
  34.     Omega AS DOUBLE
  35.     Shade AS _UNSIGNED LONG
  36.     Velocity AS Vector
  38.  
  39. ' Object storage
  40. DIM SHARED Shape(300) AS Object
  41. DIM SHARED PointChain(300, 500) AS Vector
  42. DIM SHARED TempChain(300, 500) AS Vector
  43. DIM SHARED ShapeCount AS INTEGER
  44.  
  45. ' Dynamics
  46. DIM SHARED CollisionCount AS INTEGER
  47. DIM SHARED ProximalPairs(300 / 2, 1 TO 2)
  48. DIM SHARED ProximalPairsCount
  49. DIM SHARED CPC, FPC, RST, VD, SV
  50.  
  51. ' Environment
  52. DIM SHARED ForceField AS Vector ' Gravity
  53.  
  54. ' Initialize
  55. ShapeCount = 0
  56. CollisionCount = 0
  57.  
  58. ' Prompt
  60. CALL cprintstring(16 * 4, "WELCOME!                  ")
  61. CALL cprintstring(16 * 3, "Press 1 for Pool Prototype")
  62. CALL cprintstring(16 * 2, "Press 2 for Wacky Game    ")
  64.  
  66.     kk = _KEYHIT
  67.     SELECT CASE kk
  68.         CASE ASC("1")
  69.             CALL SetupPool
  70.             EXIT DO
  71.         CASE ASC("2")
  72.             CALL SetupWackyGame
  73.             EXIT DO
  74.     END SELECT
  75.     IF (kk) THEN
  76.         _KEYCLEAR
  77.     END IF
  78.     _LIMIT 30
  80.  
  81. CALL Graphics
  82. CALL cprintstring(-16 * 3, "During Play:")
  83. CALL cprintstring(-16 * 5, "Arrow keys boost most recently-created object.")
  84. CALL cprintstring(-16 * 6, "Mouse 1 moves most recently-created object.   ")
  85. CALL cprintstring(-16 * 7, "ESC halts all motion.                         ")
  86. CALL cprintstring(-16 * 8, "Space enters creative mode.                   ")
  87. CALL cprintstring(-16 * 9, "Press 'r' to restart.                         ")
  88. CALL cprintstring(-16 * 11, "PRESS ANY KEY TO BEGIN.")
  93.  
  94. ' Main loop
  96.     IF (UserInput = -1) THEN GOTO start
  97.     CALL PairDynamics(CPC, FPC, RST)
  98.     CALL FleetDynamics(VD, SV)
  99.     CALL Graphics
  100.     _LIMIT 120
  102.  
  104.  
  105. FUNCTION UserInput
  106.     TheReturn = 0
  107.     ' Keyboard input
  108.     kk = _KEYHIT
  109.     SELECT CASE kk
  110.         CASE 32
  111.             DO: LOOP UNTIL _KEYHIT
  112.             WHILE _MOUSEINPUT: WEND
  113.             _KEYCLEAR
  114.             CALL cprintstring(16 * 17, "Drag mouse counter-clockwise to draw a new shape.")
  115.             CALL cprintstring(16 * 16, "Make sure centroid is inside body.")
  116.             'CALL Graphics
  117.             CALL NewMouseShape(7.5, 75, 25)
  118.             CLS
  119.         CASE 18432, ASC("w") ' Up arrow
  120.             Shape(ShapeCount).Velocity.y = Shape(ShapeCount).Velocity.y * 1.1 + 2
  121.         CASE 20480, ASC("s") ' Down arrow
  122.             Shape(ShapeCount).Velocity.y = Shape(ShapeCount).Velocity.y * 0.9 - 2
  123.         CASE 19200, ASC("a") ' Left arrow
  124.             Shape(ShapeCount).Velocity.x = Shape(ShapeCount).Velocity.x * 0.9 - 2
  125.         CASE 19712, ASC("d") ' Right arrow
  126.             Shape(ShapeCount).Velocity.x = Shape(ShapeCount).Velocity.x * 1.1 + 2
  127.         CASE ASC("r")
  128.             TheReturn = -1
  129.         CASE 27
  130.             FOR k = 1 TO ShapeCount
  131.                 Shape(k).Velocity.x = .000001
  132.                 Shape(k).Velocity.y = .000001
  133.                 Shape(k).Omega = .000001
  134.             NEXT
  135.     END SELECT
  136.     IF (kk) THEN
  137.         _KEYCLEAR
  138.     END IF
  139.  
  140.     ' Mouse input
  141.     mb = 0
  143.         x = _MOUSEX
  144.         y = _MOUSEY
  145.         IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
  146.             IF (_MOUSEBUTTON(1)) THEN
  147.                 IF (mb = 0) THEN
  148.                     mb = 1
  149.                     x = x - (_WIDTH / 2)
  150.                     y = -y + (_HEIGHT / 2)
  151.                     vtemp.x = x - Shape(ShapeCount).Centroid.x
  152.                     vtemp.y = y - Shape(ShapeCount).Centroid.y
  153.                     CALL TranslateShape(ShapeCount, vtemp)
  154.                     Shape(ShapeCount).Velocity.x = 0
  155.                     Shape(ShapeCount).Velocity.y = 0
  156.                     Shape(ShapeCount).Omega = 0
  157.                 END IF
  158.             END IF
  159.             IF (_MOUSEBUTTON(2)) THEN
  160.                 IF (mb = 0) THEN
  161.                     mb = 1
  162.                     x = x - (_WIDTH / 2)
  163.                     y = -y + (_HEIGHT / 2)
  164.                     CALL NewAutoBall(x, y, 5, 0, 1, 1, 1)
  165.                     _DELAY .1
  166.                 END IF
  167.             END IF
  168.         END IF
  169.     LOOP
  170.     UserInput = TheReturn
  172.  
  173. SUB PairDynamics (CoarseProximityConstant, FineProximityConstant, Restitution)
  174.  
  175.     ' Proximity detection
  176.     ProximalPairsCount = 0
  177.     Shape1 = 0
  178.     Shape2 = 0
  179.     FOR j = 1 TO ShapeCount
  180.         Shape(j).CollisionSwitch = 0
  181.         Shape(j).DeltaO = 0
  182.         Shape(j).DeltaV.x = 0
  183.         Shape(j).DeltaV.y = 0
  184.         Shape(j).PartialNormal.x = 0
  185.         Shape(j).PartialNormal.y = 0
  186.         FOR k = j + 1 TO ShapeCount
  187.             dx = Shape(j).Centroid.x - Shape(k).Centroid.x
  188.             dy = Shape(j).Centroid.y - Shape(k).Centroid.y
  189.             dr = SQR(dx * dx + dy * dy)
  190.             IF (dr < (CoarseProximityConstant) * (Shape(j).DiameterMax + Shape(k).DiameterMax)) THEN
  191.                 ProximalPairsCount = ProximalPairsCount + 1
  192.                 ProximalPairs(ProximalPairsCount, 1) = j
  193.                 ProximalPairs(ProximalPairsCount, 2) = k
  194.                 Shape1 = j
  195.                 Shape2 = k
  196.             END IF
  197.         NEXT
  198.     NEXT
  199.  
  200.     IF (ProximalPairsCount > 0) THEN
  201.         FOR n = 1 TO ProximalPairsCount
  202.             Shape1 = ProximalPairs(n, 1)
  203.             Shape2 = ProximalPairs(n, 2)
  204.  
  205.             ' Collision detection
  206.             rmin = 999999999
  207.             ClosestIndex1 = 0
  208.             ClosestIndex2 = 0
  209.             FOR j = 1 TO Shape(Shape1).Elements
  210.                 FOR k = 1 TO Shape(Shape2).Elements
  211.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
  212.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
  213.                     r2 = dx * dx + dy * dy
  214.  
  215.                     IF (r2 <= FineProximityConstant) THEN
  216.  
  217.                         ' Normal vector 1
  218.                         nx1 = CalculateNormalY(Shape1, j)
  219.                         ny1 = -CalculateNormalX(Shape1, j)
  220.                         nn = SQR(nx1 * nx1 + ny1 * ny1)
  221.                         nx1 = nx1 / nn
  222.                         ny1 = ny1 / nn
  223.                         Shape(Shape1).PartialNormal.x = Shape(Shape1).PartialNormal.x + nx1
  224.                         Shape(Shape1).PartialNormal.y = Shape(Shape1).PartialNormal.y + ny1
  225.  
  226.                         ' Normal vector 2
  227.                         nx2 = CalculateNormalY(Shape2, k)
  228.                         ny2 = -CalculateNormalX(Shape2, k)
  229.                         nn = SQR(nx2 * nx2 + ny2 * ny2)
  230.                         nx2 = nx2 / nn
  231.                         ny2 = ny2 / nn
  232.                         Shape(Shape2).PartialNormal.x = Shape(Shape2).PartialNormal.x + nx2
  233.                         Shape(Shape2).PartialNormal.y = Shape(Shape2).PartialNormal.y + ny2
  234.  
  235.                     END IF
  236.                     IF (r2 < rmin) THEN
  237.                         rmin = r2
  238.                         ClosestIndex1 = j
  239.                         ClosestIndex2 = k
  240.                     END IF
  241.                 NEXT
  242.             NEXT
  243.  
  244.             IF (rmin <= FineProximityConstant) THEN
  245.  
  246.                 CollisionCount = CollisionCount + 1
  247.                 Shape(Shape1).CollisionSwitch = 1
  248.                 Shape(Shape2).CollisionSwitch = 1
  249.  
  250.                 ' Undo previous motion
  251.                 IF (Shape(Shape1).Collisions = 0) THEN
  252.                     CALL RotShape(Shape1, Shape(Shape1).Centroid, -Shape(Shape1).Omega)
  253.                     vtemp.x = -(Shape(Shape1).Velocity.x)
  254.                     vtemp.y = -(Shape(Shape1).Velocity.y)
  255.                     CALL TranslateShape(Shape1, vtemp)
  256.                 END IF
  257.                 IF (Shape(Shape2).Collisions = 0) THEN
  258.                     CALL RotShape(Shape2, Shape(Shape2).Centroid, -Shape(Shape2).Omega)
  259.                     vtemp.x = -(Shape(Shape2).Velocity.x)
  260.                     vtemp.y = -(Shape(Shape2).Velocity.y)
  261.                     CALL TranslateShape(Shape2, vtemp)
  262.                 END IF
  263.  
  264.                 IF (Shape(Shape1).Collisions = 0) THEN
  265.                     Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * Restitution
  266.                     Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * Restitution
  267.                 END IF
  268.                 IF (Shape(Shape2).Collisions = 0) THEN
  269.                     Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * Restitution
  270.                     Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * Restitution
  271.                 END IF
  272.  
  273.                 ' Normal vector 1 (nx1, ny1)
  274.                 nn = SQR(Shape(Shape1).PartialNormal.x * Shape(Shape1).PartialNormal.x + Shape(Shape1).PartialNormal.y * Shape(Shape1).PartialNormal.y)
  275.                 nx1 = Shape(Shape1).PartialNormal.x / nn
  276.                 ny1 = Shape(Shape1).PartialNormal.y / nn
  277.                 Shape(Shape1).PartialNormal.x = nx1
  278.                 Shape(Shape1).PartialNormal.y = ny1
  279.  
  280.                 ' Normal vector 2 (nx2, ny2)
  281.                 nn = SQR(Shape(Shape2).PartialNormal.x * Shape(Shape2).PartialNormal.x + Shape(Shape2).PartialNormal.y * Shape(Shape2).PartialNormal.y)
  282.                 nx2 = Shape(Shape2).PartialNormal.x / nn
  283.                 ny2 = Shape(Shape2).PartialNormal.y / nn
  284.                 Shape(Shape2).PartialNormal.x = nx2
  285.                 Shape(Shape2).PartialNormal.y = ny2
  286.  
  287.                 ' Contact-centroid differentials 1 (dx1, dy1)
  288.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).Centroid.x
  289.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).Centroid.y
  290.  
  291.                 ' Contact-centroid differentials 2 (dx2, dy2)
  292.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).Centroid.x
  293.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).Centroid.y
  294.  
  295.                 ' Perpendicular vector 1 (px1, py1)
  296.                 px1 = -dy1
  297.                 py1 = dx1
  298.                 pp = SQR(px1 * px1 + py1 * py1)
  299.                 px1 = px1 / pp
  300.                 py1 = py1 / pp
  301.  
  302.                 ' Perpendicular vector 2 (px2, py2)
  303.                 px2 = -dy2
  304.                 py2 = dx2
  305.                 pp = SQR(px2 * px2 + py2 * py2)
  306.                 px2 = px2 / pp
  307.                 py2 = py2 / pp
  308.  
  309.                 ' Angular velocity vector 1 (w1, r1, vx1, vy1)
  310.                 w1 = Shape(Shape1).Omega
  311.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
  312.                 vx1 = w1 * r1 * px1
  313.                 vy1 = w1 * r1 * py1
  314.  
  315.                 ' Angular velocity vector 2 (w2, r2, vx2, vy2)
  316.                 w2 = Shape(Shape2).Omega
  317.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
  318.                 vx2 = w2 * r2 * px2
  319.                 vy2 = w2 * r2 * py2
  320.  
  321.                 ' Mass terms (m1, m2, mu)
  322.                 m1 = Shape(Shape1).Mass
  323.                 m2 = Shape(Shape2).Mass
  324.                 mu = 1 / (1 / m1 + 1 / m2)
  325.  
  326.                 ' Re-Calculate moment of inertia (i1, i2)
  327.                 vtemp.x = PointChain(Shape1, ClosestIndex1).x
  328.                 vtemp.y = PointChain(Shape1, ClosestIndex1).y
  329.                 CALL CalculateMOI(Shape1, vtemp)
  330.                 vtemp.x = PointChain(Shape2, ClosestIndex2).x
  331.                 vtemp.y = PointChain(Shape2, ClosestIndex2).y
  332.                 CALL CalculateMOI(Shape2, vtemp)
  333.                 i1 = Shape(Shape1).MOI
  334.                 i2 = Shape(Shape2).MOI
  335.  
  336.                 ' Velocity differentials (v1, v2, dvtx, dvty)
  337.                 vcx1 = Shape(Shape1).Velocity.x
  338.                 vcy1 = Shape(Shape1).Velocity.y
  339.                 vcx2 = Shape(Shape2).Velocity.x
  340.                 vcy2 = Shape(Shape2).Velocity.y
  341.                 vtx1 = vcx1 + vx1
  342.                 vty1 = vcy1 + vy1
  343.                 vtx2 = vcx2 + vx2
  344.                 vty2 = vcy2 + vy2
  345.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
  346.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
  347.                 dvtx = vtx2 - vtx1
  348.                 dvty = vty2 - vty1
  349.  
  350.                 ' Geometry (n1dotdvt, n2dotdvt)
  351.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
  352.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
  353.  
  354.                 ' Momentum exchange (qx1, qy1, qx2, qy2)
  355.                 qx1 = nx1 * 2 * mu * n1dotdvt
  356.                 qy1 = ny1 * 2 * mu * n1dotdvt
  357.                 qx2 = nx2 * 2 * mu * n2dotdvt
  358.                 qy2 = ny2 * 2 * mu * n2dotdvt
  359.  
  360.                 ' Momentum exchange unit vector
  361.                 qq = SQR(qx1 * qx1 + qy1 * qy1)
  362.                 qhatx1 = qx1 / qq
  363.                 qhaty1 = qy1 / qq
  364.                 qq = SQR(qx2 * qx2 + qy2 * qy2)
  365.                 qhatx2 = qx2 / qq
  366.                 qhaty2 = qy2 / qq
  367.  
  368.                 ' Translational impulse
  369.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
  370.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
  371.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
  372.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
  373.                 f1 = -q1dotn1 * n1dotr1hat
  374.                 f2 = -q2dotn2 * n2dotr2hat
  375.                 Shape(Shape1).DeltaV.x = Shape(Shape1).DeltaV.x + f1 * qx1 / m1
  376.                 Shape(Shape1).DeltaV.y = Shape(Shape1).DeltaV.y + f1 * qy1 / m1
  377.                 Shape(Shape2).DeltaV.x = Shape(Shape2).DeltaV.x + f2 * qx2 / m2
  378.                 Shape(Shape2).DeltaV.y = Shape(Shape2).DeltaV.y + f2 * qy2 / m2
  379.  
  380.                 ' Angular impulse
  381.                 q1dotp1 = qx1 * px1 + qy1 * py1
  382.                 q2dotp2 = qx2 * px2 + qy2 * py2
  383.                 dw1 = r1 * q1dotp1 / i1
  384.                 dw2 = -r2 * q2dotp2 / i2
  385.                 Shape(Shape1).DeltaO = Shape(Shape1).DeltaO + dw1
  386.                 Shape(Shape2).DeltaO = Shape(Shape2).DeltaO + dw2
  387.  
  388.                 ' Separate along normal
  389.                 'IF (Shape(Shape1).Collisions = 0) THEN
  390.                 vtemp.x = -nx1 * 1 * ((v1 + 0) / m1)
  391.                 vtemp.y = -ny1 * 1 * ((v1 + 0) / m1)
  392.                 CALL TranslateShape(Shape1, vtemp)
  393.                 'END IF
  394.                 'IF (Shape(Shape2).Collisions = 0) THEN
  395.                 vtemp.x = -nx2 * 1 * ((v2 + 0) / m2)
  396.                 vtemp.y = -ny2 * 1 * ((v2 + 0) / m2)
  397.                 CALL TranslateShape(Shape2, vtemp)
  398.                 'END IF
  399.  
  400.                 ' External torque
  401.                 'IF (Shape(Shape1).Collisions > 0) THEN
  402.                 torque1 = m1 * (dx1 * ForceField.y - dy1 * ForceField.x)
  403.                 Shape(Shape1).DeltaO = Shape(Shape1).DeltaO - torque1 / i1
  404.                 'END IF
  405.                 'IF (Shape(Shape2).Collisions > 0) THEN
  406.                 torque2 = m2 * (dx2 * ForceField.y - dy2 * ForceField.x)
  407.                 Shape(Shape2).DeltaO = Shape(Shape2).DeltaO - torque2 / i2
  408.                 'END IF
  409.  
  410.                 ' Feedback
  411.                 IF (Shape(Shape1).Collisions = 0) AND (Shape(Shape2).Collisions = 0) THEN
  412.                     CALL snd(100 * (v1 + v2) / 2, .5)
  413.                 END IF
  414.  
  415.             END IF
  416.         NEXT
  417.     END IF
  419.  
  420. SUB FleetDynamics (VelocityDamping, StoppingVelocity)
  421.     FOR ShapeIndex = 1 TO ShapeCount
  422.  
  423.         ' Contact update
  424.         IF (Shape(ShapeIndex).CollisionSwitch = 1) THEN
  425.             Shape(ShapeIndex).Collisions = Shape(ShapeIndex).Collisions + 1
  426.         ELSE
  427.             Shape(ShapeIndex).Collisions = 0
  428.         END IF
  429.  
  430.         IF ((Shape(ShapeIndex).Fixed = 0)) THEN
  431.  
  432.             ' Angular velocity update
  433.             Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + Shape(ShapeIndex).DeltaO
  434.  
  435.             ' Linear velocity update
  436.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Shape(ShapeIndex).DeltaV.x
  437.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Shape(ShapeIndex).DeltaV.y
  438.  
  439.             IF (Shape(ShapeIndex).Collisions = 0) THEN
  440.                 ' Freefall (if airborne)
  441.                 Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + ForceField.x
  442.                 Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + ForceField.y
  443.             ELSE
  444.                 ' Static friction
  445.                 IF (Shape(ShapeIndex).Velocity.x * Shape(ShapeIndex).Velocity.x) < StoppingVelocity THEN Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .05
  446.                 IF (Shape(ShapeIndex).Velocity.y * Shape(ShapeIndex).Velocity.y) < StoppingVelocity THEN Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .05
  447.                 IF (Shape(ShapeIndex).Omega * Shape(ShapeIndex).Omega) < .0001 * StoppingVelocity THEN Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .05
  448.             END IF
  449.  
  450.             ' Rotation update
  451.             CALL RotShape(ShapeIndex, Shape(ShapeIndex).Centroid, Shape(ShapeIndex).Omega)
  452.  
  453.             ' Position update
  454.             CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
  455.  
  456.             ' Velocity Damping
  457.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * VelocityDamping
  458.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * VelocityDamping
  459.             Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * VelocityDamping
  460.         END IF
  461.     NEXT
  463.  
  464. SUB Graphics
  465.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
  466.     'LOCATE 1, 1: PRINT ProximalPairsCount, CollisionCount
  467.     FOR ShapeIndex = 1 TO ShapeCount
  468.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
  469.             CALL cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
  470.             CALL cline(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, PointChain(ShapeIndex, i + 1).x, PointChain(ShapeIndex, i + 1).y, Shape(ShapeIndex).Shade)
  471.         NEXT
  472.         CALL cpset(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, Shape(ShapeIndex).Shade)
  473.         CALL cline(PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, Shape(ShapeIndex).Shade)
  474.         CALL ccircle(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, 3, Shape(ShapeIndex).Shade)
  475.     NEXT
  476.     _DISPLAY
  478.  
  479. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
  480.     DIM l AS Vector
  481.     DIM r AS Vector
  482.     li = i - 1
  483.     ri = i + 1
  484.     IF (i = 1) THEN li = Shape(k).Elements
  485.     IF (i = Shape(k).Elements) THEN ri = 1
  486.     l.x = PointChain(k, li).x
  487.     r.x = PointChain(k, ri).x
  488.     dx = r.x - l.x
  489.     CalculateNormalX = dx
  491.  
  492. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
  493.     DIM l AS Vector
  494.     DIM r AS Vector
  495.     li = i - 1
  496.     ri = i + 1
  497.     IF (i = 1) THEN li = Shape(k).Elements
  498.     IF (i = Shape(k).Elements) THEN ri = 1
  499.     l.y = PointChain(k, li).y
  500.     r.y = PointChain(k, ri).y
  501.     dy = r.y - l.y
  502.     CalculateNormalY = dy
  504.  
  505. SUB CalculateCentroid (k AS INTEGER)
  506.     xx = 0
  507.     yy = 0
  508.     FOR i = 1 TO Shape(k).Elements
  509.         xx = xx + PointChain(k, i).x
  510.         yy = yy + PointChain(k, i).y
  511.     NEXT
  512.     Shape(k).Centroid.x = xx / Shape(k).Elements
  513.     Shape(k).Centroid.y = yy / Shape(k).Elements
  515.  
  516. SUB CalculateDiameterMin (k AS INTEGER)
  517.     r2min = 999 ^ 999
  518.     FOR i = 1 TO Shape(k).Elements
  519.         xx = Shape(k).Centroid.x - PointChain(k, i).x
  520.         yy = Shape(k).Centroid.y - PointChain(k, i).y
  521.         r2 = xx * xx + yy * yy
  522.         IF (r2 < r2min) THEN
  523.             r2min = r2
  524.         END IF
  525.     NEXT
  526.     Shape(k).DiameterMin = SQR(r2min)
  528.  
  529. SUB CalculateDiameterMax (k AS INTEGER)
  530.     r2max = -1
  531.     FOR i = 1 TO Shape(k).Elements
  532.         xx = Shape(k).Centroid.x - PointChain(k, i).x
  533.         yy = Shape(k).Centroid.y - PointChain(k, i).y
  534.         r2 = xx * xx + yy * yy
  535.         IF (r2 > r2max) THEN
  536.             r2max = r2
  537.         END IF
  538.     NEXT
  539.     Shape(k).DiameterMax = SQR(r2max)
  541.  
  542. SUB CalculateMass (k AS INTEGER, factor AS DOUBLE)
  543.     aa = 0
  544.     FOR i = 2 TO Shape(k).Elements
  545.         x = PointChain(k, i).x - Shape(k).Centroid.x
  546.         y = PointChain(k, i).y - Shape(k).Centroid.y
  547.         dx = (PointChain(k, i).x - PointChain(k, i - 1).x)
  548.         dy = (PointChain(k, i).y - PointChain(k, i - 1).y)
  549.         da = .5 * (x * dy - y * dx)
  550.         aa = aa + da
  551.     NEXT
  552.     Shape(k).Mass = factor * SQR(aa * aa)
  554.  
  555. SUB CalculateMOI (k AS INTEGER, ctrvec AS Vector)
  556.     xx = 0
  557.     yy = 0
  558.     FOR i = 1 TO Shape(k).Elements
  559.         a = ctrvec.x - PointChain(k, i).x
  560.         b = ctrvec.y - PointChain(k, i).y
  561.         xx = xx + a * a
  562.         yy = yy + b * b
  563.     NEXT
  564.     Shape(k).MOI = SQR((xx + yy) * (xx + yy)) * (Shape(k).Mass / Shape(k).Elements)
  566.  
  567. SUB TranslateShape (k AS INTEGER, c AS Vector)
  568.     FOR i = 1 TO Shape(k).Elements
  569.         PointChain(k, i).x = PointChain(k, i).x + c.x
  570.         PointChain(k, i).y = PointChain(k, i).y + c.y
  571.     NEXT
  572.     Shape(k).Centroid.x = Shape(k).Centroid.x + c.x
  573.     Shape(k).Centroid.y = Shape(k).Centroid.y + c.y
  575.  
  576. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
  577.     FOR i = 1 TO Shape(k).Elements
  578.         xx = PointChain(k, i).x - c.x
  579.         yy = PointChain(k, i).y - c.y
  580.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
  581.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
  582.     NEXT
  583.     xx = Shape(k).Centroid.x - c.x
  584.     yy = Shape(k).Centroid.y - c.y
  585.     Shape(k).Centroid.x = c.x + xx * COS(da) - yy * SIN(da)
  586.     Shape(k).Centroid.y = c.y + yy * COS(da) + xx * SIN(da)
  588.  
  589. SUB NewAutoBall (x1, y1, r1, r2, pa, pb, fx)
  590.     ShapeCount = ShapeCount + 1
  591.     Shape(ShapeCount).Fixed = fx
  592.     Shape(ShapeCount).Collisions = 0
  593.     i = 0
  594.     FOR j = 0 TO 2 * 4 * ATN(1) STEP .15
  595.         i = i + 1
  596.         r = r1 + r2 * COS(pa * j) ^ pb
  597.         PointChain(ShapeCount, i).x = x1 + r * COS(j)
  598.         PointChain(ShapeCount, i).y = y1 + r * SIN(j)
  599.     NEXT
  600.     Shape(ShapeCount).Elements = i
  601.     CALL CalculateCentroid(ShapeCount)
  602.     IF (fx = 0) THEN
  603.         CALL CalculateMass(ShapeCount, 1)
  604.     ELSE
  605.         CALL CalculateMass(ShapeCount, 999999)
  606.     END IF
  607.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  608.     CALL CalculateDiameterMin(ShapeCount)
  609.     CALL CalculateDiameterMax(ShapeCount)
  610.     Shape(ShapeCount).Velocity.x = 0
  611.     Shape(ShapeCount).Velocity.y = 0
  612.     Shape(ShapeCount).Omega = 0
  613.     IF (fx = 0) THEN
  614.         Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
  615.     ELSE
  616.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
  617.     END IF
  619.  
  620. SUB NewAutoBrick (x1, y1, wx, wy, ang)
  621.     ShapeCount = ShapeCount + 1
  622.     Shape(ShapeCount).Fixed = 1
  623.     Shape(ShapeCount).Collisions = 0
  624.     i = 0
  625.     FOR j = -wy / 2 TO wy / 2 STEP 5
  626.         i = i + 1
  627.         PointChain(ShapeCount, i).x = x1 + wx / 2
  628.         PointChain(ShapeCount, i).y = y1 + j
  629.     NEXT
  630.     FOR j = wx / 2 TO -wx / 2 STEP -5
  631.         i = i + 1
  632.         PointChain(ShapeCount, i).x = x1 + j
  633.         PointChain(ShapeCount, i).y = y1 + wy / 2
  634.     NEXT
  635.     FOR j = wy / 2 TO -wy / 2 STEP -5
  636.         i = i + 1
  637.         PointChain(ShapeCount, i).x = x1 - wx / 2
  638.         PointChain(ShapeCount, i).y = y1 + j
  639.     NEXT
  640.     FOR j = -wx / 2 TO wx / 2 STEP 5
  641.         i = i + 1
  642.         PointChain(ShapeCount, i).x = x1 + j
  643.         PointChain(ShapeCount, i).y = y1 - wy / 2
  644.     NEXT
  645.     Shape(ShapeCount).Elements = i
  646.     CALL CalculateCentroid(ShapeCount)
  647.     CALL CalculateMass(ShapeCount, 99999)
  648.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  649.     CALL CalculateDiameterMin(ShapeCount)
  650.     CALL CalculateDiameterMax(ShapeCount)
  651.     Shape(ShapeCount).MOI = 999 ^ 999
  652.     Shape(ShapeCount).Velocity.x = 0
  653.     Shape(ShapeCount).Velocity.y = 0
  654.     Shape(ShapeCount).Omega = 0
  655.     Shape(ShapeCount).Shade = _RGB(100, 100, 100)
  656.     CALL RotShape(ShapeCount, Shape(ShapeCount).Centroid, ang)
  658.  
  659. SUB NewBrickLine (xi, yi, xf, yf, wx, wy)
  660.     d1 = SQR((xf - xi) ^ 2 + (yf - yi) ^ 2)
  661.     d2 = SQR(wx ^ 2 + wy ^ 2)
  662.     ang = ATN((yf - yi) / (xf - xi))
  663.     f = 1.2 * d2 / d1
  664.     FOR t = 0 TO 1 + f STEP f
  665.         CALL NewAutoBrick(xi * (1 - t) + xf * t, yi * (1 - t) + yf * t, wx, wy, ang)
  666.     NEXT
  668.  
  669. SUB NewMouseShape (rawresolution AS DOUBLE, targetpoints AS INTEGER, smoothiterations AS INTEGER)
  670.  
  671.     ShapeCount = ShapeCount + 1
  672.     Shape(ShapeCount).Fixed = 0
  673.     Shape(ShapeCount).Collisions = 0
  674.  
  675.     numpoints = 0
  676.  
  677.     xold = 999999
  678.     yold = 999999
  679.     DO
  680.         DO WHILE _MOUSEINPUT
  681.             x = _MOUSEX
  682.             y = _MOUSEY
  683.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
  684.                 IF _MOUSEBUTTON(1) THEN
  685.                     x = x - (_WIDTH / 2)
  686.                     y = -y + (_HEIGHT / 2)
  687.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
  688.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
  689.                         numpoints = numpoints + 1
  690.                         PointChain(ShapeCount, numpoints).x = x
  691.                         PointChain(ShapeCount, numpoints).y = y
  692.                         CALL cpset(x, y, _RGB(0, 255, 255))
  693.                         xold = x
  694.                         yold = y
  695.                     END IF
  696.                 END IF
  697.             END IF
  698.         LOOP
  699.         _DISPLAY
  700.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
  701.  
  702.     DO WHILE (numpoints < targetpoints)
  703.         rad2max = -1
  704.         kmax = -1
  705.         FOR k = 1 TO numpoints - 1
  706.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
  707.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
  708.             rad2 = xfac ^ 2 + yfac ^ 2
  709.             IF rad2 > rad2max THEN
  710.                 kmax = k
  711.                 rad2max = rad2
  712.             END IF
  713.         NEXT
  714.         edgecase = 0
  715.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
  716.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
  717.         rad2 = xfac ^ 2 + yfac ^ 2
  718.         IF (rad2 > rad2max) THEN
  719.             kmax = numpoints
  720.             rad2max = rad2
  721.             edgecase = 1
  722.         END IF
  723.         IF (edgecase = 0) THEN
  724.             numpoints = numpoints + 1
  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.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
  730.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
  731.         ELSE
  732.             numpoints = numpoints + 1
  733.             xx = PointChain(ShapeCount, numpoints - 1).x
  734.             yy = PointChain(ShapeCount, numpoints - 1).y
  735.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
  736.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
  737.         END IF
  738.     LOOP
  739.  
  740.     FOR j = 1 TO smoothiterations
  741.         FOR k = 2 TO n - 1
  742.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
  743.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
  744.         NEXT
  745.         FOR k = 2 TO n - 1
  746.             PointChain(i, k).x = TempChain(i, k).x
  747.             PointChain(i, k).y = TempChain(i, k).y
  748.         NEXT
  749.     NEXT
  750.  
  751.     Shape(ShapeCount).Elements = numpoints
  752.     CALL CalculateCentroid(ShapeCount)
  753.     CALL CalculateMass(ShapeCount, 1)
  754.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  755.     CALL CalculateDiameterMin(ShapeCount)
  756.     CALL CalculateDiameterMax(ShapeCount)
  757.     Shape(ShapeCount).Velocity.x = 0
  758.     Shape(ShapeCount).Velocity.y = 0
  759.     Shape(ShapeCount).Omega = 0
  760.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
  762.  
  763. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
  764.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
  766.  
  767. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
  768.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
  770.  
  771. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
  772.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
  774.  
  775. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
  776.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
  778.  
  779. SUB cprintstring (y, a AS STRING)
  780.     _PRINTSTRING (_WIDTH / 2 - (LEN(a) * 8) / 2, -y + _HEIGHT / 2), a
  782.  
  783. SUB snd (frq, dur)
  784.     IF ((frq >= 37) AND (frq <= 2000)) THEN
  785.         SOUND frq, dur
  786.     END IF
  788.  
  789. SUB SetupPool
  790.  
  791.     ' Set external field
  792.     ForceField.x = 0
  793.     ForceField.y = 0 '-.08
  794.  
  795.     ' Rectangular border
  796.     wx = 42
  797.     wy = 10
  798.     CALL NewBrickLine(-_WIDTH / 2 + wx, _HEIGHT / 2 - wy, _WIDTH / 2 - wx, _HEIGHT / 2 - wy, wx, wy)
  799.     CALL NewBrickLine(-_WIDTH / 2 + wx, -_HEIGHT / 2 + wy, _WIDTH / 2 - wx, -_HEIGHT / 2 + wy, wx, wy)
  800.     wx = 40
  801.     wy = 10
  802.     CALL NewBrickLine(-_WIDTH / 2 + wy, -_HEIGHT / 2 + 2 * wx, -_WIDTH / 2 + wy, _HEIGHT / 2 - 2 * wx, wx, wy)
  803.     CALL NewBrickLine(_WIDTH / 2 - wy, -_HEIGHT / 2 + 2 * wx, _WIDTH / 2 - wy, _HEIGHT / 2 - 2 * wx, wx, wy)
  804.  
  805.     ' Balls (billiard setup)
  806.     x0 = 160
  807.     y0 = 0
  808.     r = 15
  809.     gg = 2 * r + 3.5
  810.     xf = COS(30 * 3.14159 / 180)
  811.     yf = SIN(30 * 3.14159 / 180)
  812.     gx = gg * xf
  813.     gy = gg * yf
  814.  
  815.     CALL NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, r, 0, 1, 1, 0)
  816.     CALL NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, r, 0, 1, 1, 0)
  817.     CALL NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, r, 0, 1, 1, 0)
  818.     CALL NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, r, 0, 1, 1, 0)
  819.     CALL NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, r, 0, 1, 1, 0)
  820.     CALL NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, r, 0, 1, 1, 0)
  821.     CALL NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, r, 0, 1, 1, 0)
  822.     CALL NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, r, 0, 1, 1, 0)
  823.     CALL NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, r, 0, 1, 1, 0)
  824.     CALL NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, r, 0, 1, 1, 0)
  825.  
  826.     ' Cue ball
  827.     CALL NewAutoBall(-220, 0, r, 0, 1, 1, 0)
  828.     Shape(ShapeCount).Velocity.x = 8 + 5 * RND
  829.     Shape(ShapeCount).Velocity.y = .5 * (RND - .5)
  830.     Shape(ShapeCount).Shade = _RGB(255, 255, 255)
  831.  
  832.     ' Parameters
  833.     CPC = 1.15
  834.     FPC = 8
  835.     RST = 0.75
  836.     VD = 0.995
  837.     SV = 0
  839.  
  840. SUB SetupWackyGame
  841.     ' Set external field
  842.     ForceField.x = 0
  843.     ForceField.y = -.08
  844.  
  845.     ' Rectangular border
  846.     wx = 42
  847.     wy = 10
  848.     CALL NewBrickLine(-_WIDTH / 2 + wx, _HEIGHT / 2 - wy, _WIDTH / 2 - wx, _HEIGHT / 2 - wy, wx, wy)
  849.     CALL NewBrickLine(-_WIDTH / 2 + wx, -_HEIGHT / 2 + wy, _WIDTH / 2 - wx, -_HEIGHT / 2 + wy, wx, wy)
  850.     wx = 40
  851.     wy = 10
  852.     CALL NewBrickLine(-_WIDTH / 2 + wy, -_HEIGHT / 2 + 2 * wx, -_WIDTH / 2 + wy, _HEIGHT / 2 - 2 * wx, wx, wy)
  853.     CALL NewBrickLine(_WIDTH / 2 - wy, -_HEIGHT / 2 + 2 * wx, _WIDTH / 2 - wy, _HEIGHT / 2 - 2 * wx, wx, wy)
  854.  
  855.     ' Balls
  856.     x0 = -70
  857.     y0 = 120
  858.     r1 = 15
  859.     r2 = 2.5
  860.     gg = 2 * (r1 + r2) + 3.5
  861.     xf = COS(30 * 3.14159 / 180)
  862.     yf = SIN(30 * 3.14159 / 180)
  863.     gx = gg * xf
  864.     gy = gg * yf
  865.     CALL NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  866.     CALL NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  867.     CALL NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  868.     CALL NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  869.     CALL NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  870.     CALL NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  871.     CALL NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  872.     CALL NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  873.     CALL NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  874.     CALL NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  875.  
  876.     ' Misc. bricks
  877.     wx = 60
  878.     wy = 10
  879.     ww = SQR(wx * wx + wy * wy) * .75
  880.     CALL NewBrickLine(ww, 0, 100 + ww, 100, wx, wy)
  881.     CALL NewBrickLine(-ww, 0, -100 - ww, 100, wx, wy)
  882.  
  883.     ' Fidget spinner
  884.     CALL NewAutoBall(-220, 0, 20, 15, 1.5, 2, 0)
  885.     Shape(ShapeCount).Shade = _RGB(255, 255, 255)
  886.  
  887.     ' Parameters
  888.     CPC = 1.15
  889.     FPC = 8
  890.     RST = 0.75
  891.     VD = 0.995
  892.     SV = 0.025
  894.  
ss.png
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« Last Edit: March 01, 2020, 07:46:48 pm by STxAxTIC »
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Offline STxAxTIC

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #21 on: March 01, 2020, 11:48:42 pm »
Almighty, this is coming along nicely. It's usable in its current state, but can also be extended if I want to go on capturing more physics and simulating more kinds of things. Since the weekend is about over, time to let this cook out in public for a few days. In this version you have two options at startup. You can use the mouse to click and drag any piece. Do so carefully. Press "r" to restart during play.

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. start:
  9.  
  11.  
  12. ' Data structures
  13. TYPE Vector
  14.     x AS DOUBLE
  15.     y AS DOUBLE
  17.  
  18. DIM SHARED vtemp AS Vector
  19.  
  20. ' Object type
  21. TYPE Object
  22.     Centroid AS Vector
  23.     Collisions AS LONG
  24.     CollisionSwitch AS INTEGER
  25.     DeltaO AS DOUBLE
  26.     DeltaV AS Vector
  27.     DiameterMax AS DOUBLE
  28.     DiameterMin AS DOUBLE
  29.     Elements AS INTEGER
  30.     Fixed AS INTEGER
  31.     Mass AS DOUBLE
  32.     MOI AS DOUBLE
  33.     PartialNormal AS Vector
  34.     Omega AS DOUBLE
  35.     Shade AS _UNSIGNED LONG
  36.     Velocity AS Vector
  38.  
  39. ' Object storage
  40. DIM SHARED Shape(300) AS Object
  41. DIM SHARED PointChain(300, 500) AS Vector
  42. DIM SHARED TempChain(300, 500) AS Vector
  43. DIM SHARED ShapeCount AS INTEGER
  44. DIM SHARED SelectedShape AS INTEGER
  45.  
  46. ' Dynamics
  47. DIM SHARED CollisionCount AS INTEGER
  48. DIM SHARED ProximalPairs(300 / 2, 1 TO 2)
  49. DIM SHARED ProximalPairsCount
  50. DIM SHARED CPC, FPC, RST, VD, SV
  51.  
  52. ' Environment
  53. DIM SHARED ForceField AS Vector ' Gravity
  54.  
  55. ' Initialize
  56. ShapeCount = 0
  57. CollisionCount = 0
  58.  
  59. ' Prompt
  61. CALL cprintstring(16 * 4, "WELCOME!                  ")
  62. CALL cprintstring(16 * 3, "Press 1 for Pool Prototype")
  63. CALL cprintstring(16 * 2, "Press 2 for Wacky Game    ")
  65.  
  67.     kk = _KEYHIT
  68.     SELECT CASE kk
  69.         CASE ASC("1")
  70.             CALL SetupPool
  71.             EXIT DO
  72.         CASE ASC("2")
  73.             CALL SetupWackyGame
  74.             EXIT DO
  75.     END SELECT
  76.     IF (kk) THEN
  77.         _KEYCLEAR
  78.     END IF
  79.     _LIMIT 30
  81.  
  82. CALL Graphics
  83. CALL cprintstring(-16 * 3, "During Play:")
  84. CALL cprintstring(-16 * 5, "Arrow keys boost most recently-selected object.")
  85. CALL cprintstring(-16 * 6, "Mouse 1 moves most recently-selected object.   ")
  86. CALL cprintstring(-16 * 7, "ESC halts all motion.                         ")
  87. CALL cprintstring(-16 * 8, "Space enters creative mode.                   ")
  88. CALL cprintstring(-16 * 9, "Press 'r' to restart.                         ")
  89. CALL cprintstring(-16 * 11, "PRESS ANY KEY TO BEGIN.")
  94.  
  95. ' Main loop
  97.     IF (UserInput = -1) THEN GOTO start
  98.     CALL PairDynamics(CPC, FPC, RST)
  99.     CALL FleetDynamics(VD, SV)
  100.     CALL Graphics
  101.     _LIMIT 120
  103.  
  105.  
  106. FUNCTION UserInput
  107.     TheReturn = 0
  108.     ' Keyboard input
  109.     kk = _KEYHIT
  110.     SELECT CASE kk
  111.         CASE 32
  112.             DO: LOOP UNTIL _KEYHIT
  113.             WHILE _MOUSEINPUT: WEND
  114.             _KEYCLEAR
  115.             CALL cprintstring(16 * 17, "Drag mouse counter-clockwise to draw a new shape.")
  116.             CALL cprintstring(16 * 16, "Make sure centroid is inside body.")
  117.             'CALL Graphics
  118.             CALL NewMouseShape(7.5, 75, 25)
  119.             CLS
  120.         CASE 18432, ASC("w") ' Up arrow
  121.             Shape(SelectedShape).Velocity.y = Shape(SelectedShape).Velocity.y * 1.1 + 2
  122.         CASE 20480, ASC("s") ' Down arrow
  123.             Shape(SelectedShape).Velocity.y = Shape(SelectedShape).Velocity.y * 0.9 - 2
  124.         CASE 19200, ASC("a") ' Left arrow
  125.             Shape(SelectedShape).Velocity.x = Shape(SelectedShape).Velocity.x * 0.9 - 2
  126.         CASE 19712, ASC("d") ' Right arrow
  127.             Shape(SelectedShape).Velocity.x = Shape(SelectedShape).Velocity.x * 1.1 + 2
  128.         CASE ASC("r")
  129.             TheReturn = -1
  130.         CASE 27
  131.             FOR k = 1 TO ShapeCount
  132.                 Shape(k).Velocity.x = .000001 * (RND - .5)
  133.                 Shape(k).Velocity.y = .000001 * (RND - .5)
  134.                 Shape(k).Omega = .000001 * (RND - .5)
  135.             NEXT
  136.     END SELECT
  137.     IF (kk) THEN
  138.         _KEYCLEAR
  139.     END IF
  140.  
  141.     ' Mouse input
  142.     mb = 0
  144.         x = _MOUSEX
  145.         y = _MOUSEY
  146.         IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
  147.             x = x - (_WIDTH / 2)
  148.             y = -y + (_HEIGHT / 2)
  149.  
  150.             rmin = 999999999
  151.             FOR k = 1 TO ShapeCount
  152.                 dx = x - Shape(k).Centroid.x
  153.                 dy = y - Shape(k).Centroid.y
  154.                 r2 = dx * dx + dy * dy
  155.                 IF (r2 < rmin) THEN
  156.                     rmin = r2
  157.                     SelectedShape = k
  158.                 END IF
  159.             NEXT
  160.             IF (_MOUSEBUTTON(1)) THEN
  161.                 IF (mb = 0) THEN
  162.                     mb = 1
  163.                     vtemp.x = x - Shape(SelectedShape).Centroid.x
  164.                     vtemp.y = y - Shape(SelectedShape).Centroid.y
  165.                     CALL TranslateShape(SelectedShape, vtemp)
  166.                     Shape(SelectedShape).Velocity.x = 0
  167.                     Shape(SelectedShape).Velocity.y = 0
  168.                     Shape(SelectedShape).Omega = 0
  169.                 END IF
  170.             END IF
  171.             IF (_MOUSEBUTTON(2)) THEN
  172.                 IF (mb = 0) THEN
  173.                     mb = 1
  174.                     CALL NewAutoBall(x, y, 5, 0, 1, 1, 1)
  175.                     _DELAY .1
  176.                 END IF
  177.             END IF
  178.         END IF
  179.     LOOP
  180.     UserInput = TheReturn
  182.  
  183. SUB PairDynamics (CoarseProximityConstant, FineProximityConstant, Restitution)
  184.  
  185.     ' Proximity detection
  186.     ProximalPairsCount = 0
  187.     Shape1 = 0
  188.     Shape2 = 0
  189.     FOR j = 1 TO ShapeCount
  190.         Shape(j).CollisionSwitch = 0
  191.         Shape(j).DeltaO = 0
  192.         Shape(j).DeltaV.x = 0
  193.         Shape(j).DeltaV.y = 0
  194.         Shape(j).PartialNormal.x = 0
  195.         Shape(j).PartialNormal.y = 0
  196.         FOR k = j + 1 TO ShapeCount
  197.             dx = Shape(j).Centroid.x - Shape(k).Centroid.x
  198.             dy = Shape(j).Centroid.y - Shape(k).Centroid.y
  199.             dr = SQR(dx * dx + dy * dy)
  200.             IF (dr < (CoarseProximityConstant) * (Shape(j).DiameterMax + Shape(k).DiameterMax)) THEN
  201.                 ProximalPairsCount = ProximalPairsCount + 1
  202.                 ProximalPairs(ProximalPairsCount, 1) = j
  203.                 ProximalPairs(ProximalPairsCount, 2) = k
  204.                 Shape1 = j
  205.                 Shape2 = k
  206.             END IF
  207.         NEXT
  208.     NEXT
  209.  
  210.     IF (ProximalPairsCount > 0) THEN
  211.         FOR n = 1 TO ProximalPairsCount
  212.             Shape1 = ProximalPairs(n, 1)
  213.             Shape2 = ProximalPairs(n, 2)
  214.  
  215.             ' Collision detection
  216.             rmin = 999999999
  217.             ClosestIndex1 = 0
  218.             ClosestIndex2 = 0
  219.             FOR j = 1 TO Shape(Shape1).Elements
  220.                 FOR k = 1 TO Shape(Shape2).Elements
  221.                     dx = PointChain(Shape1, j).x - PointChain(Shape2, k).x
  222.                     dy = PointChain(Shape1, j).y - PointChain(Shape2, k).y
  223.                     r2 = dx * dx + dy * dy
  224.  
  225.                     IF (r2 <= FineProximityConstant) THEN
  226.  
  227.                         ' Normal vector 1
  228.                         nx1 = CalculateNormalY(Shape1, j)
  229.                         ny1 = -CalculateNormalX(Shape1, j)
  230.                         nn = SQR(nx1 * nx1 + ny1 * ny1)
  231.                         nx1 = nx1 / nn
  232.                         ny1 = ny1 / nn
  233.                         Shape(Shape1).PartialNormal.x = Shape(Shape1).PartialNormal.x + nx1
  234.                         Shape(Shape1).PartialNormal.y = Shape(Shape1).PartialNormal.y + ny1
  235.  
  236.                         ' Normal vector 2
  237.                         nx2 = CalculateNormalY(Shape2, k)
  238.                         ny2 = -CalculateNormalX(Shape2, k)
  239.                         nn = SQR(nx2 * nx2 + ny2 * ny2)
  240.                         nx2 = nx2 / nn
  241.                         ny2 = ny2 / nn
  242.                         Shape(Shape2).PartialNormal.x = Shape(Shape2).PartialNormal.x + nx2
  243.                         Shape(Shape2).PartialNormal.y = Shape(Shape2).PartialNormal.y + ny2
  244.  
  245.                     END IF
  246.                     IF (r2 < rmin) THEN
  247.                         rmin = r2
  248.                         ClosestIndex1 = j
  249.                         ClosestIndex2 = k
  250.                     END IF
  251.                 NEXT
  252.             NEXT
  253.  
  254.             IF (rmin <= FineProximityConstant) THEN
  255.  
  256.                 CollisionCount = CollisionCount + 1
  257.                 Shape(Shape1).CollisionSwitch = 1
  258.                 Shape(Shape2).CollisionSwitch = 1
  259.  
  260.                 ' Undo previous motion
  261.                 IF (Shape(Shape1).Collisions = 0) THEN
  262.                     CALL RotShape(Shape1, Shape(Shape1).Centroid, -Shape(Shape1).Omega)
  263.                     vtemp.x = -(Shape(Shape1).Velocity.x)
  264.                     vtemp.y = -(Shape(Shape1).Velocity.y)
  265.                     CALL TranslateShape(Shape1, vtemp)
  266.                 END IF
  267.                 IF (Shape(Shape2).Collisions = 0) THEN
  268.                     CALL RotShape(Shape2, Shape(Shape2).Centroid, -Shape(Shape2).Omega)
  269.                     vtemp.x = -(Shape(Shape2).Velocity.x)
  270.                     vtemp.y = -(Shape(Shape2).Velocity.y)
  271.                     CALL TranslateShape(Shape2, vtemp)
  272.                 END IF
  273.  
  274.                 IF (Shape(Shape1).Collisions = 0) THEN
  275.                     Shape(Shape1).Velocity.x = Shape(Shape1).Velocity.x * Restitution
  276.                     Shape(Shape1).Velocity.y = Shape(Shape1).Velocity.y * Restitution
  277.                 END IF
  278.                 IF (Shape(Shape2).Collisions = 0) THEN
  279.                     Shape(Shape2).Velocity.x = Shape(Shape2).Velocity.x * Restitution
  280.                     Shape(Shape2).Velocity.y = Shape(Shape2).Velocity.y * Restitution
  281.                 END IF
  282.  
  283.                 ' Normal vector 1 (nx1, ny1)
  284.                 nn = SQR(Shape(Shape1).PartialNormal.x * Shape(Shape1).PartialNormal.x + Shape(Shape1).PartialNormal.y * Shape(Shape1).PartialNormal.y)
  285.                 nx1 = Shape(Shape1).PartialNormal.x / nn
  286.                 ny1 = Shape(Shape1).PartialNormal.y / nn
  287.                 Shape(Shape1).PartialNormal.x = nx1
  288.                 Shape(Shape1).PartialNormal.y = ny1
  289.  
  290.                 ' Normal vector 2 (nx2, ny2)
  291.                 nn = SQR(Shape(Shape2).PartialNormal.x * Shape(Shape2).PartialNormal.x + Shape(Shape2).PartialNormal.y * Shape(Shape2).PartialNormal.y)
  292.                 nx2 = Shape(Shape2).PartialNormal.x / nn
  293.                 ny2 = Shape(Shape2).PartialNormal.y / nn
  294.                 Shape(Shape2).PartialNormal.x = nx2
  295.                 Shape(Shape2).PartialNormal.y = ny2
  296.  
  297.                 ' Contact-centroid differentials 1 (dx1, dy1)
  298.                 dx1 = PointChain(Shape1, ClosestIndex1).x - Shape(Shape1).Centroid.x
  299.                 dy1 = PointChain(Shape1, ClosestIndex1).y - Shape(Shape1).Centroid.y
  300.  
  301.                 ' Contact-centroid differentials 2 (dx2, dy2)
  302.                 dx2 = PointChain(Shape2, ClosestIndex2).x - Shape(Shape2).Centroid.x
  303.                 dy2 = PointChain(Shape2, ClosestIndex2).y - Shape(Shape2).Centroid.y
  304.  
  305.                 ' Perpendicular vector 1 (px1, py1)
  306.                 px1 = -dy1
  307.                 py1 = dx1
  308.                 pp = SQR(px1 * px1 + py1 * py1)
  309.                 px1 = px1 / pp
  310.                 py1 = py1 / pp
  311.  
  312.                 ' Perpendicular vector 2 (px2, py2)
  313.                 px2 = -dy2
  314.                 py2 = dx2
  315.                 pp = SQR(px2 * px2 + py2 * py2)
  316.                 px2 = px2 / pp
  317.                 py2 = py2 / pp
  318.  
  319.                 ' Angular velocity vector 1 (w1, r1, vx1, vy1)
  320.                 w1 = Shape(Shape1).Omega
  321.                 r1 = SQR(dx1 * dx1 + dy1 * dy1)
  322.                 vx1 = w1 * r1 * px1
  323.                 vy1 = w1 * r1 * py1
  324.  
  325.                 ' Angular velocity vector 2 (w2, r2, vx2, vy2)
  326.                 w2 = Shape(Shape2).Omega
  327.                 r2 = SQR(dx2 * dx2 + dy2 * dy2)
  328.                 vx2 = w2 * r2 * px2
  329.                 vy2 = w2 * r2 * py2
  330.  
  331.                 ' Mass terms (m1, m2, mu)
  332.                 m1 = Shape(Shape1).Mass
  333.                 m2 = Shape(Shape2).Mass
  334.                 mu = 1 / (1 / m1 + 1 / m2)
  335.  
  336.                 ' Re-Calculate moment of inertia (i1, i2)
  337.                 vtemp.x = PointChain(Shape1, ClosestIndex1).x
  338.                 vtemp.y = PointChain(Shape1, ClosestIndex1).y
  339.                 CALL CalculateMOI(Shape1, vtemp)
  340.                 vtemp.x = PointChain(Shape2, ClosestIndex2).x
  341.                 vtemp.y = PointChain(Shape2, ClosestIndex2).y
  342.                 CALL CalculateMOI(Shape2, vtemp)
  343.                 i1 = Shape(Shape1).MOI
  344.                 i2 = Shape(Shape2).MOI
  345.  
  346.                 ' Velocity differentials (v1, v2, dvtx, dvty)
  347.                 vcx1 = Shape(Shape1).Velocity.x
  348.                 vcy1 = Shape(Shape1).Velocity.y
  349.                 vcx2 = Shape(Shape2).Velocity.x
  350.                 vcy2 = Shape(Shape2).Velocity.y
  351.                 vtx1 = vcx1 + vx1
  352.                 vty1 = vcy1 + vy1
  353.                 vtx2 = vcx2 + vx2
  354.                 vty2 = vcy2 + vy2
  355.                 v1 = SQR(vtx1 * vtx1 + vty1 * vty1)
  356.                 v2 = SQR(vtx2 * vtx2 + vty2 * vty2)
  357.                 dvtx = vtx2 - vtx1
  358.                 dvty = vty2 - vty1
  359.  
  360.                 ' Geometry (n1dotdvt, n2dotdvt)
  361.                 n1dotdvt = nx1 * dvtx + ny1 * dvty
  362.                 n2dotdvt = nx2 * dvtx + ny2 * dvty
  363.  
  364.                 ' Momentum exchange (qx1, qy1, qx2, qy2)
  365.                 qx1 = nx1 * 2 * mu * n1dotdvt
  366.                 qy1 = ny1 * 2 * mu * n1dotdvt
  367.                 qx2 = nx2 * 2 * mu * n2dotdvt
  368.                 qy2 = ny2 * 2 * mu * n2dotdvt
  369.  
  370.                 ' Momentum exchange unit vector
  371.                 qq = SQR(qx1 * qx1 + qy1 * qy1)
  372.                 qhatx1 = qx1 / qq
  373.                 qhaty1 = qy1 / qq
  374.                 qq = SQR(qx2 * qx2 + qy2 * qy2)
  375.                 qhatx2 = qx2 / qq
  376.                 qhaty2 = qy2 / qq
  377.  
  378.                 ' Translational impulse
  379.                 q1dotn1 = qhatx1 * nx1 + qhaty1 * ny1
  380.                 q2dotn2 = qhatx2 * nx2 + qhaty2 * ny2
  381.                 n1dotr1hat = (nx1 * dx1 + ny1 * dy1) / r1
  382.                 n2dotr2hat = (nx2 * dx2 + ny2 * dy2) / r2
  383.                 f1 = -q1dotn1 * n1dotr1hat
  384.                 f2 = -q2dotn2 * n2dotr2hat
  385.                 Shape(Shape1).DeltaV.x = Shape(Shape1).DeltaV.x + f1 * qx1 / m1
  386.                 Shape(Shape1).DeltaV.y = Shape(Shape1).DeltaV.y + f1 * qy1 / m1
  387.                 Shape(Shape2).DeltaV.x = Shape(Shape2).DeltaV.x + f2 * qx2 / m2
  388.                 Shape(Shape2).DeltaV.y = Shape(Shape2).DeltaV.y + f2 * qy2 / m2
  389.  
  390.                 ' Angular impulse
  391.                 q1dotp1 = qx1 * px1 + qy1 * py1
  392.                 q2dotp2 = qx2 * px2 + qy2 * py2
  393.                 dw1 = r1 * q1dotp1 / i1
  394.                 dw2 = -r2 * q2dotp2 / i2
  395.                 Shape(Shape1).DeltaO = Shape(Shape1).DeltaO + dw1
  396.                 Shape(Shape2).DeltaO = Shape(Shape2).DeltaO + dw2
  397.  
  398.                 ' Separate along normal
  399.                 'IF (Shape(Shape1).Collisions = 0) THEN
  400.                 vtemp.x = -nx1 * 1 * ((v1 + 0) / m1)
  401.                 vtemp.y = -ny1 * 1 * ((v1 + 0) / m1)
  402.                 CALL TranslateShape(Shape1, vtemp)
  403.                 'END IF
  404.                 'IF (Shape(Shape2).Collisions = 0) THEN
  405.                 vtemp.x = -nx2 * 1 * ((v2 + 0) / m2)
  406.                 vtemp.y = -ny2 * 1 * ((v2 + 0) / m2)
  407.                 CALL TranslateShape(Shape2, vtemp)
  408.                 'END IF
  409.  
  410.                 ' External torque
  411.                 'IF (Shape(Shape1).Collisions > 0) THEN
  412.                 torque1 = m1 * (dx1 * ForceField.y - dy1 * ForceField.x)
  413.                 Shape(Shape1).DeltaO = Shape(Shape1).DeltaO - torque1 / i1
  414.                 'END IF
  415.                 'IF (Shape(Shape2).Collisions > 0) THEN
  416.                 torque2 = m2 * (dx2 * ForceField.y - dy2 * ForceField.x)
  417.                 Shape(Shape2).DeltaO = Shape(Shape2).DeltaO - torque2 / i2
  418.                 'END IF
  419.  
  420.                 ' Feedback
  421.                 IF (Shape(Shape1).Collisions = 0) AND (Shape(Shape2).Collisions = 0) THEN
  422.                     CALL snd(100 * (v1 + v2) / 2, .5)
  423.                 END IF
  424.  
  425.             END IF
  426.         NEXT
  427.     END IF
  429.  
  430. SUB FleetDynamics (VelocityDamping, StoppingVelocity)
  431.     FOR ShapeIndex = 1 TO ShapeCount
  432.  
  433.         ' Contact update
  434.         IF (Shape(ShapeIndex).CollisionSwitch = 1) THEN
  435.             Shape(ShapeIndex).Collisions = Shape(ShapeIndex).Collisions + 1
  436.         ELSE
  437.             Shape(ShapeIndex).Collisions = 0
  438.         END IF
  439.  
  440.         IF ((Shape(ShapeIndex).Fixed = 0)) THEN
  441.  
  442.             ' Angular velocity update
  443.             Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega + Shape(ShapeIndex).DeltaO
  444.  
  445.             ' Linear velocity update
  446.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + Shape(ShapeIndex).DeltaV.x
  447.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + Shape(ShapeIndex).DeltaV.y
  448.  
  449.             IF (Shape(ShapeIndex).Collisions = 0) THEN
  450.                 ' Freefall (if airborne)
  451.                 Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x + ForceField.x
  452.                 Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y + ForceField.y
  453.             ELSE
  454.                 ' Static friction
  455.                 IF (Shape(ShapeIndex).Velocity.x * Shape(ShapeIndex).Velocity.x) < StoppingVelocity THEN Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * .05
  456.                 IF (Shape(ShapeIndex).Velocity.y * Shape(ShapeIndex).Velocity.y) < StoppingVelocity THEN Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * .05
  457.                 IF (Shape(ShapeIndex).Omega * Shape(ShapeIndex).Omega) < .0001 * StoppingVelocity THEN Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * .05
  458.             END IF
  459.  
  460.             ' Rotation update
  461.             CALL RotShape(ShapeIndex, Shape(ShapeIndex).Centroid, Shape(ShapeIndex).Omega)
  462.  
  463.             ' Position update
  464.             CALL TranslateShape(ShapeIndex, Shape(ShapeIndex).Velocity)
  465.  
  466.             ' Velocity Damping
  467.             Shape(ShapeIndex).Velocity.x = Shape(ShapeIndex).Velocity.x * VelocityDamping
  468.             Shape(ShapeIndex).Velocity.y = Shape(ShapeIndex).Velocity.y * VelocityDamping
  469.             Shape(ShapeIndex).Omega = Shape(ShapeIndex).Omega * VelocityDamping
  470.         END IF
  471.     NEXT
  473.  
  474. SUB Graphics
  475.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 200), BF
  476.     'LOCATE 1, 1: PRINT ProximalPairsCount, CollisionCount
  477.     FOR ShapeIndex = 1 TO ShapeCount
  478.         FOR i = 1 TO Shape(ShapeIndex).Elements - 1
  479.             CALL cpset(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, Shape(ShapeIndex).Shade)
  480.             CALL cline(PointChain(ShapeIndex, i).x, PointChain(ShapeIndex, i).y, PointChain(ShapeIndex, i + 1).x, PointChain(ShapeIndex, i + 1).y, Shape(ShapeIndex).Shade)
  481.         NEXT
  482.         CALL cpset(PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, Shape(ShapeIndex).Shade)
  483.         CALL cline(PointChain(ShapeIndex, 1).x, PointChain(ShapeIndex, 1).y, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).x, PointChain(ShapeIndex, Shape(ShapeIndex).Elements).y, Shape(ShapeIndex).Shade)
  484.         IF (ShapeIndex = SelectedShape) THEN
  485.             CALL cpaint(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, Shape(ShapeIndex).Shade, Shape(ShapeIndex).Shade)
  486.         END IF
  487.         CALL ccircle(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, 3, _RGB(0, 0, 0))
  488.         CALL cpaint(Shape(ShapeIndex).Centroid.x, Shape(ShapeIndex).Centroid.y, _RGB(0, 0, 0), _RGB(0, 0, 0))
  489.     NEXT
  490.     _DISPLAY
  492.  
  493. FUNCTION CalculateNormalX (k AS INTEGER, i AS INTEGER)
  494.     DIM l AS Vector
  495.     DIM r AS Vector
  496.     li = i - 1
  497.     ri = i + 1
  498.     IF (i = 1) THEN li = Shape(k).Elements
  499.     IF (i = Shape(k).Elements) THEN ri = 1
  500.     l.x = PointChain(k, li).x
  501.     r.x = PointChain(k, ri).x
  502.     dx = r.x - l.x
  503.     CalculateNormalX = dx
  505.  
  506. FUNCTION CalculateNormalY (k AS INTEGER, i AS INTEGER)
  507.     DIM l AS Vector
  508.     DIM r AS Vector
  509.     li = i - 1
  510.     ri = i + 1
  511.     IF (i = 1) THEN li = Shape(k).Elements
  512.     IF (i = Shape(k).Elements) THEN ri = 1
  513.     l.y = PointChain(k, li).y
  514.     r.y = PointChain(k, ri).y
  515.     dy = r.y - l.y
  516.     CalculateNormalY = dy
  518.  
  519. SUB CalculateCentroid (k AS INTEGER)
  520.     xx = 0
  521.     yy = 0
  522.     FOR i = 1 TO Shape(k).Elements
  523.         xx = xx + PointChain(k, i).x
  524.         yy = yy + PointChain(k, i).y
  525.     NEXT
  526.     Shape(k).Centroid.x = xx / Shape(k).Elements
  527.     Shape(k).Centroid.y = yy / Shape(k).Elements
  529.  
  530. SUB CalculateDiameterMin (k AS INTEGER)
  531.     r2min = 999 ^ 999
  532.     FOR i = 1 TO Shape(k).Elements
  533.         xx = Shape(k).Centroid.x - PointChain(k, i).x
  534.         yy = Shape(k).Centroid.y - PointChain(k, i).y
  535.         r2 = xx * xx + yy * yy
  536.         IF (r2 < r2min) THEN
  537.             r2min = r2
  538.         END IF
  539.     NEXT
  540.     Shape(k).DiameterMin = SQR(r2min)
  542.  
  543. SUB CalculateDiameterMax (k AS INTEGER)
  544.     r2max = -1
  545.     FOR i = 1 TO Shape(k).Elements
  546.         xx = Shape(k).Centroid.x - PointChain(k, i).x
  547.         yy = Shape(k).Centroid.y - PointChain(k, i).y
  548.         r2 = xx * xx + yy * yy
  549.         IF (r2 > r2max) THEN
  550.             r2max = r2
  551.         END IF
  552.     NEXT
  553.     Shape(k).DiameterMax = SQR(r2max)
  555.  
  556. SUB CalculateMass (k AS INTEGER, factor AS DOUBLE)
  557.     aa = 0
  558.     FOR i = 2 TO Shape(k).Elements
  559.         x = PointChain(k, i).x - Shape(k).Centroid.x
  560.         y = PointChain(k, i).y - Shape(k).Centroid.y
  561.         dx = (PointChain(k, i).x - PointChain(k, i - 1).x)
  562.         dy = (PointChain(k, i).y - PointChain(k, i - 1).y)
  563.         da = .5 * (x * dy - y * dx)
  564.         aa = aa + da
  565.     NEXT
  566.     Shape(k).Mass = factor * SQR(aa * aa)
  568.  
  569. SUB CalculateMOI (k AS INTEGER, ctrvec AS Vector)
  570.     xx = 0
  571.     yy = 0
  572.     FOR i = 1 TO Shape(k).Elements
  573.         a = ctrvec.x - PointChain(k, i).x
  574.         b = ctrvec.y - PointChain(k, i).y
  575.         xx = xx + a * a
  576.         yy = yy + b * b
  577.     NEXT
  578.     Shape(k).MOI = SQR((xx + yy) * (xx + yy)) * (Shape(k).Mass / Shape(k).Elements)
  580.  
  581. SUB TranslateShape (k AS INTEGER, c AS Vector)
  582.     FOR i = 1 TO Shape(k).Elements
  583.         PointChain(k, i).x = PointChain(k, i).x + c.x
  584.         PointChain(k, i).y = PointChain(k, i).y + c.y
  585.     NEXT
  586.     Shape(k).Centroid.x = Shape(k).Centroid.x + c.x
  587.     Shape(k).Centroid.y = Shape(k).Centroid.y + c.y
  589.  
  590. SUB RotShape (k AS INTEGER, c AS Vector, da AS DOUBLE)
  591.     FOR i = 1 TO Shape(k).Elements
  592.         xx = PointChain(k, i).x - c.x
  593.         yy = PointChain(k, i).y - c.y
  594.         PointChain(k, i).x = c.x + xx * COS(da) - yy * SIN(da)
  595.         PointChain(k, i).y = c.y + yy * COS(da) + xx * SIN(da)
  596.     NEXT
  597.     xx = Shape(k).Centroid.x - c.x
  598.     yy = Shape(k).Centroid.y - c.y
  599.     Shape(k).Centroid.x = c.x + xx * COS(da) - yy * SIN(da)
  600.     Shape(k).Centroid.y = c.y + yy * COS(da) + xx * SIN(da)
  602.  
  603. SUB NewAutoBall (x1, y1, r1, r2, pa, pb, fx)
  604.     ShapeCount = ShapeCount + 1
  605.     Shape(ShapeCount).Fixed = fx
  606.     Shape(ShapeCount).Collisions = 0
  607.     i = 0
  608.     FOR j = 0 TO 2 * 4 * ATN(1) STEP .15
  609.         i = i + 1
  610.         r = r1 + r2 * COS(pa * j) ^ pb
  611.         PointChain(ShapeCount, i).x = x1 + r * COS(j)
  612.         PointChain(ShapeCount, i).y = y1 + r * SIN(j)
  613.     NEXT
  614.     Shape(ShapeCount).Elements = i
  615.     CALL CalculateCentroid(ShapeCount)
  616.     IF (fx = 0) THEN
  617.         CALL CalculateMass(ShapeCount, 1)
  618.     ELSE
  619.         CALL CalculateMass(ShapeCount, 999999)
  620.     END IF
  621.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  622.     CALL CalculateDiameterMin(ShapeCount)
  623.     CALL CalculateDiameterMax(ShapeCount)
  624.     Shape(ShapeCount).Velocity.x = 0
  625.     Shape(ShapeCount).Velocity.y = 0
  626.     Shape(ShapeCount).Omega = 0
  627.     IF (fx = 0) THEN
  628.         Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
  629.     ELSE
  630.         Shape(ShapeCount).Shade = _RGB(100, 100, 100)
  631.     END IF
  632.     SelectedShape = ShapeCount
  634.  
  635. SUB NewAutoBrick (x1, y1, wx, wy, ang)
  636.     ShapeCount = ShapeCount + 1
  637.     Shape(ShapeCount).Fixed = 1
  638.     Shape(ShapeCount).Collisions = 0
  639.     i = 0
  640.     FOR j = -wy / 2 TO wy / 2 STEP 5
  641.         i = i + 1
  642.         PointChain(ShapeCount, i).x = x1 + wx / 2
  643.         PointChain(ShapeCount, i).y = y1 + j
  644.     NEXT
  645.     FOR j = wx / 2 TO -wx / 2 STEP -5
  646.         i = i + 1
  647.         PointChain(ShapeCount, i).x = x1 + j
  648.         PointChain(ShapeCount, i).y = y1 + wy / 2
  649.     NEXT
  650.     FOR j = wy / 2 TO -wy / 2 STEP -5
  651.         i = i + 1
  652.         PointChain(ShapeCount, i).x = x1 - wx / 2
  653.         PointChain(ShapeCount, i).y = y1 + j
  654.     NEXT
  655.     FOR j = -wx / 2 TO wx / 2 STEP 5
  656.         i = i + 1
  657.         PointChain(ShapeCount, i).x = x1 + j
  658.         PointChain(ShapeCount, i).y = y1 - wy / 2
  659.     NEXT
  660.     Shape(ShapeCount).Elements = i
  661.     CALL CalculateCentroid(ShapeCount)
  662.     CALL CalculateMass(ShapeCount, 99999)
  663.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  664.     CALL CalculateDiameterMin(ShapeCount)
  665.     CALL CalculateDiameterMax(ShapeCount)
  666.     Shape(ShapeCount).MOI = 999 ^ 999
  667.     Shape(ShapeCount).Velocity.x = 0
  668.     Shape(ShapeCount).Velocity.y = 0
  669.     Shape(ShapeCount).Omega = 0
  670.     Shape(ShapeCount).Shade = _RGB(100, 100, 100)
  671.     SelectedShape = ShapeCount
  672.     CALL RotShape(ShapeCount, Shape(ShapeCount).Centroid, ang)
  674.  
  675. SUB NewBrickLine (xi, yi, xf, yf, wx, wy)
  676.     d1 = SQR((xf - xi) ^ 2 + (yf - yi) ^ 2)
  677.     d2 = SQR(wx ^ 2 + wy ^ 2)
  678.     ang = ATN((yf - yi) / (xf - xi))
  679.     f = 1.2 * d2 / d1
  680.     FOR t = 0 TO 1 + f STEP f
  681.         CALL NewAutoBrick(xi * (1 - t) + xf * t, yi * (1 - t) + yf * t, wx, wy, ang)
  682.     NEXT
  684.  
  685. SUB NewMouseShape (rawresolution AS DOUBLE, targetpoints AS INTEGER, smoothiterations AS INTEGER)
  686.  
  687.     ShapeCount = ShapeCount + 1
  688.     Shape(ShapeCount).Fixed = 0
  689.     Shape(ShapeCount).Collisions = 0
  690.  
  691.     numpoints = 0
  692.  
  693.     xold = 999999
  694.     yold = 999999
  695.     DO
  696.         DO WHILE _MOUSEINPUT
  697.             x = _MOUSEX
  698.             y = _MOUSEY
  699.             IF (x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT) THEN
  700.                 IF _MOUSEBUTTON(1) THEN
  701.                     x = x - (_WIDTH / 2)
  702.                     y = -y + (_HEIGHT / 2)
  703.                     delta = SQR((x - xold) ^ 2 + (y - yold) ^ 2)
  704.                     IF (delta > rawresolution) AND (numpoints < targetpoints - 1) THEN
  705.                         numpoints = numpoints + 1
  706.                         PointChain(ShapeCount, numpoints).x = x
  707.                         PointChain(ShapeCount, numpoints).y = y
  708.                         CALL cpset(x, y, _RGB(0, 255, 255))
  709.                         xold = x
  710.                         yold = y
  711.                     END IF
  712.                 END IF
  713.             END IF
  714.         LOOP
  715.         _DISPLAY
  716.     LOOP UNTIL NOT _MOUSEBUTTON(1) AND (numpoints > 1)
  717.  
  718.     DO WHILE (numpoints < targetpoints)
  719.         rad2max = -1
  720.         kmax = -1
  721.         FOR k = 1 TO numpoints - 1
  722.             xfac = PointChain(ShapeCount, k).x - PointChain(ShapeCount, k + 1).x
  723.             yfac = PointChain(ShapeCount, k).y - PointChain(ShapeCount, k + 1).y
  724.             rad2 = xfac ^ 2 + yfac ^ 2
  725.             IF rad2 > rad2max THEN
  726.                 kmax = k
  727.                 rad2max = rad2
  728.             END IF
  729.         NEXT
  730.         edgecase = 0
  731.         xfac = PointChain(ShapeCount, numpoints).x - PointChain(ShapeCount, 1).x
  732.         yfac = PointChain(ShapeCount, numpoints).y - PointChain(ShapeCount, 1).y
  733.         rad2 = xfac ^ 2 + yfac ^ 2
  734.         IF (rad2 > rad2max) THEN
  735.             kmax = numpoints
  736.             rad2max = rad2
  737.             edgecase = 1
  738.         END IF
  739.         IF (edgecase = 0) THEN
  740.             numpoints = numpoints + 1
  741.             FOR j = numpoints TO kmax + 1 STEP -1
  742.                 PointChain(ShapeCount, j).x = PointChain(ShapeCount, j - 1).x
  743.                 PointChain(ShapeCount, j).y = PointChain(ShapeCount, j - 1).y
  744.             NEXT
  745.             PointChain(ShapeCount, kmax + 1).x = (1 / 2) * (PointChain(ShapeCount, kmax).x + PointChain(ShapeCount, kmax + 2).x)
  746.             PointChain(ShapeCount, kmax + 1).y = (1 / 2) * (PointChain(ShapeCount, kmax).y + PointChain(ShapeCount, kmax + 2).y)
  747.         ELSE
  748.             numpoints = numpoints + 1
  749.             xx = PointChain(ShapeCount, numpoints - 1).x
  750.             yy = PointChain(ShapeCount, numpoints - 1).y
  751.             PointChain(ShapeCount, numpoints).x = (1 / 2) * (PointChain(ShapeCount, 1).x + xx)
  752.             PointChain(ShapeCount, numpoints).y = (1 / 2) * (PointChain(ShapeCount, 1).y + yy)
  753.         END IF
  754.     LOOP
  755.  
  756.     FOR j = 1 TO smoothiterations
  757.         FOR k = 2 TO n - 1
  758.             TempChain(i, k).x = (1 / 2) * (PointChain(i, k - 1).x + PointChain(i, k + 1).x)
  759.             TempChain(i, k).y = (1 / 2) * (PointChain(i, k - 1).y + PointChain(i, k + 1).y)
  760.         NEXT
  761.         FOR k = 2 TO n - 1
  762.             PointChain(i, k).x = TempChain(i, k).x
  763.             PointChain(i, k).y = TempChain(i, k).y
  764.         NEXT
  765.     NEXT
  766.  
  767.     Shape(ShapeCount).Elements = numpoints
  768.     CALL CalculateCentroid(ShapeCount)
  769.     CALL CalculateMass(ShapeCount, 1)
  770.     CALL CalculateMOI(ShapeCount, Shape(ShapeCount).Centroid)
  771.     CALL CalculateDiameterMin(ShapeCount)
  772.     CALL CalculateDiameterMax(ShapeCount)
  773.     Shape(ShapeCount).Velocity.x = 0
  774.     Shape(ShapeCount).Velocity.y = 0
  775.     Shape(ShapeCount).Omega = 0
  776.     Shape(ShapeCount).Shade = _RGB(100 + INT(RND * 155), 100 + INT(RND * 155), 100 + INT(RND * 155))
  777.     SelectedShape = ShapeCount
  779.  
  780. SUB cline (x1, y1, x2, y2, col AS _UNSIGNED LONG)
  781.     LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), col
  783.  
  784. SUB ccircle (x1, y1, rad, col AS _UNSIGNED LONG)
  785.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
  787.  
  788. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
  789.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
  791.  
  792. SUB cpaint (x1, y1, col1 AS _UNSIGNED LONG, col2 AS _UNSIGNED LONG)
  793.     PAINT (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col1, col2
  795.  
  796. SUB cprintstring (y, a AS STRING)
  797.     _PRINTSTRING (_WIDTH / 2 - (LEN(a) * 8) / 2, -y + _HEIGHT / 2), a
  799.  
  800. SUB snd (frq, dur)
  801.     IF ((frq >= 37) AND (frq <= 2000)) THEN
  802.         SOUND frq, dur
  803.     END IF
  805.  
  806. SUB SetupPool
  807.  
  808.     ' Set external field
  809.     ForceField.x = 0
  810.     ForceField.y = 0 '-.08
  811.  
  812.     ' Rectangular border
  813.     wx = 42
  814.     wy = 10
  815.     CALL NewBrickLine(-_WIDTH / 2 + wx, _HEIGHT / 2 - wy, _WIDTH / 2 - wx, _HEIGHT / 2 - wy, wx, wy)
  816.     CALL NewBrickLine(-_WIDTH / 2 + wx, -_HEIGHT / 2 + wy, _WIDTH / 2 - wx, -_HEIGHT / 2 + wy, wx, wy)
  817.     wx = 40
  818.     wy = 10
  819.     CALL NewBrickLine(-_WIDTH / 2 + wy, -_HEIGHT / 2 + 2 * wx, -_WIDTH / 2 + wy, _HEIGHT / 2 - 2 * wx, wx, wy)
  820.     CALL NewBrickLine(_WIDTH / 2 - wy, -_HEIGHT / 2 + 2 * wx, _WIDTH / 2 - wy, _HEIGHT / 2 - 2 * wx, wx, wy)
  821.  
  822.     ' Balls (billiard setup)
  823.     x0 = 160
  824.     y0 = 0
  825.     r = 15
  826.     gg = 2 * r + 3.5
  827.     xf = COS(30 * 3.14159 / 180)
  828.     yf = SIN(30 * 3.14159 / 180)
  829.     gx = gg * xf
  830.     gy = gg * yf
  831.  
  832.     CALL NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, r, 0, 1, 1, 0)
  833.     CALL NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, r, 0, 1, 1, 0)
  834.     CALL NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, r, 0, 1, 1, 0)
  835.     CALL NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, r, 0, 1, 1, 0)
  836.     CALL NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, r, 0, 1, 1, 0)
  837.     CALL NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, r, 0, 1, 1, 0)
  838.     CALL NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, r, 0, 1, 1, 0)
  839.     CALL NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, r, 0, 1, 1, 0)
  840.     CALL NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, r, 0, 1, 1, 0)
  841.     CALL NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, r, 0, 1, 1, 0)
  842.  
  843.     ' Cue ball
  844.     CALL NewAutoBall(-220, 0, r, 0, 1, 1, 0)
  845.     Shape(ShapeCount).Velocity.x = 8 + 5 * RND
  846.     Shape(ShapeCount).Velocity.y = .5 * (RND - .5)
  847.     Shape(ShapeCount).Shade = _RGB(255, 255, 255)
  848.  
  849.     ' Parameters
  850.     CPC = 1.15
  851.     FPC = 8
  852.     RST = 0.75
  853.     VD = 0.995
  854.     SV = 0
  856.  
  857. SUB SetupWackyGame
  858.     ' Set external field
  859.     ForceField.x = 0
  860.     ForceField.y = -.08
  861.  
  862.     ' Rectangular border
  863.     wx = 42
  864.     wy = 10
  865.     CALL NewBrickLine(-_WIDTH / 2 + wx, _HEIGHT / 2 - wy, _WIDTH / 2 - wx, _HEIGHT / 2 - wy, wx, wy)
  866.     CALL NewBrickLine(-_WIDTH / 2 + wx, -_HEIGHT / 2 + wy, _WIDTH / 2 - wx, -_HEIGHT / 2 + wy, wx, wy)
  867.     wx = 40
  868.     wy = 10
  869.     CALL NewBrickLine(-_WIDTH / 2 + wy, -_HEIGHT / 2 + 2 * wx, -_WIDTH / 2 + wy, _HEIGHT / 2 - 2 * wx, wx, wy)
  870.     CALL NewBrickLine(_WIDTH / 2 - wy, -_HEIGHT / 2 + 2 * wx, _WIDTH / 2 - wy, _HEIGHT / 2 - 2 * wx, wx, wy)
  871.  
  872.     ' Balls
  873.     x0 = -70
  874.     y0 = 120
  875.     r1 = 15
  876.     r2 = 2.5
  877.     gg = 2 * (r1 + r2) + 3.5
  878.     xf = COS(30 * 3.14159 / 180)
  879.     yf = SIN(30 * 3.14159 / 180)
  880.     gx = gg * xf
  881.     gy = gg * yf
  882.     CALL NewAutoBall(x0 + 0 * gx, y0 + 0 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  883.     CALL NewAutoBall(x0 + 1 * gx, y0 + 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  884.     CALL NewAutoBall(x0 + 1 * gx, y0 - 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  885.     CALL NewAutoBall(x0 + 2 * gx, y0 + 2 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  886.     CALL NewAutoBall(x0 + 2 * gx, y0 + 0 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  887.     CALL NewAutoBall(x0 + 2 * gx, y0 - 2 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  888.     CALL NewAutoBall(x0 + 3 * gx, y0 + 3 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  889.     CALL NewAutoBall(x0 + 3 * gx, y0 + 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  890.     CALL NewAutoBall(x0 + 3 * gx, y0 - 1 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  891.     CALL NewAutoBall(x0 + 3 * gx, y0 - 3 * gy, r1, r2, INT(RND * 3) + 1, INT(RND * 1) + 2, 0)
  892.  
  893.     ' Misc. bricks
  894.     wx = 60
  895.     wy = 10
  896.     ww = SQR(wx * wx + wy * wy) * .75
  897.     CALL NewBrickLine(ww, 0, 100 + ww, 100, wx, wy)
  898.     CALL NewBrickLine(-ww, 0, -100 - ww, 100, wx, wy)
  899.  
  900.     ' Fidget spinner
  901.     CALL NewAutoBall(-220, 0, 20, 15, 1.5, 2, 0)
  902.     Shape(ShapeCount).Shade = _RGB(255, 255, 255)
  903.  
  904.     ' Parameters
  905.     CPC = 1.15
  906.     FPC = 8
  907.     RST = 0.75
  908.     VD = 0.995
  909.     SV = 0.025
  911.  
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Offline Ashish

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #22 on: March 02, 2020, 05:49:11 am »
Wow @STxAxTIC Now this is something.. :O
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Marked as best answer by STxAxTIC on March 05, 2020, 03:13:04 pm

Offline STxAxTIC

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Re: Generalized physics engine prototype with arbitrary shapes and collisions
« Reply #23 on: March 05, 2020, 07:54:33 pm »
Discussion on this project is continued elsewhere:

https://www.qb64.org/forum/index.php?topic=2295
« Last Edit: March 05, 2020, 08:11:01 pm by STxAxTIC »
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