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Author Topic: 3D Graph Plotter  (Read 4607 times)

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Offline STxAxTIC

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Re: 3D Graph Plotter
« Reply #15 on: January 31, 2021, 08:24:16 pm »
Holy cow I forgot all about that. Beautiful!
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Offline _vince

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Re: 3D Graph Plotter
« Reply #16 on: February 01, 2021, 07:49:49 pm »
Thx, I really enjoy playing with it.  I've been improving the colour scheme over time as well, trying to go for 'textbook quality'

I really wanted to write some kind of PDF reviewing basic complex analysis topics from the visual perspective, ie zeros, poles, filters, integrals, Cauchy's etc because it's so rarely done and stunningly beautiful but don't have the willpower for it
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Offline STxAxTIC

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Re: 3D Graph Plotter
« Reply #17 on: February 01, 2021, 08:10:28 pm »
That looks textbook quality already vince for sure. As for the writeup, yikes. That's a lot of explaining to do. For anyone interested, this isn't your Kansas math anymore. This speaks of residue calculus:

 
ss.png
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Offline _vince

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Re: 3D Graph Plotter
« Reply #18 on: February 01, 2021, 08:33:05 pm »
Seeing cauchy's integral formula evaluated numerically converge to the function was amazing to discover, but yes, too much writing and notation.  There's so much neat stuff out there that's probably never been plotted before (afaik), I think it is a worthwhile artistic pursuit
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Offline STxAxTIC

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Re: 3D Graph Plotter
« Reply #19 on: February 05, 2021, 11:53:55 am »
Alrighty, had to keep going with this one more step. This version of the 3d plotter replaces z=f(x,y) with parametric equations instead. This lets you make all kinds of exotic shapes. The full project, including all test curves, is at:

https://github.com/wfbarnes/3D-Grapher

A bare-bones way to test it yourself is of course included below.

 
trefoil.png

 
mobius.png

 
ellipse.png

 
trig.png

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* sxript.bm (Filesize: 99 KB, Downloads: 158)
* 3D Grapher - Parametric.bas (Filesize: 27.64 KB, Downloads: 150)
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Offline _vince

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Re: 3D Graph Plotter
« Reply #20 on: February 05, 2021, 06:23:50 pm »
nice work, I wanted to suggest that z = f(x, y) is just a special case of parametric surface but you're ahead.  Adding a time dimension t for animation is also neat too.

The other cool thing worth plotting is vector fields and perhaps the option of randomly spawned particles
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Offline STxAxTIC

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Re: 3D Graph Plotter
« Reply #21 on: February 05, 2021, 06:29:51 pm »
Hey, I like the idea of vector fields and time animation. Maybe I'll do that next time 3D season comes up for me. I did enough yesterday to last half an eon.

In the meantime, this 2D demo does exactly that, sorta:

Code: QB64: [Select]
  2.  
  4. _TITLE "Vector Field"
  5.  
  6. ' Meta
  8.  
  9. CONST Aquamarine = _RGB32(127, 255, 212)
  10. CONST Lime = _RGB32(0, 255, 0)
  11.  
  12. DIM SHARED XSize
  13. DIM SHARED YSize
  14. DIM SHARED XCells
  15. DIM SHARED YCells
  17. XSize = 30
  18. YSize = 30
  19. XCells = 30
  20. YCells = 30
  21. NPC = .1 * SQR(XCells * YCells)
  22. SCREEN _NEWIMAGE(XSize * XCells, YSize * YCells, 32)
  23.  
  24.  
  25. TYPE Vector
  26.     x AS DOUBLE
  27.     y AS DOUBLE
  29.  
  30. TYPE FieldLine
  31.     Center AS Vector
  32.     Tangent AS Vector
  34.  
  35. TYPE Particle
  36.     Displacement AS Vector
  37.     Velocity AS Vector
  38.     Shade AS _UNSIGNED LONG
  40.  
  41. TYPE Charge
  42.     Center AS Vector
  43.     Radial AS Vector
  44.     Angular AS Vector
  46.  
  47. DIM SHARED VectorField(XCells, YCells) AS FieldLine
  48. DIM SHARED Particles(XCells, YCells, NPC) AS Particle
  49. DIM SHARED Charges(100) AS Charge
  50. DIM SHARED ChargeCount
  51.  
  52. ChargeCount = 1
  53. Charges(ChargeCount).Center.x = 0
  54. Charges(ChargeCount).Center.y = 0
  55. Charges(ChargeCount).Radial.x = .05
  56. Charges(ChargeCount).Radial.y = .05
  57. Charges(ChargeCount).Angular.x = 0
  58. Charges(ChargeCount).Angular.y = 0
  59.  
  63.  
  64. FOR i = 1 TO XCells
  65.     FOR j = 1 TO YCells
  66.         VectorField(i, j).Center.x = (1 / 2) * XSize * (2 * i - XCells) - XSize / 2
  67.         VectorField(i, j).Center.y = (1 / 2) * YSize * (2 * j - YCells) - YSize / 2
  68.         FOR k = 1 TO NPC
  69.             Particles(i, j, k).Shade = Lime
  70.             Particles(i, j, k).Displacement.x = XSize * (RND - .5)
  71.             Particles(i, j, k).Displacement.y = YSize * (RND - .5)
  72.         NEXT
  73.     NEXT
  75.  
  76. CALL CalculateField
  77.  
  80.  
  83.         x = _MOUSEX
  84.         y = _MOUSEY
  85.         IF ((x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT)) THEN
  86.             Charges(ChargeCount).Center.x = (x - _WIDTH / 2)
  87.             Charges(ChargeCount).Center.y = (-y + _HEIGHT / 2)
  88.             CALL CalculateField
  89.         END IF
  90.     LOOP
  91.  
  92.     k = _KEYHIT
  93.     SELECT CASE k
  94.         CASE 49
  95.             Charges(ChargeCount).Radial.x = .05
  96.             Charges(ChargeCount).Radial.y = .05
  97.             Charges(ChargeCount).Angular.x = 0
  98.             Charges(ChargeCount).Angular.y = 0
  99.         CASE 50
  100.             Charges(ChargeCount).Radial.x = -.05
  101.             Charges(ChargeCount).Radial.y = -.05
  102.             Charges(ChargeCount).Angular.x = 0
  103.             Charges(ChargeCount).Angular.y = 0
  104.         CASE 51
  105.             Charges(ChargeCount).Radial.x = .05
  106.             Charges(ChargeCount).Radial.y = -.05
  107.             Charges(ChargeCount).Angular.x = 0
  108.             Charges(ChargeCount).Angular.y = 0
  109.         CASE 52
  110.             Charges(ChargeCount).Radial.x = -.05
  111.             Charges(ChargeCount).Radial.y = .05
  112.             Charges(ChargeCount).Angular.x = 0
  113.             Charges(ChargeCount).Angular.y = 0
  114.         CASE 53
  115.             Charges(ChargeCount).Radial.x = 0
  116.             Charges(ChargeCount).Radial.y = 0
  117.             Charges(ChargeCount).Angular.x = .05
  118.             Charges(ChargeCount).Angular.y = -.05
  119.         CASE 54
  120.             Charges(ChargeCount).Radial.x = 0
  121.             Charges(ChargeCount).Radial.y = 0
  122.             Charges(ChargeCount).Angular.x = -.05
  123.             Charges(ChargeCount).Angular.y = .05
  124.         CASE 48
  125.             ChargeCount = 1
  126.         CASE 32
  127.             ChargeCount = ChargeCount + 1
  128.             Charges(ChargeCount).Center.x = Charges(ChargeCount - 1).Center.x
  129.             Charges(ChargeCount).Center.y = Charges(ChargeCount - 1).Center.y
  130.             Charges(ChargeCount).Radial.x = Charges(ChargeCount - 1).Radial.x
  131.             Charges(ChargeCount).Radial.y = Charges(ChargeCount - 1).Radial.y
  132.             Charges(ChargeCount).Angular.x = Charges(ChargeCount - 1).Angular.x
  133.             Charges(ChargeCount).Angular.y = Charges(ChargeCount - 1).Angular.y
  134.     END SELECT
  135.     IF (k <> 0) THEN
  136.         CALL CalculateField
  137.     END IF
  138.     _KEYCLEAR
  139.  
  140.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 20), BF
  141.  
  142.     DIM xc AS DOUBLE
  143.     DIM yc AS DOUBLE
  144.     DIM xd AS DOUBLE
  145.     DIM yd AS DOUBLE
  146.     DIM xx AS DOUBLE
  147.     DIM yy AS DOUBLE
  148.  
  149.     LOCATE 1, 1: PRINT "Press 1-6 to change charge type. Press space to fix charge, 0 to clear."
  150.     FOR i = 1 TO XCells
  151.         FOR j = 1 TO YCells
  152.             xc = VectorField(i, j).Center.x
  153.             yc = VectorField(i, j).Center.y
  154.             FOR k = 1 TO NPC
  155.                 xd = 0
  156.                 yd = 0
  157.                 xx = Particles(i, j, k).Displacement.x + .1 * Particles(i, j, k).Velocity.x
  158.                 yy = Particles(i, j, k).Displacement.y + .1 * Particles(i, j, k).Velocity.y
  159.                 IF (xx < -XSize / 2) THEN
  160.                     xd = -xx + XSize / 2
  161.                 END IF
  162.                 IF (xx > XSize / 2) THEN
  163.                     xd = -xx - XSize / 2
  164.                 END IF
  165.                 IF (yy < -YSize / 2) THEN
  166.                     yd = -yy + YSize / 2
  167.                 END IF
  168.                 IF (yy > YSize / 2) THEN
  169.                     yd = -yy + -YSize / 2
  170.                 END IF
  171.                 Particles(i, j, k).Displacement.x = xx + xd
  172.                 Particles(i, j, k).Displacement.y = yy + yd
  173.                 CALL cpset(xc + Particles(i, j, k).Displacement.x, yc + Particles(i, j, k).Displacement.y, Particles(i, j, k).Shade)
  174.             NEXT
  175.         NEXT
  176.     NEXT
  177.     _LIMIT 60
  178.     _DISPLAY
  180.  
  182.  
  183. SUB CalculateField
  184.     DIM i AS INTEGER
  185.     DIM j AS INTEGER
  186.     DIM k AS INTEGER
  187.     DIM dx AS DOUBLE
  188.     DIM dy AS DOUBLE
  189.     DIM d2 AS DOUBLE
  190.     DIM xx AS DOUBLE
  191.     DIM yy AS DOUBLE
  192.     FOR i = 1 TO XCells
  193.         FOR j = 1 TO YCells
  194.             xx = 0
  195.             yy = 0
  196.             FOR k = 1 TO ChargeCount
  197.                 dx = VectorField(i, j).Center.x - Charges(k).Center.x
  198.                 dy = VectorField(i, j).Center.y - Charges(k).Center.y
  199.                 d2 = 5000 / (dx * dx + dy * dy)
  200.                 xx = xx + (Charges(k).Radial.x * dx * d2) + (Charges(k).Angular.x * dy * d2)
  201.                 yy = yy + (Charges(k).Radial.y * dy * d2) + (Charges(k).Angular.y * dx * d2)
  202.             NEXT
  203.             VectorField(i, j).Tangent.x = xx
  204.             VectorField(i, j).Tangent.y = yy
  205.             FOR k = 1 TO NPC
  206.                 Particles(i, j, k).Velocity.x = VectorField(i, j).Tangent.x
  207.                 Particles(i, j, k).Velocity.y = VectorField(i, j).Tangent.y
  208.             NEXT
  209.         NEXT
  210.     NEXT
  212.  
  213. SUB cpset (x1, y1, col AS _UNSIGNED LONG)
  214.     PSET (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), col
  216.  
  217.  

 
ss.png

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