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FellippeHeitor

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Lissajous Curve Table
« on: October 09, 2018, 04:28:14 am »
Adapted from https://editor.p5js.org/codingtrain/sketches/BJbj5l3Y7 (as seen on YouTube: https://www.youtube.com/watch?v=--6eyLO78CY)

Window is resizable to display more patterns.

Code: QB64: [Select]
  1. _TITLE "Lissajous Curve Table"
  2.  
  4.  
  5. TYPE vector
  6.     x AS SINGLE
  7.     y AS SINGLE
  9.  
  10. DIM SHARED angle
  12. DIM SHARED rows, cols
  13.  
  14. SCREEN _NEWIMAGE(800, 800, 32)
  15.  
  16. setup:
  17. angle = 0
  18. w = 80
  19. rows = INT(_HEIGHT / w) - 1
  20. cols = INT(_WIDTH / w) - 1
  21. REDIM dot(rows, cols) AS vector
  22.  
  23. plot = _NEWIMAGE(_WIDTH, _HEIGHT, 32)
  24. _DEST plot
  27.  
  30.         oldScreen = _DEST
  32.         _FREEIMAGE oldScreen
  33.         _FREEIMAGE plot
  34.         GOTO setup
  35.     END IF
  36.  
  37.     _PUTIMAGE , plot
  38.  
  39.     d = w - 0.2 * w
  40.     r = d / 2
  41.  
  42.     FOR i = 0 TO cols
  43.         cx = w + i * w + w / 2
  44.         cy = w / 2
  45.         CIRCLE (cx, cy), r
  46.  
  47.         x = r * COS(angle * (i + 1) - _PI(.5))
  48.         y = r * SIN(angle * (i + 1) - _PI(.5))
  49.  
  50.         LINE (cx + x, 0)-(cx + x, _HEIGHT), _RGB32(127, 127, 127)
  51.         CircleFill cx + x, cy + y, 4, _RGB32(28, 222, 50)
  52.         CircleFill cx + x, cy + y, 2, _RGB32(11, 33, 249)
  53.  
  54.         FOR j = 0 TO rows
  55.             dot(j, i).x = cx + x
  56.         NEXT
  57.     NEXT
  58.  
  59.     FOR i = 0 TO rows
  60.         cx = w / 2
  61.         cy = w + i * w + w / 2
  62.         CIRCLE (cx, cy), r
  63.  
  64.         x = r * COS(angle * (i + 1) - _PI(.5))
  65.         y = r * SIN(angle * (i + 1) - _PI(.5))
  66.  
  67.         LINE (0, cy + y)-(_WIDTH, cy + y), _RGB32(127, 127, 127)
  68.         CircleFill cx + x, cy + y, 4, _RGB32(28, 222, 50)
  69.         CircleFill cx + x, cy + y, 2, _RGB32(11, 33, 249)
  70.  
  71.         FOR j = 0 TO cols
  72.             dot(i, j).y = cy + y
  73.         NEXT
  74.     NEXT
  75.  
  76.     _DEST plot
  77.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA32(0, 0, 0, 2), BF
  78.     FOR j = 0 TO rows
  79.         FOR i = 0 TO cols
  80.             CircleFill dot(j, i).x, dot(j, i).y, 1, _RGB32(255, 0, 0)
  81.         NEXT
  82.     NEXT
  83.  
  84.     angle = angle + 0.01
  85.     IF angle > _PI(2) THEN angle = 0
  86.  
  87.     _DEST 0
  88.  
  89.     _DISPLAY
  90.     _LIMIT 30
  92.  
  93. SUB CircleFill (x AS LONG, y AS LONG, R AS LONG, C AS _UNSIGNED LONG)
  94.     DIM x0 AS SINGLE, y0 AS SINGLE
  95.     DIM e AS SINGLE
  96.  
  97.     x0 = R
  98.     y0 = 0
  99.     e = -R
  100.     DO WHILE y0 < x0
  101.         IF e <= 0 THEN
  102.             y0 = y0 + 1
  103.             LINE (x - x0, y + y0)-(x + x0, y + y0), C, BF
  104.             LINE (x - x0, y - y0)-(x + x0, y - y0), C, BF
  105.             e = e + 2 * y0
  106.         ELSE
  107.             LINE (x - y0, y - x0)-(x + y0, y - x0), C, BF
  108.             LINE (x - y0, y + x0)-(x + y0, y + x0), C, BF
  109.             x0 = x0 - 1
  110.             e = e - 2 * x0
  111.         END IF
  112.     LOOP
  113.     LINE (x - R, y)-(x + R, y), C, BF
  115.  

2018-10-09 05_27_53-Lissajous Curve Table.png
« Last Edit: October 09, 2018, 04:37:26 am by FellippeHeitor »
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Offline STxAxTIC

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Re: Lissajous Curve Table
« Reply #1 on: October 09, 2018, 08:27:00 am »
Why code them when you can make them?

Stretch a balloon or rubber piece over a drinking glass, tight as a drum. Mount a tiny mirror or piece of foil in the center, roughly 1cm^2. Next mount a laser pointer a few feet away, and aim carefully so the beam hits the mirror when the system is at rest. Observe the stationary dot on a wall or screen that is reflected from the mirror. When you play sound into the glass or vibrate the table, the reflected dot will produce those curves, depending on the energy added. Some of the modes are hard to capture...

Yeah on second thought, just code it. Looks beautiful as ever Fellippe!
« Last Edit: October 09, 2018, 08:28:02 am by STxAxTIC »
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Offline bplus

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Re: Lissajous Curve Table
« Reply #2 on: October 09, 2018, 08:28:30 am »
This is best demo of Lissajous I've ever seen!
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FellippeHeitor

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Re: Lissajous Curve Table
« Reply #3 on: October 09, 2018, 08:55:54 am »
Thanks, guys! I take little credit (color choice, slow fade). Calculations were all done as stated.
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Offline TerryRitchie

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Re: Lissajous Curve Table
« Reply #4 on: October 09, 2018, 12:21:39 pm »
After studying the video and reading on-line I realize that I could use these curves for path making functions in my library.

Very interesting stuff. Thanks!
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FellippeHeitor

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Re: Lissajous Curve Table
« Reply #5 on: October 09, 2018, 12:27:13 pm »
I remember Walter had a flying saucer demo in his forum that used Lissajous Curves for the path of the sprite as well. Sounds like a good idea.
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Offline bplus

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Re: Lissajous Curve Table
« Reply #6 on: October 09, 2018, 12:48:08 pm »
I used something like it for Air Hockey AI defender, talk about Ninja fingers! ;)
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Offline Dav

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Re: Lissajous Curve Table
« Reply #7 on: October 09, 2018, 12:57:25 pm »
Nice coding, Fellippe!

- Dav
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FellippeHeitor

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Re: Lissajous Curve Table
« Reply #8 on: October 09, 2018, 02:48:07 pm »
Thanks, Dav!

For added eye-candy-ness, I've changed the plot line to paint using HSB colors (functions borrowed from p5js.bas) so that ink color will vary according to the current rotational angle.

Code: QB64: [Select]
  1. _TITLE "Lissajous Curve Table"
  2.  
  4.  
  5. TYPE vector
  6.     x AS SINGLE
  7.     y AS SINGLE
  9.  
  10. DIM SHARED angle
  12. DIM SHARED rows, cols
  13.  
  14. SCREEN _NEWIMAGE(800, 800, 32)
  15.  
  16. setup:
  17. angle = 0
  18. w = 80
  19. rows = INT(_HEIGHT / w) - 1
  20. cols = INT(_WIDTH / w) - 1
  21. REDIM dot(rows, cols) AS vector
  22.  
  23. plot = _NEWIMAGE(_WIDTH, _HEIGHT, 32)
  24. _DEST plot
  27.  
  30.         oldScreen = _DEST
  32.         _FREEIMAGE oldScreen
  33.         _FREEIMAGE plot
  34.         GOTO setup
  35.     END IF
  36.  
  37.     _PUTIMAGE , plot
  38.  
  39.     d = w - 0.2 * w
  40.     r = d / 2
  41.  
  42.     FOR i = 0 TO cols
  43.         cx = w + i * w + w / 2
  44.         cy = w / 2
  45.         CIRCLE (cx, cy), r
  46.  
  47.         x = r * COS(angle * (i + 1) - _PI(.5))
  48.         y = r * SIN(angle * (i + 1) - _PI(.5))
  49.  
  50.         LINE (cx + x, 0)-(cx + x, _HEIGHT), _RGB32(127, 127, 127)
  51.         CircleFill cx + x, cy + y, 4, _RGB32(28, 222, 50)
  52.         CircleFill cx + x, cy + y, 2, _RGB32(11, 33, 249)
  53.  
  54.         FOR j = 0 TO rows
  55.             dot(j, i).x = cx + x
  56.         NEXT
  57.     NEXT
  58.  
  59.     FOR i = 0 TO rows
  60.         cx = w / 2
  61.         cy = w + i * w + w / 2
  62.         CIRCLE (cx, cy), r
  63.  
  64.         x = r * COS(angle * (i + 1) - _PI(.5))
  65.         y = r * SIN(angle * (i + 1) - _PI(.5))
  66.  
  67.         LINE (0, cy + y)-(_WIDTH, cy + y), _RGB32(127, 127, 127)
  68.         CircleFill cx + x, cy + y, 4, _RGB32(28, 222, 50)
  69.         CircleFill cx + x, cy + y, 2, _RGB32(11, 33, 249)
  70.  
  71.         FOR j = 0 TO cols
  72.             dot(i, j).y = cy + y
  73.         NEXT
  74.     NEXT
  75.  
  76.     _DEST plot
  77.     LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA32(0, 0, 0, 4), BF
  78.     FOR j = 0 TO rows
  79.         FOR i = 0 TO cols
  80.             CircleFill dot(j, i).x, dot(j, i).y, 1, hsb(_R2D(angle), 127, 127, 255)
  81.         NEXT
  82.     NEXT
  83.  
  84.     angle = angle + 0.01
  85.     IF angle > _PI(2) THEN angle = 0
  86.  
  87.     _DEST 0
  88.  
  89.     _DISPLAY
  90.     _LIMIT 30
  92.  
  93. SUB CircleFill (x AS LONG, y AS LONG, R AS LONG, C AS _UNSIGNED LONG)
  94.     DIM x0 AS SINGLE, y0 AS SINGLE
  95.     DIM e AS SINGLE
  96.  
  97.     x0 = R
  98.     y0 = 0
  99.     e = -R
  100.     DO WHILE y0 < x0
  101.         IF e <= 0 THEN
  102.             y0 = y0 + 1
  103.             LINE (x - x0, y + y0)-(x + x0, y + y0), C, BF
  104.             LINE (x - x0, y - y0)-(x + x0, y - y0), C, BF
  105.             e = e + 2 * y0
  106.         ELSE
  107.             LINE (x - y0, y - x0)-(x + y0, y - x0), C, BF
  108.             LINE (x - y0, y + x0)-(x + y0, y + x0), C, BF
  109.             x0 = x0 - 1
  110.             e = e - 2 * x0
  111.         END IF
  112.     LOOP
  113.     LINE (x - R, y)-(x + R, y), C, BF
  115.  
  116. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
  117.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
  119.  
  120. FUNCTION hsb~& (__H AS _FLOAT, __S AS _FLOAT, __B AS _FLOAT, A AS _FLOAT)
  121.     DIM H AS _FLOAT, S AS _FLOAT, B AS _FLOAT
  122.  
  123.     H = map(__H, 0, 255, 0, 360)
  124.     S = map(__S, 0, 255, 0, 1)
  125.     B = map(__B, 0, 255, 0, 1)
  126.  
  127.     IF S = 0 THEN
  128.         hsb~& = _RGBA32(B * 255, B * 255, B * 255, A)
  129.         EXIT FUNCTION
  130.     END IF
  131.  
  132.     DIM fmx AS _FLOAT, fmn AS _FLOAT
  133.     DIM fmd AS _FLOAT, iSextant AS INTEGER
  134.     DIM imx AS INTEGER, imd AS INTEGER, imn AS INTEGER
  135.  
  136.     IF B > .5 THEN
  137.         fmx = B - (B * S) + S
  138.         fmn = B + (B * S) - S
  139.     ELSE
  140.         fmx = B + (B * S)
  141.         fmn = B - (B * S)
  142.     END IF
  143.  
  144.     iSextant = INT(H / 60)
  145.  
  146.     IF H >= 300 THEN
  147.         H = H - 360
  148.     END IF
  149.  
  150.     H = H / 60
  151.     H = H - (2 * INT(((iSextant + 1) MOD 6) / 2))
  152.  
  153.     IF iSextant MOD 2 = 0 THEN
  154.         fmd = (H * (fmx - fmn)) + fmn
  155.     ELSE
  156.         fmd = fmn - (H * (fmx - fmn))
  157.     END IF
  158.  
  159.     imx = _ROUND(fmx * 255)
  160.     imd = _ROUND(fmd * 255)
  161.     imn = _ROUND(fmn * 255)
  162.  
  163.     SELECT CASE INT(iSextant)
  164.         CASE 1
  165.             hsb~& = _RGBA32(imd, imx, imn, A)
  166.         CASE 2
  167.             hsb~& = _RGBA32(imn, imx, imd, A)
  168.         CASE 3
  169.             hsb~& = _RGBA32(imn, imd, imx, A)
  170.         CASE 4
  171.             hsb~& = _RGBA32(imd, imn, imx, A)
  172.         CASE 5
  173.             hsb~& = _RGBA32(imx, imn, imd, A)
  174.         CASE ELSE
  175.             hsb~& = _RGBA32(imx, imd, imn, A)
  176.     END SELECT
  177.  

Capturar.PNG
« Last Edit: October 09, 2018, 03:02:36 pm by FellippeHeitor »
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Offline STxAxTIC

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Re: Lissajous Curve Table
« Reply #9 on: October 09, 2018, 04:27:39 pm »
Alright we've had our fun. Time for a splash of water: when it comes to applying this stuff to actual paths of motion for physical objects in other coding projects... by all means go ahead, but the motions will be inconsistent with whatever laws of physics the rest of the program uses, supposing you're using any. These kinds of curves typically appear when taking the plot or projection of some kind of harmonic system, or looking at a phase diagram. This means that no projectile, airplane, mosquito, or other flying, gliding, or floating thing will *actually* trace out paths like this. Springy stuff at best like my balloon-laser example from above. Just sayin.
« Last Edit: October 09, 2018, 04:29:20 pm by STxAxTIC »
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FellippeHeitor

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Re: Lissajous Curve Table
« Reply #10 on: October 09, 2018, 04:35:32 pm »
I understand the technicalities may render anything seriously physics-intense useless, but it does look darn close.

I realize now my trash can with flies had similar paths in the end now that Lissajous is on the table: https://www.qb64.org/forum/index.php?action=dlattach;topic=255.0;attach=605
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Offline STxAxTIC

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Re: Lissajous Curve Table
« Reply #11 on: October 09, 2018, 04:51:52 pm »
Not that I'm nitpicking (I guess I am)... but "darn close" to what? The only physical Lissajous curves I've ever seen were made by devices contrived to produce them.
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Marked as best answer by on Today at 04:00:41 am

FellippeHeitor

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Re: Lissajous Curve Table
« Reply #12 on: October 09, 2018, 05:01:01 pm »
  • Undo Best Answer
    • Looks like a fly, buzzes like a fly,... you know the drill. "Darn Close" as in the layman will look and say "oh, flies!".
    « Last Edit: October 09, 2018, 05:02:42 pm by FellippeHeitor »
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    Offline STxAxTIC

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    Re: Lissajous Curve Table
    « Reply #13 on: October 09, 2018, 07:03:59 pm »
    Ah, my bad buddy - didn't see the fly demo earlier. Incidentally, the projection (shadow) of spiral-ish things can make such a figure... So the shadow of a moth perpetually finding the streetlight is one "natural" example... basically...

    EDIT: Ha, just noticed this too... So on the main *.org page, the icon for Samples is my 3D world in screen zero. It turns out that the 3d pink "snake" on the bottom-right, when animated and viewed from flat-on - is yet again a Lissajous curve. This begs an interesting question - are all Lissajous figures in 2d actually the projections of something else in 3d? Or just some....?
    « Last Edit: October 09, 2018, 07:23:06 pm by STxAxTIC »
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    Offline codeguy

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    Re: Lissajous Curve Table
    « Reply #14 on: October 09, 2018, 10:43:17 pm »
    I liked this demo. It was actually fine without the _DELAY.
    Here's a flight pattern for a drunken fly:
    Code: QB64: [Select]
    1. demo& = _NEWIMAGE(1366, 768, 256)
    2. CONST Iterations = 8191
    3. SCREEN demo&
    5. pi! = 4 * ATN(1)
    6. r = 100
    7. time! = .001
    8. M& = 100
    10.     FOR k = 0 TO Iterations
    11.  
    12.         X = r * _WIDTH / 2 * COS(14 * pi! * k / Iterations) * (1 - (3 / 4) * (SIN(2 * pi! * k / Iterations)) ^ 4 - (1 / 4) * (COS(6 * pi! * k / Iterations)) ^ 3)
    13.  
    14.  
    15.         Y = r * _HEIGHT / 2 * SIN(14 * pi! * k / Iterations) * (1 - (3 / 4) * (SIN(2 * pi! * k / Iterations)) ^ 4 - (1 / 4) * (COS(6 * pi! * k / Iterations)) ^ 3)
    16.  
    17.  
    18.         r = M& * (1 / 120) + (1 / 18) * (SIN(6 * pi! * k / Iterations)) ^ 4 + (1 / 18) * (SIN(16 * pi! * k / Iterations)) ^ 4
    19.  
    20.         PSET (_WIDTH / 2 + r * X, _HEIGHT / 2 + r * Y), 255 * (k / Iterations)
    21.         _LIMIT Iterations / time!
    22.     NEXT
    23.     _DISPLAY
    24.     M& = M& - 1
    25. LOOP UNTIL M& < 1
    31.  
    « Last Edit: October 09, 2018, 10:55:18 pm by codeguy »
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