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Offline RhoSigma

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Bézier Curves (Demo)
« on: July 03, 2021, 07:59:39 pm »
Playing with Bézier curves in 2D and 3D space, see also: https://en.wikipedia.org/wiki/B%C3%A9zier_curve

SUB CalcFracPoints is calculating all intersection points for a specific fraction down from the given start degree to the final curve point, hence the very last point (UBOUND) in the output array contains the regular curve point, while the other points building the intersection lines from the start degree down to the first degree. Each degree ends with a stop flag.

Code: QB64: [Select]
  1. _TITLE "Bezier Curve 2D"
  2.  
  3. SCREEN _NEWIMAGE(640, 480, 256)
  4. ti& = _NEWIMAGE(640, 480, 256)
  5.  
  7.     x AS DOUBLE
  8.     y AS DOUBLE
  9.     z AS DOUBLE
  10.     s AS INTEGER
  12. REDIM points(0 TO 4) AS point
  13. REDIM spans(0 TO 2) AS point
  14.  
  15. points(0).x = 150 'start point
  16. points(0).y = 50
  17.  
  18. points(1).x = 50 'control point (handle)
  19. points(1).y = 430
  20.  
  21. points(2).x = 590 'control point (handle)
  22. points(2).y = 350
  23.  
  24. points(3).x = 320 'control point (handle)
  25. points(3).y = 160
  26.  
  27. points(4).x = 590 'end point
  28. points(4).y = 50
  29.  
  30. again:
  31. FOR f# = 0 TO 1.0 STEP 0.0025
  32.     _LIMIT 30
  33.     CalcFracPoints points(), spans(), f#
  34.     _DEST ti&
  35.     x# = spans(UBOUND(spans)).x
  36.     y# = spans(UBOUND(spans)).y
  37.     CIRCLE (x#, y#), 1, 12
  38.     CIRCLE (x#, y#), 2, 12
  39.     CIRCLE (x#, y#), 3, 12
  40.     _DEST 0
  41.     CLS
  42.     _PUTIMAGE , ti&
  43.     LOCATE 1, 1
  44.     PRINT "Fraction ="; f#
  45.     DrawLines points(), &HFFFF
  46.     DrawLines spans(), &B1001100110011001
  47.     FOR i% = LBOUND(spans) TO UBOUND(spans) - 1
  48.         CIRCLE (spans(i%).x, spans(i%).y), 1, 14
  49.         CIRCLE (spans(i%).x, spans(i%).y), 2, 14
  50.     NEXT i%
  51.     CIRCLE (x#, y#), 1, 4
  52.     CIRCLE (x#, y#), 2, 4
  53.     CIRCLE (x#, y#), 3, 12
  54.     CIRCLE (x#, y#), 4, 15
  55.     CIRCLE (x#, y#), 5, 15
  56.     _DISPLAY
  57. NEXT f#
  60. GOTO again
  62.  
  63. SUB CalcFracPoints (pIn() AS point, pOut() AS point, frac#)
  64. iLns% = UBOUND(pIn) - LBOUND(pIn) 'no +1 here, as lines = 1 less than points
  65. oPts% = (iLns% * (iLns% + 1)) / 2 'sum 1 to n, which is n(n+1)/2
  66. REDIM pOut(0 TO oPts% - 1) AS point
  67.  
  68. p% = 0
  69. FOR i% = LBOUND(pIn) TO UBOUND(pIn) - 1
  70.     pOut(p%).x = pIn(i%).x + frac# * (pIn(i% + 1).x - pIn(i%).x)
  71.     pOut(p%).y = pIn(i%).y + frac# * (pIn(i% + 1).y - pIn(i%).y)
  72.     pOut(p%).z = pIn(i%).z + frac# * (pIn(i% + 1).z - pIn(i%).z)
  73.     p% = p% + 1
  74. NEXT i%
  75. pOut(p% - 1).s = -1 'stop flag for drawing
  76.  
  77. FOR j% = iLns% TO 2 STEP -1
  78.     FOR i% = p% - j% TO p% - 2
  79.         pOut(p%).x = pOut(i%).x + frac# * (pOut(i% + 1).x - pOut(i%).x)
  80.         pOut(p%).y = pOut(i%).y + frac# * (pOut(i% + 1).y - pOut(i%).y)
  81.         pOut(p%).z = pOut(i%).z + frac# * (pOut(i% + 1).z - pOut(i%).z)
  82.         p% = p% + 1
  83.     NEXT i%
  84.     pOut(p% - 1).s = -1 'stop flag for drawing
  85. NEXT j%
  87.  
  88. SUB DrawLines (pIn() AS point, sty%)
  89. col~& = 1
  90. FOR i% = LBOUND(pIn) TO UBOUND(pIn) - 1
  91.     LINE (pIn(i%).x, pIn(i%).y)-(pIn(i% + 1).x, pIn(i% + 1).y), col~&, , sty%
  92.     IF pIn(i% + 1).s THEN
  93.         col~& = (col~& + 1) AND 15
  94.         i% = i% + 1 'skip to next sequence
  95.     END IF
  96. NEXT i%
  98.  
  99.  

Code: QB64: [Select]
  1. _TITLE "Bezier Curve 3D"
  2.  
  3. SCREEN _NEWIMAGE(640, 480, 256)
  4. ti& = _NEWIMAGE(640, 480, 256)
  5.  
  7.     x AS DOUBLE
  8.     y AS DOUBLE
  9.     z AS DOUBLE
  10.     s AS INTEGER
  12. REDIM points(0 TO 4) AS point
  13. REDIM spans(0 TO 2) AS point
  14.  
  15. DIM SHARED cx%, cy%
  16. cx% = -100: cy% = 400 '3D space origin
  17.  
  18. points(0).x = 150 'start point
  19. points(0).y = 50
  20. points(0).z = 0
  21.  
  22. points(1).x = 50 'control point (handle)
  23. points(1).y = 430
  24. points(1).z = 300
  25.  
  26. points(2).x = 590 'control point (handle)
  27. points(2).y = 350
  28. points(2).z = -500
  29.  
  30. points(3).x = 320 'control point (handle)
  31. points(3).y = 160
  32. points(3).z = 300
  33.  
  34. points(4).x = 590 'end point
  35. points(4).y = 50
  36. points(4).z = 0
  37.  
  38. again:
  39. _DEST ti&
  40. FOR i% = 0 TO 700 STEP 50
  41.     Line3D i%, 0, 0, i%, 700, 0, 15
  42.     Line3D 0, i%, 0, 700, i%, 0, 15
  43. NEXT i%
  45.  
  46. FOR f# = 0 TO 1.0 STEP 0.0025
  47.     _LIMIT 30
  48.     CalcFracPoints points(), spans(), f#
  49.     _DEST ti&
  50.     x# = spans(UBOUND(spans)).x
  51.     y# = spans(UBOUND(spans)).y
  52.     z# = spans(UBOUND(spans)).z
  53.     Circle3D x#, y#, z#, 1, 0, 12
  54.     _DEST 0
  55.     CLS
  56.     _PUTIMAGE , ti&
  57.     LOCATE 1, 1
  58.     PRINT "Fraction ="; f#
  59.     DrawLines points()
  60.     DrawLines spans()
  61.     FOR i% = LBOUND(spans) TO UBOUND(spans) - 1
  62.         Circle3D spans(i%).x, spans(i%).y, spans(i%).z, 1, 0, 14
  63.     NEXT i%
  64.     Circle3D x#, y#, z#, 2, 0, 4
  65.     _DISPLAY
  66. NEXT f#
  69. GOTO again
  71.  
  72. SUB CalcFracPoints (pIn() AS point, pOut() AS point, frac#)
  73. iLns% = UBOUND(pIn) - LBOUND(pIn) 'no +1 here, as lines = 1 less than points
  74. oPts% = (iLns% * (iLns% + 1)) / 2 'sum 1 to n, which is n(n+1)/2
  75. REDIM pOut(0 TO oPts% - 1) AS point
  76.  
  77. p% = 0
  78. FOR i% = LBOUND(pIn) TO UBOUND(pIn) - 1
  79.     pOut(p%).x = pIn(i%).x + frac# * (pIn(i% + 1).x - pIn(i%).x)
  80.     pOut(p%).y = pIn(i%).y + frac# * (pIn(i% + 1).y - pIn(i%).y)
  81.     pOut(p%).z = pIn(i%).z + frac# * (pIn(i% + 1).z - pIn(i%).z)
  82.     p% = p% + 1
  83. NEXT i%
  84. pOut(p% - 1).s = -1 'stop flag for drawing
  85.  
  86. FOR j% = iLns% TO 2 STEP -1
  87.     FOR i% = p% - j% TO p% - 2
  88.         pOut(p%).x = pOut(i%).x + frac# * (pOut(i% + 1).x - pOut(i%).x)
  89.         pOut(p%).y = pOut(i%).y + frac# * (pOut(i% + 1).y - pOut(i%).y)
  90.         pOut(p%).z = pOut(i%).z + frac# * (pOut(i% + 1).z - pOut(i%).z)
  91.         p% = p% + 1
  92.     NEXT i%
  93.     pOut(p% - 1).s = -1 'stop flag for drawing
  94. NEXT j%
  96.  
  97. SUB DrawLines (pIn() AS point)
  98. col~& = 1
  99. FOR i% = LBOUND(pIn) TO UBOUND(pIn) - 1
  100.     Line3D pIn(i%).x, pIn(i%).y, pIn(i%).z, pIn(i% + 1).x, pIn(i% + 1).y, pIn(i% + 1).z, col~&
  101.     IF pIn(i% + 1).s THEN
  102.         col~& = (col~& + 1) AND 15
  103.         i% = i% + 1 'skip to next sequence
  104.     END IF
  105. NEXT i%
  107.  
  108. SUB Line3D (x1%, y1%, z1%, x2%, y2%, z2%, col%)
  109. 'x1%/y1%/z1% = start, x2%/y2%/z2% = end, col% = color pen
  110. x1# = (x1% + (y1% * 0.1)): z1# = (z1% + (y1% * 0.1))
  111. x2# = (x2% + (y2% * 0.1)): z2# = (z2% + (y2% * 0.1))
  112. LINE (x1# + cx% - 1, -z1# + cy%)-(x2# + cx% - 1, -z2# + cy%), col%
  113. LINE (x1# + cx%, -z1# + cy%)-(x2# + cx%, -z2# + cy%), col%
  114. LINE (x1# + cx% + 1, -z1# + cy%)-(x2# + cx% + 1, -z2# + cy%), col%
  116.  
  117. SUB Circle3D (x%, y%, z%, r%, ba%, col%)
  118. 'x%/y%/z% = center, r% = radius, ba% = B-Axis angle, col% = color pen
  119. mx# = (x% + (y% * 0.1)): mz# = (z% + (y% * 0.1))
  120. zx# = r% * COS(ba% * 0.017453292519943)
  121. zz# = r% * SIN(ba% * 0.017453292519943)
  122. FOR cir% = 0 TO 359 STEP 5
  123.     x# = zx# * COS(cir% * 0.017453292519943)
  124.     y# = r% * SIN(cir% * 0.017453292519943)
  125.     z# = zz# * COS(cir% * 0.017453292519943)
  126.     x# = (x# + (y# * 0.1)): z# = (z# + (y# * 0.1))
  127.     LINE (x# + mx# + cx% - 1, -z# + -mz# + cy% - 1)-(x# + mx# + cx% + 1, -z# + -mz# + cy% + 1), col%, BF
  128. NEXT cir%
  130.  
  131.  
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Offline _vince

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Re: Bézier Curves (Demo)
« Reply #1 on: July 16, 2021, 03:56:38 am »
nice, it's a parallel projected 3D

I found a similar demo where you can use the mouse to drag the curve:
Code: QB64: [Select]
  1. deflng a-z
  2. const sw = 800
  3. const sh = 600
  5. pi = 4*atn(1)
  6. declare sub circlef(x, y, r, c)
  7.  
  8. n = 8
  9. dim x(n), y(n)
  10.  
  11. x(0) = 0: y(0) = -200
  12. x(1) = -130: y(1) = -130
  13. x(2) = -200: y(2) = 0
  14. x(3) = -30: y(3) = 30
  15. x(4) = 0: y(4) = 200
  16. x(5) = 230: y(5) = 230
  17. x(6) = 200: y(6) = 0
  18. x(7) = 130: y(7) = -30
  19. 'x(n) = x(0)
  20. 'y(n) = y(0)
  21.  
  22. 'for i=0 to n-1
  23. '       x(i) = 200*cos(2*pi*i/n)
  24. '       y(i) = 200*sin(2*pi*i/n)
  25. 'next
  26.  
  27. 'screenres sw, sh, 32
  28. screen _newimage(sw, sh, 32)
  29. redraw = -1
  30. drag = 0
  32.         'm = getmouse(mx, my, mw, mb)
  33.         do
  34.                 mx = _mousex
  35.                 my = _mousey
  36.                 mb = -_mousebutton(1)
  37.         loop while _mouseinput
  38.  
  39.         if drag then
  40.                 if mb = 1 then
  41.                         x(ii) = mx - sw/2
  42.                         y(ii) = sh/2 - my
  43.                 else
  44.                         drag = 0
  45.                 end if
  46.         else
  47.                 dmin = 1e10
  48.                 for i=0 to n - 1
  49.                         dx = (mx - sw/2) - x(i)
  50.                         dy = (sh/2 - my) - y(i)
  51.                         d = (dx*dx + dy*dy)
  52.                         if d < dmin then
  53.                                 dmin = d
  54.                                 ii = i
  55.                         end if
  56.                 next
  57.  
  58.                 if mb = 1 then
  59.                         omx = mx
  60.                         omy = my
  61.                         drag = -1
  62.                 end if
  63.         end if
  64.  
  65.  
  66.         redraw = -1
  67.  
  68.         if redraw then
  69.                 'screenlock
  70.                 line (0,0)-(sw,sh),_rgb(0,0,0),bf
  71.                 locate 1,1: ? m, mx, my, mw, mb
  72.  
  73.  
  74.  
  75.                 dim t as double, bx as double, by as double
  76.                 pset (sw/2 + x(0), sh/2 - y(0)), _rgb(0,255,0)
  77.                 for t=0 to 1 step 0.01
  78.                         bx = 0
  79.                         by = 0
  80.  
  81.                         for i=0 to n-1
  82.                                 bin = 1
  83.                                 for j=1 to i
  84.                                         bin = bin*(n - j)/j
  85.                                 next
  86.  
  87.                                 bx = bx + bin*((1 - t)^(n - 1 - i))*(t^i)*x(i)
  88.                                 by = by + bin*((1 - t)^(n - 1 - i))*(t^i)*y(i)
  89.                         next
  90.  
  91.                         line -(sw/2 + bx, sh/2 - by), _rgb(0,255,0)
  92.                 next
  93.  
  94.  
  95.  
  96.  
  97.                 'x(n) = x(0)
  98.                 'y(n) = y(0)
  99.                 x0 = sw/2 + x(0)
  100.                 y0 = sh/2 - y(0)
  101.                 circlef x0, y0, 8, _rgb(55,55,55)
  102.                 for i=1 to n-1
  103.                         x1 = sw/2 + x(i)
  104.                         y1 = sh/2 - y(i)
  105.                         line (x0, y0)-(x1, y1), _rgb(55,55,55)
  106.                         'line -(sw/2 + cx, sh/2 - cy)
  107.                         circlef x1, y1, 8, _rgb(55,55,55)
  108.                         x0 = x1
  109.                         y0 = y1
  110.                 next
  111.                 circlef sw/2 + x(ii), sh/2 - y(ii), 8, _rgb(255,0,0)
  112.  
  113.                 'screenunlock
  114.                 'screensync
  115.  
  116.                 redraw = 0
  117.  
  118.                 _display
  119.         end if
  122.  
  123. sub circlef(x, y, r, c)
  124.         x0 = r
  125.         y0 = 0
  126.         e = -r
  127.  
  128.         do while y0 < x0
  129.                 if e <=0 then
  130.                         y0 = y0 + 1
  131.                         line (x - x0, y + y0)-(x + x0, y + y0), c, bf
  132.                         line (x - x0, y - y0)-(x + x0, y - y0), c, bf
  133.                         e = e + 2*y0
  134.                 else
  135.                         line (x - y0, y - x0)-(x + y0, y - x0), c, bf
  136.                         line (x - y0, y + x0)-(x + y0, y + x0), c, bf
  137.                         x0 = x0 - 1
  138.                         e = e - 2*x0
  139.                 end if
  140.         loop
  141.         line (x - r, y)-(x + r, y), c, bf
  143.  
  144.  
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Offline RhoSigma

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Re: Bézier Curves (Demo)
« Reply #2 on: July 16, 2021, 04:43:42 am »
Indeed @_vince, that's for sure a very nice demo too. Will take a closer look when home from work, comparing the algorithm behind it with my own, could be interesting.
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GuiTools - A graphic UI framework (can do multiple UI forms/windows in one program)
Libraries - ImageProcess, StringBuffers (virt. files), MD5/SHA2-Hash, LZW etc.
Bonus - Blankers, QB64/Notepad++ setup pack

Offline Jack002

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  • Posts: 123
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Re: Bézier Curves (Demo)
« Reply #3 on: July 16, 2021, 07:14:02 pm »
Wow, that is so cool
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