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Author Topic: On trigless starfields: remember Sanctum?  (Read 5303 times)

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Offline STxAxTIC

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On trigless starfields: remember Sanctum?
« on: August 11, 2019, 11:26:58 am »
Hey all,

As a mere coincidence, I was working on streamlining the 3D world explorer from a few months ago when the starfield subject came up. For those not familiar with this work, below is a full-fledged 3D vector engine that, due to a cool breakthrough involving linked lists, has the flexibility to backbone any 3D engine. For now it stays (almost) strictly in the QB45 domain - no textures, GL commands, libraries - basically no cheating whatsoever. The math is done (as you may have guessed) with vectors, and avoids trig completely. (The 3D calculations involve zero trig, but some objects in the world are best made using trig functions and these are completely nonessential.)

I'm still deciding what the endgame of this project will be, but I figure a refresher post wouldn't hurt. The mouse is disabled for now. Suggested hand placement is left hand on "WSAD", and right hand on numeric keypad (hybrid gamer setup)... But you can do some stuff with the arrow keys too...

For an instant starfield feeling, load the world and press "e" to rise steadily. Once you break through the sky, press "w" to zoom through the stars. Use the keypad etc to move around in any direction. Discover heaven's bottom layer, discover hell, find the pyramid, the megalith, and so on.

Kinda like minecraft, call it pixelcraft, you can press "b" to create blocks. Press "n" to destroy the nearest group. Press "k" to make it vanish.

You only need one extra file, a list of colors (attached).

Code: QB64: [Select]
  1. '$EXEICON:'sanctum.ico'
  2. REM $include:'Color32.BI'
  3.  
  4. ' Constants.
  5. pi = 3.1415926536
  6. ee = 2.7182818285
  7.  
  8. ' Scale.
  9. DIM bignumber AS LONG
  10. bignumber = 3000000
  11.  
  12. ' Video.
  13. 'SCREEN _NEWIMAGE(640, 480, 32)
  14. SCREEN _NEWIMAGE(800, 600, 32)
  15. 'SCREEN _NEWIMAGE(1024, 768, 32)
  18. screenwidth = _WIDTH
  19. screenheight = _HEIGHT
  20.  
  21. ' Camera orientation vectors.
  22. DIM uhat(3), vhat(3), nhat(3)
  23.  
  24. ' Basis vectors defined in three-space.
  25. DIM xhat(3), yhat(3), zhat(3)
  26. xhat(1) = 1: xhat(2) = 0: xhat(3) = 0
  27. yhat(1) = 0: yhat(2) = 1: yhat(3) = 0
  28. zhat(1) = 0: zhat(2) = 0: zhat(3) = 1
  29.  
  30. ' Group structure.
  31. TYPE VectorGroupElement
  32.     Identity AS LONG
  33.     Pointer AS LONG
  34.     Lagger AS LONG
  35.     FirstVector AS LONG
  36.     LastVector AS LONG
  37.     GroupName AS STRING * 50
  38.     Visible AS INTEGER
  39.     ForceAnimate AS INTEGER
  40.     COMFixed AS INTEGER
  41.     COMx AS SINGLE ' Center of mass
  42.     COMy AS SINGLE
  43.     COMz AS SINGLE
  44.     ROTx AS SINGLE ' Center of rotation
  45.     ROTy AS SINGLE
  46.     ROTz AS SINGLE
  47.     REVx AS SINGLE ' Revolution speed
  48.     REVy AS SINGLE
  49.     REVz AS SINGLE
  50.     DIMx AS SINGLE ' Maximum volume
  51.     DIMy AS SINGLE
  52.     DIMz AS SINGLE
  54. DIM VectorGroup(bignumber) AS VectorGroupElement
  55.  
  56. ' World vectors.
  57. DIM vec(bignumber, 3) ' Relative Position
  58. DIM vec3Dpos(bignumber, 3) ' Position
  59. DIM vec3Dvel(bignumber, 3) ' Linear velocity
  60. DIM vec3Dacc(bignumber, 3) ' Linear acceleration
  61. DIM vec3Danv(bignumber, 3) ' Angular velocity
  62. DIM vec3Dvis(bignumber) ' Visible toggle
  63. DIM vec2D(bignumber, 2) ' Projection onto 2D plane
  64. DIM vec3Dcolor(bignumber) AS LONG ' Original color
  65. DIM vec2Dcolor(bignumber) AS LONG ' Projected color
  66.  
  67. ' Clipping planes.
  68. DIM nearplane(4), farplane(4), rightplane(4), leftplane(4), topplane(4), bottomplane(4)
  69.  
  70. ' State.
  72. nearplane(4) = 1
  73. farplane(4) = -100
  74. rightplane(4) = 0 '*' fovd * (nhat(1) * rightplane(1) + nhat(2) * rightplane(2) + nhat(3) * rightplane(3))
  75. leftplane(4) = 0
  76. topplane(4) = 0
  77. bottomplane(4) = 0
  78. midscreenx = screenwidth / 2
  79. midscreeny = screenheight / 2
  80. fovd = -256
  81. numgroupvisible = 0
  82. numvectorvisible = 0
  83. groupidticker = 0
  84. vecgroupid = 0
  85. vectorindex = 0
  86. rotspeed = 1 / 33
  87. linspeed = 3 / 2
  88. timestep = .001
  89. camx = -40
  90. camy = 30
  91. camz = 40
  92. uhat(1) = -.2078192: uhat(2) = -.9781672: uhat(3) = 0
  93. vhat(1) = 0: vhat(2) = 0: vhat(3) = 1
  94. toggletimeanimate = 1
  95. toggleinvertmouse = -1
  96. togglehud = 1
  97.  
  98. ' Prime main loop.
  99. GOSUB initialize.objects
  100. GOSUB redraw
  101.  
  102. ' Begin main loop.
  103. fpstimer = INT(TIMER)
  104. fps = 0
  106.     GOSUB redraw
  107.     GOSUB mouseprocess
  108.     GOSUB keyprocess
  109.  
  110.     fps = fps + 1
  111.     tt = INT(TIMER)
  112.     IF tt = fpstimer + 1 THEN
  113.         fpstimer = tt
  114.         fpsreport = fps
  115.         fps = 0
  116.     END IF
  117.  
  118.     _DISPLAY
  119.     _KEYCLEAR
  120.     _LIMIT 30
  122.  
  124.  
  125. ' Gosubs.
  126.  
  127. redraw:
  128. GOSUB normalize.screen.vectors
  129. GOSUB calculate.clippingplanes
  130. GOSUB compute.visible.groups
  131. GOSUB plot.visible.vectors
  133.  
  134. mouseprocess:
  135. 'mx = 0
  136. 'my = 0
  137. 'DO WHILE _MOUSEINPUT
  138. '    mx = mx + _MOUSEMOVEMENTX
  139. '    my = my + _MOUSEMOVEMENTY
  140. '    IF _MOUSEWHEEL > 0 THEN GOSUB rotate.clockwise
  141. '    IF _MOUSEWHEEL < 0 THEN GOSUB rotate.counterclockwise
  142. '    IF mx > 0 THEN
  143. '        GOSUB rotate.uhat.plus: GOSUB normalize.screen.vectors
  144. '    END IF
  145. '    IF mx < 0 THEN
  146. '        GOSUB rotate.uhat.minus: GOSUB normalize.screen.vectors
  147. '    END IF
  148. '    IF my > 0 THEN
  149. '        IF toggleinvertmouse = -1 THEN
  150. '            GOSUB rotate.vhat.plus: GOSUB normalize.screen.vectors
  151. '        ELSE
  152. '            GOSUB rotate.vhat.minus: GOSUB normalize.screen.vectors
  153. '        END IF
  154. '    END IF
  155. '    IF my < 0 THEN
  156. '        IF toggleinvertmouse = -1 THEN
  157. '            GOSUB rotate.vhat.minus: GOSUB normalize.screen.vectors
  158. '        ELSE
  159. '            GOSUB rotate.vhat.plus: GOSUB normalize.screen.vectors
  160. '        END IF
  161. '    END IF
  162. '    mx = 0
  163. '    my = 0
  164. 'LOOP
  166.  
  167. keyprocess:
  168. IF _KEYDOWN(119) = -1 OR _KEYDOWN(18432) = -1 THEN GOSUB strafe.camera.nhat.minus ' w or uparrow
  169. IF _KEYDOWN(115) = -1 OR _KEYDOWN(20480) = -1 THEN GOSUB strafe.camera.nhat.plus ' s or downarrow
  170. IF _KEYDOWN(97) = -1 THEN GOSUB strafe.camera.uhat.minus ' a
  171. IF _KEYDOWN(100) = -1 THEN GOSUB strafe.camera.uhat.plus ' d
  172. IF _KEYDOWN(56) = -1 THEN GOSUB rotate.vhat.plus: GOSUB normalize.screen.vectors ' 8
  173. IF _KEYDOWN(50) = -1 THEN GOSUB rotate.vhat.minus: GOSUB normalize.screen.vectors ' 2
  174. IF _KEYDOWN(19200) = -1 OR _KEYDOWN(52) = -1 THEN GOSUB rotate.uhat.minus: GOSUB normalize.screen.vectors ' 4
  175. IF _KEYDOWN(19712) = -1 OR _KEYDOWN(54) = -1 THEN GOSUB rotate.uhat.plus: GOSUB normalize.screen.vectors ' 6
  176. IF _KEYDOWN(55) = -1 THEN GOSUB rotate.clockwise ' 7
  177. IF _KEYDOWN(57) = -1 THEN GOSUB rotate.counterclockwise ' 9
  178. IF _KEYDOWN(49) = -1 THEN GOSUB rotate.uhat.minus: GOSUB normalize.screen.vectors: GOSUB rotate.clockwise ' 1
  179. IF _KEYDOWN(51) = -1 THEN GOSUB rotate.uhat.plus: GOSUB normalize.screen.vectors: GOSUB rotate.counterclockwise ' 3
  180. IF _KEYDOWN(113) = -1 THEN GOSUB strafe.camera.vhat.minus ' q
  181. IF _KEYDOWN(101) = -1 THEN GOSUB strafe.camera.vhat.plus ' e
  182.  
  184. IF (key$ <> "") THEN
  185.     SELECT CASE key$
  186.         CASE "x"
  187.             uhat(1) = 0: uhat(2) = 1: uhat(3) = 0
  188.             vhat(1) = 0: vhat(2) = 0: vhat(3) = 1
  189.         CASE "X"
  190.             uhat(1) = 0: uhat(2) = -1: uhat(3) = 0
  191.             vhat(1) = 0: vhat(2) = 0: vhat(3) = 1
  192.         CASE "y"
  193.             uhat(1) = -1: uhat(2) = 0: uhat(3) = 0
  194.             vhat(1) = 0: vhat(2) = 0: vhat(3) = 1
  195.         CASE "Y"
  196.             uhat(1) = 1: uhat(2) = 0: uhat(3) = 0
  197.             vhat(1) = 0: vhat(2) = 0: vhat(3) = 1
  198.         CASE "z"
  199.             uhat(1) = 1: uhat(2) = 0: uhat(3) = 0
  200.             vhat(1) = 0: vhat(2) = 1: vhat(3) = 0
  201.             GOSUB normalize.screen.vectors
  202.         CASE "Z"
  203.             uhat(1) = 0: uhat(2) = 1: uhat(3) = 0
  204.             vhat(1) = 1: vhat(2) = 0: vhat(3) = 0
  205.         CASE "]"
  206.             farplane(4) = farplane(4) - 1
  207.         CASE "["
  208.             farplane(4) = farplane(4) + 1
  209.         CASE " "
  210.             togglehud = -togglehud
  211.         CASE "t"
  212.             toggletimeanimate = -toggletimeanimate
  213.         CASE "i"
  214.             toggleinvertmouse = -toggleinvertmouse
  215.         CASE "v"
  216.             OPEN "snapshot-camera.txt" FOR OUTPUT AS #1
  217.             PRINT #1, camx, camy, camz
  218.             PRINT #1, uhat(1), uhat(2), uhat(3)
  219.             PRINT #1, vhat(1), vhat(2), vhat(3)
  220.             CLOSE #1
  221.         CASE CHR$(27)
  222.             SYSTEM
  223.         CASE "n"
  224.             VectorGroup(closestgroup).COMFixed = 1
  225.             FOR vectorindex = VectorGroup(closestgroup).FirstVector TO VectorGroup(closestgroup).LastVector
  226.                 vec3Dvel(vectorindex, 1) = (RND - .5) * 200
  227.                 vec3Dvel(vectorindex, 2) = (RND - .5) * 200
  228.                 vec3Dvel(vectorindex, 3) = (RND - .5) * 200
  229.             NEXT
  230.         CASE "k"
  231.             p = VectorGroup(closestgroup).Pointer
  232.             l = VectorGroup(closestgroup).Lagger
  233.             VectorGroup(l).Pointer = p
  234.             IF (p <> -999) THEN
  235.                 VectorGroup(p).Lagger = l
  236.             END IF
  237.         CASE "b"
  238.             tilesize = 5
  239.             ' Determine last object id.
  240.             p = 1
  241.             DO
  242.                 k = VectorGroup(p).Identity
  243.                 p = VectorGroup(k).Pointer
  244.                 IF (p = -999) THEN EXIT DO
  245.             LOOP
  246.             lastobjectid = k
  247.             vectorindex = VectorGroup(lastobjectid).LastVector
  248.             ' Create new group.
  249.             groupidticker = groupidticker + 1
  250.             vecgroupid = groupidticker
  251.             VectorGroup(vecgroupid).Identity = vecgroupid
  252.             VectorGroup(vecgroupid).Pointer = -999
  253.             VectorGroup(vecgroupid).Lagger = lastobjectid
  254.             VectorGroup(vecgroupid).GroupName = "Block"
  255.             VectorGroup(vecgroupid).Visible = 0
  256.             VectorGroup(vecgroupid).COMFixed = 1
  257.             VectorGroup(vecgroupid).DIMx = tilesize / 2
  258.             VectorGroup(vecgroupid).DIMy = tilesize / 2
  259.             VectorGroup(vecgroupid).DIMz = tilesize / 2
  260.             VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  261.             FOR r = 1 TO 400
  262.                 vectorindex = vectorindex + 1
  263.                 vec3Dpos(vectorindex, 1) = camx + -20 * nhat(1) + (RND - .5) * tilesize
  264.                 vec3Dpos(vectorindex, 2) = camy + -20 * nhat(2) + (RND - .5) * tilesize
  265.                 vec3Dpos(vectorindex, 3) = camz + -20 * nhat(3) + (RND - .5) * tilesize
  266.                 vec3Dvis(vectorindex) = 0
  267.                 IF RND > .5 THEN
  268.                     vec3Dcolor(vectorindex) = Lime
  269.                 ELSE
  270.                     vec3Dcolor(vectorindex) = Purple
  271.                 END IF
  272.                 GOSUB integratecom
  273.             NEXT
  274.             VectorGroup(vecgroupid).LastVector = vectorindex
  275.             GOSUB calculatecom
  276.             VectorGroup(lastobjectid).Pointer = vecgroupid
  277.     END SELECT
  280.  
  281. convert:
  282. ' Convert graphics from uv-cartesian coordinates to monitor coordinates.
  283. x0 = x: y0 = y
  284. x = x0 + midscreenx
  285. y = -y0 + midscreeny
  287.  
  288. rotate.uhat.plus:
  289. uhat(1) = uhat(1) + nhat(1) * rotspeed
  290. uhat(2) = uhat(2) + nhat(2) * rotspeed
  291. uhat(3) = uhat(3) + nhat(3) * rotspeed
  293.  
  294. rotate.uhat.minus:
  295. uhat(1) = uhat(1) - nhat(1) * rotspeed
  296. uhat(2) = uhat(2) - nhat(2) * rotspeed
  297. uhat(3) = uhat(3) - nhat(3) * rotspeed
  299.  
  300. rotate.vhat.plus:
  301. vhat(1) = vhat(1) + nhat(1) * rotspeed
  302. vhat(2) = vhat(2) + nhat(2) * rotspeed
  303. vhat(3) = vhat(3) + nhat(3) * rotspeed
  305.  
  306. rotate.vhat.minus:
  307. vhat(1) = vhat(1) - nhat(1) * rotspeed
  308. vhat(2) = vhat(2) - nhat(2) * rotspeed
  309. vhat(3) = vhat(3) - nhat(3) * rotspeed
  311.  
  312. rotate.counterclockwise:
  313. v1 = vhat(1)
  314. v2 = vhat(2)
  315. v3 = vhat(3)
  316. vhat(1) = vhat(1) + uhat(1) * rotspeed
  317. vhat(2) = vhat(2) + uhat(2) * rotspeed
  318. vhat(3) = vhat(3) + uhat(3) * rotspeed
  319. uhat(1) = uhat(1) - v1 * rotspeed
  320. uhat(2) = uhat(2) - v2 * rotspeed
  321. uhat(3) = uhat(3) - v3 * rotspeed
  323.  
  324. rotate.clockwise:
  325. v1 = vhat(1)
  326. v2 = vhat(2)
  327. v3 = vhat(3)
  328. vhat(1) = vhat(1) - uhat(1) * rotspeed
  329. vhat(2) = vhat(2) - uhat(2) * rotspeed
  330. vhat(3) = vhat(3) - uhat(3) * rotspeed
  331. uhat(1) = uhat(1) + v1 * rotspeed
  332. uhat(2) = uhat(2) + v2 * rotspeed
  333. uhat(3) = uhat(3) + v3 * rotspeed
  335.  
  336. strafe.camera.uhat.plus:
  337. camx = camx + uhat(1) * linspeed
  338. camy = camy + uhat(2) * linspeed
  339. camz = camz + uhat(3) * linspeed
  341.  
  342. strafe.camera.uhat.minus:
  343. camx = camx - uhat(1) * linspeed
  344. camy = camy - uhat(2) * linspeed
  345. camz = camz - uhat(3) * linspeed
  347.  
  348. strafe.camera.vhat.plus:
  349. camx = camx + vhat(1) * linspeed
  350. camy = camy + vhat(2) * linspeed
  351. camz = camz + vhat(3) * linspeed
  353.  
  354. strafe.camera.vhat.minus:
  355. camx = camx - vhat(1) * linspeed
  356. camy = camy - vhat(2) * linspeed
  357. camz = camz - vhat(3) * linspeed
  359.  
  360. strafe.camera.nhat.plus:
  361. camx = camx + nhat(1) * linspeed
  362. camy = camy + nhat(2) * linspeed
  363. camz = camz + nhat(3) * linspeed
  365.  
  366. strafe.camera.nhat.minus:
  367. camx = camx - nhat(1) * linspeed
  368. camy = camy - nhat(2) * linspeed
  369. camz = camz - nhat(3) * linspeed
  371.  
  372. normalize.screen.vectors:
  373. uhatmag = SQR(uhat(1) * uhat(1) + uhat(2) * uhat(2) + uhat(3) * uhat(3))
  374. uhat(1) = uhat(1) / uhatmag: uhat(2) = uhat(2) / uhatmag: uhat(3) = uhat(3) / uhatmag
  375. vhatmag = SQR(vhat(1) * vhat(1) + vhat(2) * vhat(2) + vhat(3) * vhat(3))
  376. vhat(1) = vhat(1) / vhatmag: vhat(2) = vhat(2) / vhatmag: vhat(3) = vhat(3) / vhatmag
  377. uhatdotvhat = uhat(1) * vhat(1) + uhat(2) * vhat(2) + uhat(3) * vhat(3)
  378. ' The normal vector points toward the eye.
  379. nhat(1) = uhat(2) * vhat(3) - uhat(3) * vhat(2)
  380. nhat(2) = uhat(3) * vhat(1) - uhat(1) * vhat(3)
  381. nhat(3) = uhat(1) * vhat(2) - uhat(2) * vhat(1)
  382. nhatmag = SQR(nhat(1) * nhat(1) + nhat(2) * nhat(2) + nhat(3) * nhat(3))
  383. nhat(1) = nhat(1) / nhatmag: nhat(2) = nhat(2) / nhatmag: nhat(3) = nhat(3) / nhatmag
  385.  
  386. calculate.clippingplanes:
  387. ' Calculate normal vectors to all clipping planes.
  388. h2 = screenheight / 2
  389. w2 = screenwidth / 2
  390. nearplane(1) = -nhat(1)
  391. nearplane(2) = -nhat(2)
  392. nearplane(3) = -nhat(3)
  393. farplane(1) = nhat(1)
  394. farplane(2) = nhat(2)
  395. farplane(3) = nhat(3)
  396. rightplane(1) = h2 * fovd * uhat(1) - h2 * w2 * nhat(1)
  397. rightplane(2) = h2 * fovd * uhat(2) - h2 * w2 * nhat(2)
  398. rightplane(3) = h2 * fovd * uhat(3) - h2 * w2 * nhat(3)
  399. mag = SQR(rightplane(1) * rightplane(1) + rightplane(2) * rightplane(2) + rightplane(3) * rightplane(3))
  400. rightplane(1) = rightplane(1) / mag
  401. rightplane(2) = rightplane(2) / mag
  402. rightplane(3) = rightplane(3) / mag
  403. leftplane(1) = -h2 * fovd * uhat(1) - h2 * w2 * nhat(1)
  404. leftplane(2) = -h2 * fovd * uhat(2) - h2 * w2 * nhat(2)
  405. leftplane(3) = -h2 * fovd * uhat(3) - h2 * w2 * nhat(3)
  406. mag = SQR(leftplane(1) * leftplane(1) + leftplane(2) * leftplane(2) + leftplane(3) * leftplane(3))
  407. leftplane(1) = leftplane(1) / mag
  408. leftplane(2) = leftplane(2) / mag
  409. leftplane(3) = leftplane(3) / mag
  410. topplane(1) = w2 * fovd * vhat(1) - h2 * w2 * nhat(1)
  411. topplane(2) = w2 * fovd * vhat(2) - h2 * w2 * nhat(2)
  412. topplane(3) = w2 * fovd * vhat(3) - h2 * w2 * nhat(3)
  413. mag = SQR(topplane(1) * topplane(1) + topplane(2) * topplane(2) + topplane(3) * topplane(3))
  414. topplane(1) = topplane(1) / mag
  415. topplane(2) = topplane(2) / mag
  416. topplane(3) = topplane(3) / mag
  417. bottomplane(1) = -w2 * fovd * vhat(1) - h2 * w2 * nhat(1)
  418. bottomplane(2) = -w2 * fovd * vhat(2) - h2 * w2 * nhat(2)
  419. bottomplane(3) = -w2 * fovd * vhat(3) - h2 * w2 * nhat(3)
  420. mag = SQR(bottomplane(1) * bottomplane(1) + bottomplane(2) * bottomplane(2) + bottomplane(3) * bottomplane(3))
  421. bottomplane(1) = bottomplane(1) / mag
  422. bottomplane(2) = bottomplane(2) / mag
  423. bottomplane(3) = bottomplane(3) / mag
  425.  
  426. compute.visible.groups:
  427. closestdist2 = 10000000
  428. closestgroup = 1
  429. fp42 = farplane(4) * farplane(4)
  430.  
  431. k = 1
  432. k = VectorGroup(k).Identity
  433. DO ' iterates k
  434.  
  435.     VectorGroup(k).Visible = 0
  436.  
  437.     dx = VectorGroup(k).COMx - camx
  438.     dy = VectorGroup(k).COMy - camy
  439.     dz = VectorGroup(k).COMz - camz
  440.  
  441.     dist2 = dx * dx + dy * dy + dz * dz
  442.  
  443.     IF dist2 < fp42 THEN
  444.  
  445.         groupinview = 1
  446.         IF dx * nearplane(1) + dy * nearplane(2) + dz * nearplane(3) - nearplane(4) < 0 THEN groupinview = 0
  447.         'IF dx * farplane(1) + dy * farplane(2) + dz * farplane(3) - farplane(4) < 0 THEN groupinview = 0
  448.         IF dx * rightplane(1) + dy * rightplane(2) + dz * rightplane(3) - rightplane(4) < 0 THEN groupinview = 0
  449.         IF dx * leftplane(1) + dy * leftplane(2) + dz * leftplane(3) - leftplane(4) < 0 THEN groupinview = 0
  450.         IF dx * topplane(1) + dy * topplane(2) + dz * topplane(3) - topplane(4) < 0 THEN groupinview = 0
  451.         IF dx * bottomplane(1) + dy * bottomplane(2) + dz * bottomplane(3) - bottomplane(4) < 0 THEN groupinview = 0
  452.         IF groupinview = 1 THEN
  453.  
  454.             IF (dist2 < closestdist2) THEN
  455.                 closestdist2 = dist2
  456.                 closestgroup = k
  457.             END IF
  458.  
  459.             VectorGroup(k).Visible = 1
  460.  
  461.             IF (toggletimeanimate = 1) THEN
  462.                 vecgroupid = k
  463.                 GOSUB timeanimate
  464.             END IF
  465.  
  466.             FOR i = VectorGroup(k).FirstVector TO VectorGroup(k).LastVector
  467.                 GOSUB clip.project.vectors
  468.             NEXT
  469.  
  470.         ELSE
  471.             ' Force animation regardless of clipping.
  472.             IF (VectorGroup(k).ForceAnimate = 1) THEN
  473.                 vecgroupid = k
  474.                 GOSUB timeanimate
  475.             END IF
  476.         END IF
  477.     ELSE
  478.         ' Force animation regardless of distance from camera.
  479.         IF (VectorGroup(k).ForceAnimate = 1) THEN
  480.             vecgroupid = k
  481.             GOSUB timeanimate
  482.         END IF
  483.     END IF
  484.     k = VectorGroup(k).Pointer
  485.     IF k = -999 THEN EXIT DO
  486.     k = VectorGroup(k).Identity
  489.  
  490. clip.project.vectors: ' requires i
  491. vec(i, 1) = vec3Dpos(i, 1) - camx
  492. vec(i, 2) = vec3Dpos(i, 2) - camy
  493. vec(i, 3) = vec3Dpos(i, 3) - camz
  494. fogswitch = -1
  495. vec3Dvis(i) = 0
  496. vectorinview = 1
  497. ' Perform view plane clipping.
  498. IF vec(i, 1) * nearplane(1) + vec(i, 2) * nearplane(2) + vec(i, 3) * nearplane(3) - nearplane(4) < 0 THEN vectorinview = 0
  499. IF vec(i, 1) * farplane(1) + vec(i, 2) * farplane(2) + vec(i, 3) * farplane(3) - farplane(4) < 0 THEN vectorinview = 0
  500. IF vec(i, 1) * farplane(1) + vec(i, 2) * farplane(2) + vec(i, 3) * farplane(3) - farplane(4) * .85 < 0 THEN fogswitch = 1
  501. IF vec(i, 1) * rightplane(1) + vec(i, 2) * rightplane(2) + vec(i, 3) * rightplane(3) - rightplane(4) < 0 THEN vectorinview = 0
  502. IF vec(i, 1) * leftplane(1) + vec(i, 2) * leftplane(2) + vec(i, 3) * leftplane(3) - leftplane(4) < 0 THEN vectorinview = 0
  503. IF vec(i, 1) * topplane(1) + vec(i, 2) * topplane(2) + vec(i, 3) * topplane(3) - topplane(4) < 0 THEN vectorinview = 0
  504. IF vec(i, 1) * bottomplane(1) + vec(i, 2) * bottomplane(2) + vec(i, 3) * bottomplane(3) - bottomplane(4) < 0 THEN vectorinview = 0
  505. IF vectorinview = 1 THEN
  506.     vec3Dvis(i) = 1
  507.     ' Project vectors onto the screen plane.
  508.     vec3Ddotnhat = vec(i, 1) * nhat(1) + vec(i, 2) * nhat(2) + vec(i, 3) * nhat(3)
  509.     vec2D(i, 1) = (vec(i, 1) * uhat(1) + vec(i, 2) * uhat(2) + vec(i, 3) * uhat(3)) * fovd / vec3Ddotnhat
  510.     vec2D(i, 2) = (vec(i, 1) * vhat(1) + vec(i, 2) * vhat(2) + vec(i, 3) * vhat(3)) * fovd / vec3Ddotnhat
  511.     IF fogswitch = 1 THEN vec2Dcolor(i) = Gray ELSE vec2Dcolor(i) = vec3Dcolor(i)
  514.  
  515. timeanimate: ' requires vecgroupid
  516. dt = timestep
  517.  
  518. xcom = VectorGroup(vecgroupid).COMx
  519. ycom = VectorGroup(vecgroupid).COMy
  520. zcom = VectorGroup(vecgroupid).COMz
  521. xrot = VectorGroup(vecgroupid).ROTx
  522. yrot = VectorGroup(vecgroupid).ROTy
  523. zrot = VectorGroup(vecgroupid).ROTz
  524. xrev = VectorGroup(vecgroupid).ROTx
  525. yrev = VectorGroup(vecgroupid).ROTy
  526. zrev = VectorGroup(vecgroupid).ROTz
  527. xdim = VectorGroup(vecgroupid).DIMx
  528. ydim = VectorGroup(vecgroupid).DIMy
  529. zdim = VectorGroup(vecgroupid).DIMz
  530.  
  531. IF (VectorGroup(vecgroupid).COMFixed = 0) THEN GOSUB resetcom
  532.  
  533. FOR vectorindex = VectorGroup(vecgroupid).FirstVector TO VectorGroup(vecgroupid).LastVector
  534.  
  535.     ' Linear velocity update
  536.     ax = vec3Dacc(vectorindex, 1)
  537.     ay = vec3Dacc(vectorindex, 2)
  538.     az = vec3Dacc(vectorindex, 3)
  539.     IF (ax <> 0) THEN vec3Dvel(vectorindex, 1) = vec3Dvel(vectorindex, 1) + ax * dt
  540.     IF (ay <> 0) THEN vec3Dvel(vectorindex, 2) = vec3Dvel(vectorindex, 2) + ay * dt
  541.     IF (az <> 0) THEN vec3Dvel(vectorindex, 3) = vec3Dvel(vectorindex, 3) + az * dt
  542.  
  543.     ' Linear position update with periodic boundaries inside group dimension
  544.     vx = vec3Dvel(vectorindex, 1)
  545.     vy = vec3Dvel(vectorindex, 2)
  546.     vz = vec3Dvel(vectorindex, 3)
  547.     IF (vx <> 0) THEN
  548.         px = vec3Dpos(vectorindex, 1) + vx * dt
  549.         IF ABS(px - xcom) > xdim THEN
  550.             IF (px > xcom) THEN
  551.                 px = xcom - xdim
  552.             ELSE
  553.                 px = xcom + xdim
  554.             END IF
  555.         END IF
  556.         vec3Dpos(vectorindex, 1) = px
  557.     END IF
  558.     IF (vy <> 0) THEN
  559.         py = vec3Dpos(vectorindex, 2) + vy * dt
  560.         IF ABS(py - ycom) > ydim THEN
  561.             IF (py > ycom) THEN
  562.                 py = ycom - ydim
  563.             ELSE
  564.                 py = ycom + ydim
  565.             END IF
  566.         END IF
  567.         vec3Dpos(vectorindex, 2) = py
  568.     END IF
  569.     IF (vz <> 0) THEN
  570.         pz = vec3Dpos(vectorindex, 3) + vz * dt
  571.         IF ABS(pz - zcom) > zdim THEN
  572.             IF (pz > zcom) THEN
  573.                 pz = zcom - zdim
  574.             ELSE
  575.                 pz = zcom + zdim
  576.             END IF
  577.         END IF
  578.         vec3Dpos(vectorindex, 3) = pz
  579.     END IF
  580.  
  581.     ' Rotation update
  582.     IF (xrot <> 0) THEN
  583.         anv = vec3Danv(vectorindex, 1)
  584.         yy = vec3Dpos(vectorindex, 2) - yrot
  585.         zz = vec3Dpos(vectorindex, 3) - zrot
  586.         y = yy * COS(timestep * anv) - zz * SIN(timestep * anv)
  587.         z = yy * SIN(timestep * anv) + zz * COS(timestep * anv)
  588.         vec3Dpos(vectorindex, 2) = y + yrot
  589.         vec3Dpos(vectorindex, 3) = z + zrot
  590.     END IF
  591.     IF (yrot <> 0) THEN
  592.         anv = vec3Danv(vectorindex, 2)
  593.         xx = vec3Dpos(vectorindex, 1) - xrot
  594.         zz = vec3Dpos(vectorindex, 3) - zrot
  595.         x = xx * COS(timestep * anv) + zz * SIN(timestep * anv)
  596.         z = -xx * SIN(timestep * anv) + zz * COS(timestep * anv)
  597.         vec3Dpos(vectorindex, 1) = x + xrot
  598.         vec3Dpos(vectorindex, 3) = z + zrot
  599.     END IF
  600.     IF (zrot <> 0) THEN
  601.         anv = vec3Danv(vectorindex, 3)
  602.         xx = vec3Dpos(vectorindex, 1) - xrot
  603.         yy = vec3Dpos(vectorindex, 2) - yrot
  604.         x = xx * COS(timestep * anv) - yy * SIN(timestep * anv)
  605.         y = xx * SIN(timestep * anv) + yy * COS(timestep * anv)
  606.         vec3Dpos(vectorindex, 1) = x + xrot
  607.         vec3Dpos(vectorindex, 2) = y + yrot
  608.     END IF
  609.  
  610.     ' Revolution update
  611.     IF (xrev <> 0) THEN
  612.         anv = xrev
  613.         yy = vec3Dpos(vectorindex, 2) - ycom
  614.         zz = vec3Dpos(vectorindex, 3) - zcom
  615.         y = yy * COS(timestep * anv) - zz * SIN(timestep * anv)
  616.         z = yy * SIN(timestep * anv) + zz * COS(timestep * anv)
  617.         vec3Dpos(vectorindex, 2) = y + ycom
  618.         vec3Dpos(vectorindex, 3) = z + zcom
  619.     END IF
  620.     IF (yrev <> 0) THEN
  621.         anv = yrev
  622.         xx = vec3Dpos(vectorindex, 1) - xcom
  623.         zz = vec3Dpos(vectorindex, 3) - zcom
  624.         x = xx * COS(timestep * anv) + zz * SIN(timestep * anv)
  625.         z = -xx * SIN(timestep * anv) + zz * COS(timestep * anv)
  626.         vec3Dpos(vectorindex, 1) = x + xcom
  627.         vec3Dpos(vectorindex, 3) = z + zcom
  628.     END IF
  629.     IF (zrev <> 0) THEN
  630.         anv = zrev
  631.         xx = vec3Dpos(vectorindex, 1) - xcom
  632.         yy = vec3Dpos(vectorindex, 2) - ycom
  633.         x = xx * COS(timestep * anv) - yy * SIN(timestep * anv)
  634.         y = xx * SIN(timestep * anv) + yy * COS(timestep * anv)
  635.         vec3Dpos(vectorindex, 1) = x + xcom
  636.         vec3Dpos(vectorindex, 2) = y + ycom
  637.     END IF
  638.  
  639.     IF (VectorGroup(vecgroupid).COMFixed = 0) THEN GOSUB integratecom
  641. IF (VectorGroup(vecgroupid).COMFixed = 0) THEN GOSUB calculatecom
  643.  
  644. integratecom: ' requires vecgroupid
  645. VectorGroup(vecgroupid).COMx = vec3Dpos(vectorindex, 1) + VectorGroup(vecgroupid).COMx
  646. VectorGroup(vecgroupid).COMy = vec3Dpos(vectorindex, 2) + VectorGroup(vecgroupid).COMy
  647. VectorGroup(vecgroupid).COMz = vec3Dpos(vectorindex, 3) + VectorGroup(vecgroupid).COMz
  649.  
  650. calculatecom: ' requires vecgroupid
  651. f = 1 + VectorGroup(vecgroupid).LastVector - VectorGroup(vecgroupid).FirstVector
  652. VectorGroup(vecgroupid).COMx = VectorGroup(vecgroupid).COMx / f
  653. VectorGroup(vecgroupid).COMy = VectorGroup(vecgroupid).COMy / f
  654. VectorGroup(vecgroupid).COMz = VectorGroup(vecgroupid).COMz / f
  656.  
  657. resetcom: ' requires vecgroupid
  658. VectorGroup(vecgroupid).COMx = 0
  659. VectorGroup(vecgroupid).COMy = 0
  660. VectorGroup(vecgroupid).COMz = 0
  662.  
  663. plot.visible.vectors:
  664. GOSUB plot.vectors
  665. GOSUB plot.hud
  667.  
  668. plot.vectors:
  670. numgroupvisible = 0
  671. numvectorvisible = 0
  672. k = 1
  673. k = VectorGroup(k).Identity
  675.     IF (VectorGroup(k).Visible = 1) THEN
  676.         numgroupvisible = numgroupvisible + 1
  677.         FOR i = VectorGroup(k).FirstVector TO VectorGroup(k).LastVector - 1
  678.             IF (vec3Dvis(i) = 1) THEN
  679.                 numvectorvisible = numvectorvisible + 1
  680.                 IF k = closestgroup THEN col = Yellow ELSE col = vec2Dcolor(i)
  681.                 x = vec2D(i, 1): y = vec2D(i, 2): GOSUB convert: x1 = x: y1 = y
  682.                 x = vec2D(i + 1, 1): y = vec2D(i + 1, 2): GOSUB convert: x2 = x: y2 = y
  683.                 IF ((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)) < 225 THEN
  684.                     LINE (x1, y1)-(x2, y2), col
  685.                 ELSE
  686.                     CIRCLE (x1, y1), 1, col
  687.                 END IF
  688.             END IF
  689.         NEXT
  690.     END IF
  691.     k = VectorGroup(k).Pointer
  692.     IF k = -999 THEN EXIT DO
  693.     k = VectorGroup(k).Identity
  696.  
  697. plot.hud:
  698. ' Redraw compass.
  699. x = 30 * (xhat(1) * uhat(1) + xhat(2) * uhat(2) + xhat(3) * uhat(3)): y = 30 * (xhat(1) * vhat(1) + xhat(2) * vhat(2) + xhat(3) * vhat(3)): GOSUB convert
  700. LINE (midscreenx, midscreeny)-(x, y), Red
  701. x = 30 * (yhat(1) * uhat(1) + yhat(2) * uhat(2) + yhat(3) * uhat(3)): y = 30 * (yhat(1) * vhat(1) + yhat(2) * vhat(2) + yhat(3) * vhat(3)): GOSUB convert
  702. LINE (midscreenx, midscreeny)-(x, y), Green
  703. x = 30 * (zhat(1) * uhat(1) + zhat(2) * uhat(2) + zhat(3) * uhat(3)): y = 30 * (zhat(1) * vhat(1) + zhat(2) * vhat(2) + zhat(3) * vhat(3)): GOSUB convert
  704. LINE (midscreenx, midscreeny)-(x, y), Blue
  705. IF togglehud = 1 THEN
  706.     COLOR LimeGreen
  707.     LOCATE 2, 2: PRINT "- View Info -"
  708.     COLOR DarkKhaki
  709.     LOCATE 3, 2: PRINT "FPS:"; fpsreport
  710.     LOCATE 4, 2: PRINT "Vectors:"; numvectorvisible
  711.     LOCATE 5, 2: PRINT "Groups:"; numgroupvisible
  712.     LOCATE 6, 2: PRINT "Depth:"; -farplane(4)
  713.     LOCATE 7, 2: PRINT "Adjust via [ ]"
  714.     COLOR LimeGreen
  715.     LOCATE 9, 2: PRINT "- Camera -"
  716.     COLOR DarkKhaki
  717.     LOCATE 10, 2: PRINT INT(camx); INT(camy); INT(camz)
  718.     COLOR LimeGreen
  719.     LOCATE 12, 2: PRINT "- Closest: -"
  720.     COLOR DarkKhaki
  721.     LOCATE 13, 2: PRINT LTRIM$(RTRIM$(VectorGroup(closestgroup).GroupName))
  722.     COLOR LimeGreen
  723.     a$ = "MOVE - ALIGN": LOCATE 2, screenwidth / 8 - LEN(a$): PRINT a$
  724.     COLOR DarkKhaki
  725.     a$ = "q w e - x y z": LOCATE 3, screenwidth / 8 - LEN(a$): PRINT a$
  726.     a$ = "a s d - X Y Z": LOCATE 4, screenwidth / 8 - LEN(a$): PRINT a$
  727.     a$ = "i = invert ms": LOCATE 5, screenwidth / 8 - LEN(a$): PRINT a$
  728.     COLOR LimeGreen
  729.     a$ = "- ROTATE -": LOCATE 7, screenwidth / 8 - LEN(a$): PRINT a$
  730.     COLOR DarkKhaki
  731.     a$ = "7 8 9 Mouse": LOCATE 8, screenwidth / 8 - LEN(a$): PRINT a$
  732.     a$ = "4 5 6   +  ": LOCATE 9, screenwidth / 8 - LEN(a$): PRINT a$
  733.     a$ = "1 2 3 Wheel": LOCATE 10, screenwidth / 8 - LEN(a$): PRINT a$
  734.     COLOR LimeGreen
  735.     a$ = "- CONTROL -": LOCATE 12, screenwidth / 8 - LEN(a$): PRINT a$
  736.     COLOR DarkKhaki
  737.     a$ = "t = Stop time": LOCATE 13, screenwidth / 8 - LEN(a$): PRINT a$
  738.     a$ = "b = Create": LOCATE 14, screenwidth / 8 - LEN(a$): PRINT a$
  739.     a$ = "n = Destroy": LOCATE 15, screenwidth / 8 - LEN(a$): PRINT a$
  740.     a$ = "k = Delete": LOCATE 16, screenwidth / 8 - LEN(a$): PRINT a$
  741.     COLOR LimeGreen
  742.     a$ = "SPACE = Hide Info": LOCATE (screenheight / 16) - 3, (screenwidth / 8) / 2 - LEN(a$) / 2: PRINT a$
  744.     COLOR LimeGreen
  745.     a$ = "You See: " + LTRIM$(RTRIM$(VectorGroup(closestgroup).GroupName)): LOCATE (screenheight / 16) - 3, (screenwidth / 8) / 2 - LEN(a$) / 2: PRINT a$
  748.  
  749. 'groupidfromname: ' requires n$, returns k
  750. 'k = 1
  751. 'k = VectorGroup(k).Identity
  752. 'DO ' iterates k
  753. '    IF n$ = LTRIM$(RTRIM$(VectorGroup(k).GroupName)) THEN EXIT DO
  754. '    k = VectorGroup(k).Pointer
  755. '    IF k = -999 THEN EXIT DO
  756. '    k = VectorGroup(k).Identity
  757. 'LOOP
  758. 'RETURN
  759.  
  760. ' Data.
  761.  
  762. initialize.objects:
  763. vectorindex = 0
  764. groupidticker = 0
  765. gridsize = 550
  766. tilesize = 15
  767.  
  768. '__AAA
  769. groupidticker = groupidticker + 1
  770. vecgroupid = groupidticker
  771. VectorGroup(vecgroupid).Identity = vecgroupid
  772. VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  773. VectorGroup(vecgroupid).Lagger = vecgroupid - 1 ' Fancy way to say 0.
  774. VectorGroup(vecgroupid).GroupName = "__AAA"
  775. VectorGroup(vecgroupid).Visible = 0
  776. VectorGroup(vecgroupid).COMFixed = 1
  777. VectorGroup(vecgroupid).DIMx = 5
  778. VectorGroup(vecgroupid).DIMy = 5
  779. VectorGroup(vecgroupid).DIMz = 5
  780. VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  781. FOR r = 1 TO 1
  782.     vectorindex = vectorindex + 1
  783.     vec3Dpos(vectorindex, 1) = 0
  784.     vec3Dpos(vectorindex, 2) = 0
  785.     vec3Dpos(vectorindex, 3) = -1000
  786.     vec3Dcolor(vectorindex) = White
  787.     GOSUB integratecom
  789. VectorGroup(vecgroupid).LastVector = vectorindex
  790. GOSUB calculatecom
  791.  
  792. 'Dirt
  793. h = 5
  794. FOR w = 1 TO 5
  795.     FOR u = -gridsize TO gridsize STEP tilesize
  796.         FOR v = -gridsize TO gridsize STEP tilesize
  797.             groupidticker = groupidticker + 1
  798.             vecgroupid = groupidticker
  799.             VectorGroup(vecgroupid).Identity = vecgroupid
  800.             VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  801.             VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  802.             VectorGroup(vecgroupid).GroupName = "Dirt"
  803.             VectorGroup(vecgroupid).Visible = 0
  804.             VectorGroup(vecgroupid).COMFixed = 1
  805.             VectorGroup(vecgroupid).DIMx = 35
  806.             VectorGroup(vecgroupid).DIMy = 35
  807.             VectorGroup(vecgroupid).DIMz = 35
  808.             VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  809.             FOR i = u TO u + tilesize STEP h
  810.                 FOR j = v TO v + tilesize STEP h
  811.                     IF RND > 1 - w / 5 THEN
  812.                         vectorindex = vectorindex + 1
  813.                         vec3Dpos(vectorindex, 1) = i + RND * h - RND * h
  814.                         vec3Dpos(vectorindex, 2) = j + RND * h - RND * h
  815.                         vec3Dpos(vectorindex, 3) = -(w - 1) * 70 - RND * 70
  816.                         vec3Dvis(vectorindex) = 0
  817.                         IF RND > .5 THEN
  818.                             vec3Dcolor(vectorindex) = DarkGoldenRod
  819.                         ELSE
  820.                             IF RND > .5 THEN
  821.                                 vec3Dcolor(vectorindex) = SaddleBrown
  822.                             ELSE
  823.                                 vec3Dcolor(vectorindex) = Sienna
  824.                             END IF
  825.                         END IF
  826.                         GOSUB integratecom
  827.                     END IF
  828.                 NEXT
  829.             NEXT
  830.             VectorGroup(vecgroupid).LastVector = vectorindex
  831.             GOSUB calculatecom
  832.         NEXT
  833.     NEXT
  835.  
  836. 'Grass and Puddles
  837. h = 2
  838. FOR u = -gridsize TO gridsize STEP tilesize
  839.     FOR v = -gridsize TO gridsize STEP tilesize
  840.         groupidticker = groupidticker + 1
  841.         vecgroupid = groupidticker
  842.         VectorGroup(vecgroupid).Identity = vecgroupid
  843.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  844.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  845.         VectorGroup(vecgroupid).GroupName = "Grass and Puddles"
  846.         VectorGroup(vecgroupid).Visible = 0
  847.         VectorGroup(vecgroupid).COMFixed = 1
  848.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  849.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  850.         VectorGroup(vecgroupid).DIMz = 3
  851.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  852.         FOR i = u TO u + tilesize STEP h
  853.             FOR j = v TO v + tilesize STEP h
  854.                 vectorindex = vectorindex + 1
  855.                 vec3Dpos(vectorindex, 1) = i + RND * h - RND * h
  856.                 vec3Dpos(vectorindex, 2) = j + RND * h - RND * h
  857.                 vec3Dpos(vectorindex, 3) = .5 + 1 * COS((i - 15) * .08) - 1 * COS((j - 6) * .12)
  858.                 vec3Dvis(vectorindex) = 0
  859.                 IF vec3Dpos(vectorindex, 3) > 0 THEN
  860.                     IF RND > .5 THEN
  861.                         vec3Dcolor(vectorindex) = Green
  862.                     ELSE
  863.                         vec3Dcolor(vectorindex) = ForestGreen
  864.                     END IF
  865.                 ELSE
  866.                     vec3Dvel(vectorindex, 1) = (RND - .5) * 20
  867.                     vec3Dvel(vectorindex, 2) = (RND - .5) * 20
  868.                     vec3Dvel(vectorindex, 3) = (RND - .5) * 20
  869.                     IF RND > .2 THEN
  870.                         vec3Dcolor(vectorindex) = LightSeaGreen
  871.                     ELSE
  872.                         vec3Dcolor(vectorindex) = Blue
  873.                     END IF
  874.                 END IF
  875.                 GOSUB integratecom
  876.             NEXT
  877.         NEXT
  878.         VectorGroup(vecgroupid).LastVector = vectorindex
  879.         GOSUB calculatecom
  880.     NEXT
  882.  
  883. 'Grave
  884. thickness = 2.5
  885. span = 20
  886. height = 30
  887. crux = 22
  888. FOR xloc = -90 TO -290 STEP -60
  889.     FOR yloc = 0 TO 180 STEP 45
  890.         FOR k = 0 TO height
  891.             groupidticker = groupidticker + 1
  892.             vecgroupid = groupidticker
  893.             VectorGroup(vecgroupid).Identity = vecgroupid
  894.             VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  895.             VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  896.             VectorGroup(vecgroupid).GroupName = "Grave"
  897.             VectorGroup(vecgroupid).Visible = 0
  898.             VectorGroup(vecgroupid).COMFixed = 1
  899.             VectorGroup(vecgroupid).DIMx = thickness
  900.             VectorGroup(vecgroupid).DIMy = thickness
  901.             VectorGroup(vecgroupid).DIMz = thickness
  902.             VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  903.             FOR i = -thickness TO thickness STEP thickness / 2
  904.                 FOR j = -thickness TO thickness STEP thickness / 2
  905.                     vectorindex = vectorindex + 1
  906.                     vec3Dpos(vectorindex, 1) = xloc + i + (RND - .5) * 2
  907.                     vec3Dpos(vectorindex, 2) = yloc + j + (RND - .5) * 2
  908.                     vec3Dpos(vectorindex, 3) = k + (RND - .5) * 2
  909.                     vec3Dvis(vectorindex) = 0
  910.                     IF RND > .5 THEN
  911.                         vec3Dcolor(vectorindex) = SlateGray
  912.                     ELSE
  913.                         vec3Dcolor(vectorindex) = DarkGray
  914.                     END IF
  915.                     GOSUB integratecom
  916.                 NEXT
  917.             NEXT
  918.             VectorGroup(vecgroupid).LastVector = vectorindex
  919.             GOSUB calculatecom
  920.         NEXT
  921.         FOR j = -span / 2 TO -thickness
  922.             groupidticker = groupidticker + 1
  923.             vecgroupid = groupidticker
  924.             VectorGroup(vecgroupid).Identity = vecgroupid
  925.             VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  926.             VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  927.             VectorGroup(vecgroupid).GroupName = "Grave"
  928.             VectorGroup(vecgroupid).Visible = 0
  929.             VectorGroup(vecgroupid).COMFixed = 1
  930.             VectorGroup(vecgroupid).DIMx = thickness
  931.             VectorGroup(vecgroupid).DIMy = thickness
  932.             VectorGroup(vecgroupid).DIMz = thickness
  933.             VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  934.             FOR k = -thickness TO thickness STEP thickness / 2
  935.                 FOR i = -thickness TO thickness STEP thickness / 2
  936.                     vectorindex = vectorindex + 1
  937.                     vec3Dpos(vectorindex, 1) = xloc + i + (RND - .5) * 2
  938.                     vec3Dpos(vectorindex, 2) = yloc + j + (RND - .5) * 2
  939.                     vec3Dpos(vectorindex, 3) = crux + k + (RND - .5) * 2
  940.                     vec3Dvis(vectorindex) = 0
  941.                     IF RND > .5 THEN
  942.                         vec3Dcolor(vectorindex) = SlateGray
  943.                     ELSE
  944.                         vec3Dcolor(vectorindex) = DarkGray
  945.                     END IF
  946.                     GOSUB integratecom
  947.                 NEXT
  948.             NEXT
  949.             VectorGroup(vecgroupid).LastVector = vectorindex
  950.             GOSUB calculatecom
  951.         NEXT
  952.         FOR j = thickness TO span / 2
  953.             groupidticker = groupidticker + 1
  954.             vecgroupid = groupidticker
  955.             VectorGroup(vecgroupid).Identity = vecgroupid
  956.             VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  957.             VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  958.             VectorGroup(vecgroupid).GroupName = "Grave"
  959.             VectorGroup(vecgroupid).Visible = 0
  960.             VectorGroup(vecgroupid).COMFixed = 1
  961.             VectorGroup(vecgroupid).DIMx = thickness
  962.             VectorGroup(vecgroupid).DIMy = thickness
  963.             VectorGroup(vecgroupid).DIMz = thickness
  964.             VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  965.             FOR k = -thickness TO thickness STEP thickness / 2
  966.                 FOR i = -thickness TO thickness STEP thickness / 2
  967.                     vectorindex = vectorindex + 1
  968.                     vec3Dpos(vectorindex, 1) = xloc + i + (RND - .5) * 2
  969.                     vec3Dpos(vectorindex, 2) = yloc + j + (RND - .5) * 2
  970.                     vec3Dpos(vectorindex, 3) = crux + k + (RND - .5) * 2
  971.                     vec3Dvis(vectorindex) = 0
  972.                     IF RND > .5 THEN
  973.                         vec3Dcolor(vectorindex) = SlateGray
  974.                     ELSE
  975.                         vec3Dcolor(vectorindex) = DarkGray
  976.                     END IF
  977.                     GOSUB integratecom
  978.                 NEXT
  979.             NEXT
  980.             VectorGroup(vecgroupid).LastVector = vectorindex
  981.             GOSUB calculatecom
  982.         NEXT
  983.     NEXT
  985.  
  986. 'Heaven's Bottom Layer
  987. h = 2
  988. FOR u = -gridsize TO gridsize STEP tilesize
  989.     FOR v = -gridsize TO gridsize STEP tilesize
  990.         groupidticker = groupidticker + 1
  991.         vecgroupid = groupidticker
  992.         VectorGroup(vecgroupid).Identity = vecgroupid
  993.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  994.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  995.         VectorGroup(vecgroupid).GroupName = "Heaven's Bottom Layer"
  996.         VectorGroup(vecgroupid).Visible = 0
  997.         VectorGroup(vecgroupid).COMFixed = 1
  998.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  999.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1000.         VectorGroup(vecgroupid).DIMz = 3
  1001.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1002.         FOR i = u TO u + tilesize STEP h
  1003.             FOR j = v TO v + tilesize STEP h
  1004.                 vectorindex = vectorindex + 1
  1005.                 vec3Dpos(vectorindex, 1) = i + RND * h - RND * h
  1006.                 vec3Dpos(vectorindex, 2) = j + RND * h - RND * h
  1007.                 vec3Dpos(vectorindex, 3) = 420 - RND
  1008.                 vec3Dvis(vectorindex) = 0
  1009.                 IF RND > .5 THEN
  1010.                     vec3Dcolor(vectorindex) = BlueViolet
  1011.                 ELSE
  1012.                     vec3Dcolor(vectorindex) = Cyan
  1013.                 END IF
  1014.                 GOSUB integratecom
  1015.             NEXT
  1016.         NEXT
  1017.         VectorGroup(vecgroupid).LastVector = vectorindex
  1018.         GOSUB calculatecom
  1019.     NEXT
  1021.  
  1022. 'Hell Spawn
  1023. FOR u = -gridsize TO gridsize STEP tilesize
  1024.     FOR v = -gridsize TO gridsize STEP tilesize
  1025.         groupidticker = groupidticker + 1
  1026.         vecgroupid = groupidticker
  1027.         VectorGroup(vecgroupid).Identity = vecgroupid
  1028.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1029.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1030.         VectorGroup(vecgroupid).GroupName = "Hell Spawn"
  1031.         VectorGroup(vecgroupid).Visible = 0
  1032.         VectorGroup(vecgroupid).COMFixed = 1
  1033.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  1034.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1035.         VectorGroup(vecgroupid).DIMz = 35
  1036.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1037.         FOR i = u TO u + tilesize STEP tilesize / 5
  1038.             FOR j = v TO v + tilesize STEP tilesize / 5
  1039.                 vectorindex = vectorindex + 1
  1040.                 vec3Dpos(vectorindex, 1) = i + (RND - .5) * tilesize
  1041.                 vec3Dpos(vectorindex, 2) = j + (RND - .5) * tilesize
  1042.                 vec3Dpos(vectorindex, 3) = -350 - RND * 70
  1043.                 vec3Dvel(vectorindex, 1) = 0
  1044.                 vec3Dvel(vectorindex, 2) = 0
  1045.                 vec3Dvel(vectorindex, 3) = 400 * RND
  1046.                 vec3Dvis(vectorindex) = 0
  1047.                 IF RND > .2 THEN
  1048.                     vec3Dcolor(vectorindex) = Red
  1049.                 ELSE
  1050.                     vec3Dcolor(vectorindex) = DarkGoldenRod
  1051.                 END IF
  1052.                 GOSUB integratecom
  1053.             NEXT
  1054.         NEXT
  1055.         VectorGroup(vecgroupid).LastVector = vectorindex
  1056.         GOSUB calculatecom
  1057.         VectorGroup(vecgroupid).COMz = -350 - 35
  1058.     NEXT
  1060.  
  1061. 'Icewall East
  1062. h = 2
  1063. FOR u = -gridsize TO gridsize STEP tilesize
  1064.     FOR v = 0 TO 70 STEP tilesize
  1065.         groupidticker = groupidticker + 1
  1066.         vecgroupid = groupidticker
  1067.         VectorGroup(vecgroupid).Identity = vecgroupid
  1068.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1069.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1070.         VectorGroup(vecgroupid).GroupName = "Icewall East"
  1071.         VectorGroup(vecgroupid).Visible = 0
  1072.         VectorGroup(vecgroupid).COMFixed = 1
  1073.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  1074.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1075.         VectorGroup(vecgroupid).DIMz = tilesize / 2
  1076.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1077.         FOR i = u TO u + tilesize STEP h
  1078.             FOR j = v TO v + tilesize STEP h
  1079.                 vectorindex = vectorindex + 1
  1080.                 vec3Dpos(vectorindex, 1) = gridsize + tilesize / 2
  1081.                 vec3Dpos(vectorindex, 2) = i + RND * h - RND * h
  1082.                 vec3Dpos(vectorindex, 3) = j + RND * h - RND * h
  1083.                 vec3Dvis(vectorindex) = 0
  1084.                 IF RND > .5 THEN
  1085.                     vec3Dcolor(vectorindex) = White
  1086.                 ELSE
  1087.                     vec3Dcolor(vectorindex) = Ivory
  1088.                 END IF
  1089.                 GOSUB integratecom
  1090.             NEXT
  1091.         NEXT
  1092.         VectorGroup(vecgroupid).LastVector = vectorindex
  1093.         GOSUB calculatecom
  1094.     NEXT
  1096.  
  1097. 'Icewall South
  1098. h = 2
  1099. FOR u = -gridsize TO gridsize STEP tilesize
  1100.     FOR v = 0 TO 70 STEP tilesize
  1101.         groupidticker = groupidticker + 1
  1102.         vecgroupid = groupidticker
  1103.         VectorGroup(vecgroupid).Identity = vecgroupid
  1104.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1105.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1106.         VectorGroup(vecgroupid).GroupName = "Icewall South"
  1107.         VectorGroup(vecgroupid).Visible = 0
  1108.         VectorGroup(vecgroupid).COMFixed = 1
  1109.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  1110.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1111.         VectorGroup(vecgroupid).DIMz = tilesize / 2
  1112.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1113.         FOR i = u TO u + tilesize STEP h
  1114.             FOR j = v TO v + tilesize STEP h
  1115.                 vectorindex = vectorindex + 1
  1116.                 vec3Dpos(vectorindex, 1) = -gridsize
  1117.                 vec3Dpos(vectorindex, 2) = i + RND * h - RND * h
  1118.                 vec3Dpos(vectorindex, 3) = j + RND * h - RND * h
  1119.                 vec3Dvis(vectorindex) = 0
  1120.                 IF RND > .5 THEN
  1121.                     vec3Dcolor(vectorindex) = White
  1122.                 ELSE
  1123.                     vec3Dcolor(vectorindex) = Ivory
  1124.                 END IF
  1125.                 GOSUB integratecom
  1126.             NEXT
  1127.         NEXT
  1128.         VectorGroup(vecgroupid).LastVector = vectorindex
  1129.         GOSUB calculatecom
  1130.     NEXT
  1132.  
  1133. 'Icewall North
  1134. h = 2
  1135. FOR u = -gridsize TO gridsize STEP tilesize
  1136.     FOR v = 0 TO 70 STEP tilesize
  1137.         groupidticker = groupidticker + 1
  1138.         vecgroupid = groupidticker
  1139.         VectorGroup(vecgroupid).Identity = vecgroupid
  1140.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1141.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1142.         VectorGroup(vecgroupid).GroupName = "Icewall North"
  1143.         VectorGroup(vecgroupid).Visible = 0
  1144.         VectorGroup(vecgroupid).COMFixed = 1
  1145.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  1146.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1147.         VectorGroup(vecgroupid).DIMz = tilesize / 2
  1148.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1149.         FOR i = u TO u + tilesize STEP h
  1150.             FOR j = v TO v + tilesize STEP h
  1151.                 vectorindex = vectorindex + 1
  1152.                 vec3Dpos(vectorindex, 1) = i + RND * h - RND * h
  1153.                 vec3Dpos(vectorindex, 2) = gridsize + tilesize / 2
  1154.                 vec3Dpos(vectorindex, 3) = j + RND * h - RND * h
  1155.                 vec3Dvis(vectorindex) = 0
  1156.                 IF RND > .5 THEN
  1157.                     vec3Dcolor(vectorindex) = White
  1158.                 ELSE
  1159.                     vec3Dcolor(vectorindex) = Ivory
  1160.                 END IF
  1161.                 GOSUB integratecom
  1162.             NEXT
  1163.         NEXT
  1164.         VectorGroup(vecgroupid).LastVector = vectorindex
  1165.         GOSUB calculatecom
  1166.     NEXT
  1168.  
  1169. 'Icewall West
  1170. h = 2
  1171. FOR u = -gridsize TO gridsize STEP tilesize
  1172.     FOR v = 0 TO 70 STEP tilesize
  1173.         groupidticker = groupidticker + 1
  1174.         vecgroupid = groupidticker
  1175.         VectorGroup(vecgroupid).Identity = vecgroupid
  1176.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1177.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1178.         VectorGroup(vecgroupid).GroupName = "Icewall West"
  1179.         VectorGroup(vecgroupid).Visible = 0
  1180.         VectorGroup(vecgroupid).COMFixed = 1
  1181.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  1182.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1183.         VectorGroup(vecgroupid).DIMz = tilesize / 2
  1184.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1185.         FOR i = u TO u + tilesize STEP h
  1186.             FOR j = v TO v + tilesize STEP h
  1187.                 vectorindex = vectorindex + 1
  1188.                 vec3Dpos(vectorindex, 1) = i + RND * h - RND * h
  1189.                 vec3Dpos(vectorindex, 2) = -gridsize
  1190.                 vec3Dpos(vectorindex, 3) = j + RND * h - RND * h
  1191.                 vec3Dvis(vectorindex) = 0
  1192.                 IF RND > .5 THEN
  1193.                     vec3Dcolor(vectorindex) = White
  1194.                 ELSE
  1195.                     vec3Dcolor(vectorindex) = Ivory
  1196.                 END IF
  1197.                 GOSUB integratecom
  1198.             NEXT
  1199.         NEXT
  1200.         VectorGroup(vecgroupid).LastVector = vectorindex
  1201.         GOSUB calculatecom
  1202.     NEXT
  1204.  
  1205. 'Lake of Fire
  1206. h = 2
  1207. FOR u = -gridsize TO gridsize STEP tilesize
  1208.     FOR v = -gridsize TO gridsize STEP tilesize
  1209.         groupidticker = groupidticker + 1
  1210.         vecgroupid = groupidticker
  1211.         VectorGroup(vecgroupid).Identity = vecgroupid
  1212.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1213.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1214.         VectorGroup(vecgroupid).GroupName = "Lake of Fire"
  1215.         VectorGroup(vecgroupid).Visible = 0
  1216.         VectorGroup(vecgroupid).COMFixed = 1
  1217.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  1218.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1219.         VectorGroup(vecgroupid).DIMz = tilesize / 2
  1220.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1221.         FOR i = u TO u + tilesize STEP h
  1222.             FOR j = v TO v + tilesize STEP h
  1223.                 vectorindex = vectorindex + 1
  1224.                 vec3Dpos(vectorindex, 1) = i + RND * h - RND * h
  1225.                 vec3Dpos(vectorindex, 2) = j + RND * h - RND * h
  1226.                 vec3Dpos(vectorindex, 3) = -350 - 70 - RND
  1227.                 vec3Dvis(vectorindex) = 0
  1228.                 IF RND > .2 THEN
  1229.                     vec3Dcolor(vectorindex) = Red
  1230.                 ELSE
  1231.                     vec3Dcolor(vectorindex) = Indigo
  1232.                 END IF
  1233.                 GOSUB integratecom
  1234.             NEXT
  1235.         NEXT
  1236.         VectorGroup(vecgroupid).LastVector = vectorindex
  1237.         GOSUB calculatecom
  1238.     NEXT
  1240.  
  1241. 'Megalith
  1242. ctrx = -90
  1243. ctry = -320
  1244. ctrz = 4
  1245. w = 8
  1246. h = 256
  1247. dens = 100
  1248. FOR k = 1 TO h STEP w
  1249.     FOR i = -h / 20 + k / 20 TO h / 20 - k / 20 STEP w
  1250.         FOR j = -h / 20 + k / 20 TO h / 20 - k / 20 STEP w
  1251.             groupidticker = groupidticker + 1
  1252.             vecgroupid = groupidticker
  1253.             VectorGroup(vecgroupid).Identity = vecgroupid
  1254.             VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1255.             VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1256.             VectorGroup(vecgroupid).GroupName = "Megalith"
  1257.             VectorGroup(vecgroupid).Visible = 0
  1258.             VectorGroup(vecgroupid).COMFixed = 1
  1259.             VectorGroup(vecgroupid).DIMx = w / 2
  1260.             VectorGroup(vecgroupid).DIMy = w / 2
  1261.             VectorGroup(vecgroupid).DIMz = w / 2
  1262.             VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1263.             FOR q = 1 TO dens
  1264.                 vectorindex = vectorindex + 1
  1265.                 vec3Dpos(vectorindex, 1) = ctrx + i + (RND - .5) * w
  1266.                 vec3Dpos(vectorindex, 2) = ctry + j + (RND - .5) * w
  1267.                 vec3Dpos(vectorindex, 3) = ctrz + k + (RND - .5) * w
  1268.                 vec3Dvis(vectorindex) = 0
  1269.                 IF RND > .5 THEN
  1270.                     vec3Dcolor(vectorindex) = Cyan
  1271.                 ELSE
  1272.                     vec3Dcolor(vectorindex) = Teal
  1273.                 END IF
  1274.                 GOSUB integratecom
  1275.             NEXT
  1276.             VectorGroup(vecgroupid).LastVector = vectorindex
  1277.             GOSUB calculatecom
  1278.         NEXT
  1279.     NEXT
  1281.  
  1282. 'Pyramid
  1283. ctrx = -90
  1284. ctry = -120
  1285. ctrz = 4
  1286. w = 8
  1287. h = 56
  1288. dens = 50
  1289. FOR k = 1 TO h STEP w
  1290.     FOR i = -h / 2 + k / 2 TO h / 2 - k / 2 STEP w
  1291.         FOR j = -h / 2 + k / 2 TO h / 2 - k / 2 STEP w
  1292.             groupidticker = groupidticker + 1
  1293.             vecgroupid = groupidticker
  1294.             VectorGroup(vecgroupid).Identity = vecgroupid
  1295.             VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1296.             VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1297.             VectorGroup(vecgroupid).GroupName = "Pyramid"
  1298.             VectorGroup(vecgroupid).Visible = 0
  1299.             VectorGroup(vecgroupid).COMFixed = 1
  1300.             VectorGroup(vecgroupid).DIMx = tilesize / 2
  1301.             VectorGroup(vecgroupid).DIMy = tilesize / 2
  1302.             VectorGroup(vecgroupid).DIMz = tilesize / 2
  1303.             VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1304.             FOR q = 1 TO dens
  1305.                 vectorindex = vectorindex + 1
  1306.                 vec3Dpos(vectorindex, 1) = ctrx + i + (RND - .5) * w
  1307.                 vec3Dpos(vectorindex, 2) = ctry + j + (RND - .5) * w
  1308.                 vec3Dpos(vectorindex, 3) = ctrz + k + (RND - .5) * w
  1309.                 vec3Dvis(vectorindex) = 0
  1310.                 IF RND > .5 THEN
  1311.                     vec3Dcolor(vectorindex) = DarkGoldenRod
  1312.                 ELSE
  1313.                     vec3Dcolor(vectorindex) = GoldenRod
  1314.                 END IF
  1315.                 GOSUB integratecom
  1316.             NEXT
  1317.             VectorGroup(vecgroupid).LastVector = vectorindex
  1318.             GOSUB calculatecom
  1319.         NEXT
  1320.     NEXT
  1322.  
  1323. 'Rain
  1324. FOR u = -gridsize TO gridsize STEP tilesize
  1325.     FOR v = -gridsize TO gridsize STEP tilesize
  1326.         groupidticker = groupidticker + 1
  1327.         vecgroupid = groupidticker
  1328.         VectorGroup(vecgroupid).Identity = vecgroupid
  1329.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1330.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1331.         VectorGroup(vecgroupid).GroupName = "Rain"
  1332.         VectorGroup(vecgroupid).Visible = 0
  1333.         VectorGroup(vecgroupid).COMFixed = 1
  1334.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  1335.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1336.         VectorGroup(vecgroupid).DIMz = 35
  1337.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1338.         FOR i = u TO u + tilesize STEP tilesize '/ 3
  1339.             FOR j = v TO v + tilesize STEP tilesize '/ 3
  1340.                 vectorindex = vectorindex + 1
  1341.                 vec3Dpos(vectorindex, 1) = i + (RND - .5) * tilesize
  1342.                 vec3Dpos(vectorindex, 2) = j + (RND - .5) * tilesize
  1343.                 vec3Dpos(vectorindex, 3) = RND * 70
  1344.                 vec3Dvel(vectorindex, 1) = 0
  1345.                 vec3Dvel(vectorindex, 2) = 0
  1346.                 vec3Dvel(vectorindex, 3) = -400 * RND
  1347.                 vec3Dvis(vectorindex) = 0
  1348.                 IF RND > 5 THEN
  1349.                     vec3Dcolor(vectorindex) = Aquamarine
  1350.                 ELSE
  1351.                     vec3Dcolor(vectorindex) = DodgerBlue
  1352.                 END IF
  1353.                 GOSUB integratecom
  1354.             NEXT
  1355.         NEXT
  1356.         VectorGroup(vecgroupid).LastVector = vectorindex
  1357.         GOSUB calculatecom
  1358.         VectorGroup(vecgroupid).COMz = 35
  1359.     NEXT
  1361.  
  1362. 'Sky
  1363. h = 2
  1364. FOR u = -gridsize TO gridsize STEP tilesize
  1365.     FOR v = -gridsize TO gridsize STEP tilesize
  1366.         groupidticker = groupidticker + 1
  1367.         vecgroupid = groupidticker
  1368.         VectorGroup(vecgroupid).Identity = vecgroupid
  1369.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1370.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1371.         VectorGroup(vecgroupid).GroupName = "Sky"
  1372.         VectorGroup(vecgroupid).Visible = 0
  1373.         VectorGroup(vecgroupid).COMFixed = 1
  1374.         VectorGroup(vecgroupid).DIMx = tilesize / 2
  1375.         VectorGroup(vecgroupid).DIMy = tilesize / 2
  1376.         VectorGroup(vecgroupid).DIMz = 3
  1377.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1378.         FOR i = u TO u + tilesize STEP h
  1379.             FOR j = v TO v + tilesize STEP h
  1380.                 vectorindex = vectorindex + 1
  1381.                 vec3Dpos(vectorindex, 1) = i + (RND - RND) * h
  1382.                 vec3Dpos(vectorindex, 2) = j + (RND - RND) * h
  1383.                 vec3Dpos(vectorindex, 3) = 70 + (RND - RND) * h
  1384.                 vec3Dvel(vectorindex, 1) = (RND - RND) * 2
  1385.                 vec3Dvel(vectorindex, 2) = (RND - RND) * 2
  1386.                 vec3Dvel(vectorindex, 3) = (RND - RND) * 2
  1387.                 vec3Danv(vectorindex, 1) = 0
  1388.                 vec3Danv(vectorindex, 2) = 0
  1389.                 vec3Danv(vectorindex, 3) = 0
  1390.                 vec3Dvis(vectorindex) = 0
  1391.                 IF RND > .5 THEN
  1392.                     vec3Dcolor(vectorindex) = Snow
  1393.                 ELSE
  1394.                     vec3Dcolor(vectorindex) = RoyalBlue
  1395.                 END IF
  1396.                 GOSUB integratecom
  1397.             NEXT
  1398.         NEXT
  1399.         VectorGroup(vecgroupid).LastVector = vectorindex
  1400.         GOSUB calculatecom
  1401.     NEXT
  1403.  
  1404. 'Stars
  1405. h = 5
  1406. FOR w = 1 TO 5
  1407.     FOR u = -gridsize TO gridsize STEP tilesize
  1408.         FOR v = -gridsize TO gridsize STEP tilesize
  1409.             groupidticker = groupidticker + 1
  1410.             vecgroupid = groupidticker
  1411.             VectorGroup(vecgroupid).Identity = vecgroupid
  1412.             VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1413.             VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1414.             VectorGroup(vecgroupid).GroupName = "Stars"
  1415.             VectorGroup(vecgroupid).Visible = 0
  1416.             VectorGroup(vecgroupid).COMFixed = 1
  1417.             VectorGroup(vecgroupid).DIMx = tilesize / 2
  1418.             VectorGroup(vecgroupid).DIMy = tilesize / 2
  1419.             VectorGroup(vecgroupid).DIMz = tilesize / 2
  1420.             VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1421.             FOR i = u TO u + tilesize STEP h
  1422.                 FOR j = v TO v + tilesize STEP h
  1423.                     IF RND > 1 - w / 5 THEN
  1424.                         vectorindex = vectorindex + 1
  1425.                         vec3Dpos(vectorindex, 1) = i + RND * h - RND * h
  1426.                         vec3Dpos(vectorindex, 2) = j + RND * h - RND * h
  1427.                         vec3Dpos(vectorindex, 3) = w * 70 + RND * 70
  1428.                         vec3Dvis(vectorindex) = 0
  1429.                         IF RND > .5 THEN
  1430.                             vec3Dcolor(vectorindex) = GhostWhite
  1431.                         ELSE
  1432.                             IF RND > .5 THEN
  1433.                                 vec3Dcolor(vectorindex) = White
  1434.                             ELSE
  1435.                                 vec3Dcolor(vectorindex) = DarkGray
  1436.                             END IF
  1437.                         END IF
  1438.                         GOSUB integratecom
  1439.                     END IF
  1440.                 NEXT
  1441.             NEXT
  1442.             VectorGroup(vecgroupid).LastVector = vectorindex
  1443.             GOSUB calculatecom
  1444.         NEXT
  1445.     NEXT
  1447.  
  1448. 'Sun
  1449. radius = 10
  1450. dx = .0628
  1451. dy = .0628
  1452. xl = 0: xr = 2 * pi
  1453. yl = 0: yr = pi
  1454. xrange = 1 + INT((-xl + xr) / dx)
  1455. yrange = 1 + INT((-yl + yr) / dy)
  1456. FOR i = 1 TO xrange STEP 10
  1457.     FOR j = 1 TO yrange STEP 10
  1458.         groupidticker = groupidticker + 1
  1459.         vecgroupid = groupidticker
  1460.         VectorGroup(vecgroupid).Identity = vecgroupid
  1461.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1462.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1463.         VectorGroup(vecgroupid).GroupName = "Sun"
  1464.         VectorGroup(vecgroupid).Visible = 0
  1465.         VectorGroup(vecgroupid).COMFixed = 1
  1466.         VectorGroup(vecgroupid).DIMx = radius
  1467.         VectorGroup(vecgroupid).DIMy = radius
  1468.         VectorGroup(vecgroupid).DIMz = radius
  1469.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1470.         FOR u = i TO i + 10 STEP 1
  1471.             FOR v = j TO j + 10 STEP 1
  1472.                 vectorindex = vectorindex + 1
  1473.                 theta = u * dx - dx
  1474.                 phi = v * dy - dy
  1475.                 vec3Dpos(vectorindex, 1) = radius * SIN(phi) * COS(theta)
  1476.                 vec3Dpos(vectorindex, 2) = radius * SIN(phi) * SIN(theta)
  1477.                 vec3Dpos(vectorindex, 3) = 90 + radius * COS(phi)
  1478.                 vec3Dvis(vectorindex) = 0
  1479.                 IF RND > .5 THEN
  1480.                     vec3Dcolor(vectorindex) = Sunglow
  1481.                 ELSE
  1482.                     vec3Dcolor(vectorindex) = SunsetOrange
  1483.                 END IF
  1484.                 GOSUB integratecom
  1485.             NEXT
  1486.         NEXT
  1487.         GOSUB integratecom
  1488.         VectorGroup(vecgroupid).LastVector = vectorindex
  1489.         GOSUB calculatecom
  1490.     NEXT
  1492.  
  1493. 'Moon
  1494. radius = 4
  1495. au = 60
  1496. dx = (2 * pi / radius) * .05
  1497. dy = (2 * pi / radius) * .05
  1498. xl = 0: xr = 2 * pi
  1499. yl = 0: yr = pi
  1500. xrange = 1 + INT((-xl + xr) / dx)
  1501. yrange = 1 + INT((-yl + yr) / dy)
  1502. groupidticker = groupidticker + 1
  1503. vecgroupid = groupidticker
  1504. VectorGroup(vecgroupid).Identity = vecgroupid
  1505. VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1506. VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1507. VectorGroup(vecgroupid).GroupName = "Moon"
  1508. VectorGroup(vecgroupid).Visible = 0
  1509. VectorGroup(vecgroupid).ForceAnimate = 1
  1510. VectorGroup(vecgroupid).COMFixed = 0
  1511. VectorGroup(vecgroupid).ROTx = 0
  1512. VectorGroup(vecgroupid).ROTy = 0
  1513. VectorGroup(vecgroupid).ROTz = 90
  1514. VectorGroup(vecgroupid).REVx = 1.5
  1515. VectorGroup(vecgroupid).REVy = 0
  1516. VectorGroup(vecgroupid).REVz = 0
  1517. VectorGroup(vecgroupid).DIMx = 2 * radius + 1
  1518. VectorGroup(vecgroupid).DIMy = 2 * radius + 1
  1519. VectorGroup(vecgroupid).DIMz = 2 * radius + 1
  1520. VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1521. FOR i = 1 TO xrange
  1522.     FOR j = 1 TO yrange
  1523.         vectorindex = vectorindex + 1
  1524.         theta = i * dx - dx
  1525.         phi = j * dy - dy
  1526.         vec3Dpos(vectorindex, 1) = au + radius * SIN(phi) * COS(theta)
  1527.         vec3Dpos(vectorindex, 2) = radius * SIN(phi) * SIN(theta)
  1528.         vec3Dpos(vectorindex, 3) = 90 + radius * COS(phi)
  1529.         vec3Danv(vectorindex, 1) = 0
  1530.         vec3Danv(vectorindex, 2) = 0
  1531.         vec3Danv(vectorindex, 3) = 1.5
  1532.         vec3Dvis(vectorindex) = 0
  1533.         IF RND > .5 THEN
  1534.             vec3Dcolor(vectorindex) = Gray
  1535.         ELSE
  1536.             vec3Dcolor(vectorindex) = PaleGoldenRod
  1537.         END IF
  1538.         GOSUB integratecom
  1539.         VectorGroup(vecgroupid).LastVector = vectorindex
  1540.         GOSUB calculatecom
  1541.     NEXT
  1543.  
  1544. 'Waves or Particles? (1)
  1545. FOR i = 1 TO 5 STEP 1
  1546.     FOR k = 1 TO 5 STEP 1
  1547.         groupidticker = groupidticker + 1
  1548.         vecgroupid = groupidticker
  1549.         VectorGroup(vecgroupid).Identity = vecgroupid
  1550.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1551.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1552.         VectorGroup(vecgroupid).GroupName = "Waves or Particles?"
  1553.         VectorGroup(vecgroupid).Visible = 0
  1554.         VectorGroup(vecgroupid).COMFixed = 1
  1555.         VectorGroup(vecgroupid).DIMx = 4
  1556.         VectorGroup(vecgroupid).DIMy = 1
  1557.         VectorGroup(vecgroupid).DIMz = 4
  1558.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1559.         FOR u = i TO i + 1 STEP .05
  1560.             FOR v = k TO k + 1 STEP .05
  1561.                 vectorindex = vectorindex + 1
  1562.                 vec3Dpos(vectorindex, 1) = 70 + 7 * u
  1563.                 vec3Dpos(vectorindex, 2) = 80 + 1 * COS((u ^ 2 - v ^ 2))
  1564.                 vec3Dpos(vectorindex, 3) = 10 + 7 * v
  1565.                 vec3Dvis(vectorindex) = 0
  1566.                 IF vec3Dpos(vectorindex, 2) < 80 THEN
  1567.                     vec3Dcolor(vectorindex) = DarkBlue
  1568.                 ELSE
  1569.                     vec3Dcolor(vectorindex) = DeepPink
  1570.                 END IF
  1571.                 GOSUB integratecom
  1572.             NEXT
  1573.         NEXT
  1574.         VectorGroup(vecgroupid).LastVector = vectorindex
  1575.         GOSUB calculatecom
  1576.     NEXT
  1578.  
  1579. 'Waves or Particles? (2)
  1580. FOR i = 1 TO 5 STEP 1
  1581.     FOR k = 1 TO 5 STEP 1
  1582.         groupidticker = groupidticker + 1
  1583.         vecgroupid = groupidticker
  1584.         VectorGroup(vecgroupid).Identity = vecgroupid
  1585.         VectorGroup(vecgroupid).Pointer = vecgroupid + 1
  1586.         VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1587.         VectorGroup(vecgroupid).GroupName = "Particles or Waves?"
  1588.         VectorGroup(vecgroupid).Visible = 0
  1589.         VectorGroup(vecgroupid).COMFixed = 1
  1590.         VectorGroup(vecgroupid).DIMx = 4
  1591.         VectorGroup(vecgroupid).DIMy = 1
  1592.         VectorGroup(vecgroupid).DIMz = 4
  1593.         VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1594.         FOR u = i TO i + 1 STEP .05
  1595.             FOR v = k TO k + 1 STEP .05
  1596.                 vectorindex = vectorindex + 1
  1597.                 vec3Dpos(vectorindex, 1) = -7 * u
  1598.                 vec3Dpos(vectorindex, 2) = 80 + 1 * COS(2 * ((u - 7) ^ 2 - (v - 5) ^ 2))
  1599.                 vec3Dpos(vectorindex, 3) = 10 + 7 * v
  1600.                 vec3Dvis(vectorindex) = 0
  1601.                 IF vec3Dpos(vectorindex, 2) < 80 THEN
  1602.                     vec3Dcolor(vectorindex) = Magenta
  1603.                 ELSE
  1604.                     vec3Dcolor(vectorindex) = Chocolate
  1605.                 END IF
  1606.                 GOSUB integratecom
  1607.             NEXT
  1608.         NEXT
  1609.         VectorGroup(vecgroupid).LastVector = vectorindex
  1610.         GOSUB calculatecom
  1611.     NEXT
  1613.  
  1614. '__ZZZ
  1615. groupidticker = groupidticker + 1
  1616. vecgroupid = groupidticker
  1617. VectorGroup(vecgroupid).Identity = vecgroupid
  1618. VectorGroup(vecgroupid).Pointer = -999
  1619. VectorGroup(vecgroupid).Lagger = vecgroupid - 1
  1620. VectorGroup(vecgroupid).GroupName = "__ZZZ"
  1621. VectorGroup(vecgroupid).COMFixed = 1
  1622. VectorGroup(vecgroupid).FirstVector = vectorindex + 1
  1623. FOR r = 1 TO 1
  1624.     vectorindex = vectorindex + 1
  1625.     vec3Dpos(vectorindex, 1) = 0
  1626.     vec3Dpos(vectorindex, 2) = 0
  1627.     vec3Dpos(vectorindex, 3) = -1000
  1628.     vec3Dcolor(vectorindex) = White
  1629.     GOSUB integratecom
  1631. VectorGroup(vecgroupid).LastVector = vectorindex
  1632. GOSUB calculatecom
screenshot.png
* screenshot.png (Filesize: 52.21 KB, Dimensions: 801x643, Views: 274)
* Color32.BI (Filesize: 10.89 KB, Downloads: 196)
« Last Edit: August 12, 2019, 07:43:50 am by STxAxTIC »
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Offline TempodiBasic

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Re: On trigless starfields: remember Sanctum?
« Reply #1 on: August 11, 2019, 12:55:23 pm »
pixelcraft!?!
 https://img.youtube.com/vi/X6P9M8IX7qc/hqdefault.jpg
https://i.ytimg.com/vi/BbS5blDdrMI/hqdefault.jpg
It is so intriguing...
well let's build up a daycycle, an AI and Mobs :-))

Does Who follow STxAxTIC steps?
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Offline STxAxTIC

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Re: On trigless starfields: remember Sanctum?
« Reply #2 on: August 11, 2019, 01:42:15 pm »
Thanks TempodiBasic, I shouldn't have been so loose with an obviously-taken name!
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Offline SierraKen

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Re: On trigless starfields: remember Sanctum?
« Reply #3 on: August 11, 2019, 04:53:04 pm »
This program is incredible! I made some blocks all around me to make a circle and flew up and down. I think Q or W is down. Thanks for posting this!
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Offline TempodiBasic

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Re: On trigless starfields: remember Sanctum?
« Reply #4 on: August 11, 2019, 06:12:08 pm »
Hi STxAxTIC
if I could suggest and alternative name I guess ExSTxAxTICxCraft  a fusion of Ectasy plus STxATxIC  plus Craft.

PS (please no affirmation about drugs!)
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Offline Petr

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Hi StXaXtic,
« Reply #5 on: August 12, 2019, 04:15:59 am »
Of course I did not give up and I did not end my efforts. I have a finished level editor for my version of the 3D maze, which we talked about with Steve in the 3D MAPTRIANGLE thread. Currently, I have a very primitive 3D object editor that will be inserted into the map through the 3D maze editor before I finish. I have 2 to 3 months left to finish because I don't have much time to do this. Then I will improve my own program for browsing 3D rooms. They are basically currently written three large programs, which cooperate with each other and whose size of the source code already greatly exceeds 100 KB.

This is all based on MAPTRINGLE3D, because OpenGL is not stable with some statements (and this caused 14 days of futile attempts and delays).
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Offline STxAxTIC

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Re: On trigless starfields: remember Sanctum?
« Reply #6 on: August 12, 2019, 07:42:20 am »
Morning Petr,

I surely didn't forget that you broke the 3D barrier as well! I once went down the path of textures, maptriangle, underscore commands, and so on - but pulled back for a handful of reasons, including the ones you allude to. I've had more satisfaction staying close to the QB45 core in all my projects, a habit that is fueled by the existential dread that surrounds QB64 - will the next Windows update kill it entirely? etc. - so when the day comes, my code is already that much tighter and closer to being ready for the next language, but I digress.

Do you know where you want to go with your 3D work? Make a Quake clone maybe? Flight simulator? Finish with mazes and call it done?

I'm still deciding what in the world I want this code to do. It's a perfect skeleton for textures if I want, but on the other hand it seems "playable" just as particles. I'm the last person in the world who's going to write a formal "game", so maybe it'll be just an engine forever... iiiiiiddddkkkk man. Ya'll tell me.
« Last Edit: August 12, 2019, 07:50:11 am by STxAxTIC »
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