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Active Forums => Programs => Topic started by: STxAxTIC on November 24, 2020, 08:38:40 pm

Title: How to properly move stuff
Post by: STxAxTIC on November 24, 2020, 08:38:40 pm
Hi folks.

I keep teasing this concept, and occasionally quietly solve this-or-that problem using these methods without really explaining things, so it's finally time for a bare-bones demo of... drum roll please... parameterized motion.

Punchline first: If you see what's going on here, you will know how to move anything on screen, to anywhere, in any way you want, in full generality. This code ignores rotations, there is plenty to study with just translations.

When you run the code below, what you see, simply, is a circle moving from a beginning point A to an ending point B. The motion is of course not linear. The moving ball is doing two things:
(i) Trying to move straight in a straight line from A to B, using a speed function governed by the hyperbolic tangent. It starts slow, gets quick, and ends slow.
(ii) Trying to wiggle in a direction perpendicular to the motion, using wacky sine function stuff.

The combination of (i) and (ii) is what you see on screen. While it's running, even right in the middle of the motion, click+drag to move the target point around, and all of the motion adjusts seamlessly. Once you see the power and ease of this, you can imagine that literally *any* kind of motion can be tuned into this thing.

Play with some numbers and see how it applies to your projects:

Code: QB64: [Select]
  2.  
  3. SCREEN _NEWIMAGE(800, 600, 32)
  4.  
  6. pi = 4 * ATN(1)
  7.  
  8. TYPE Vector
  9.     x AS DOUBLE
  10.     y AS DOUBLE
  12.  
  13. DIM SHARED PointA AS Vector
  14. DIM SHARED PointB AS Vector
  15. PointA.x = -200
  16. PointA.y = -100
  17. PointB.x = 200
  18. PointB.y = 100
  19.  
  20. DIM SHARED Displacement AS Vector
  21. DIM SHARED Tangential AS Vector
  22. DIM SHARED Player AS Vector
  23.  
  24. CALL SetMotion
  25.  
  26. ' Main loop
  31.     FOR t = 0 TO 1 STEP .01
  32.         q = -4 * (1 - 2 * t)
  33.         p = .5 * (1 + tanh(q)) ' Goes from 0 to 1.
  34.  
  35.         DO WHILE _MOUSEINPUT
  36.             IF (_MOUSEBUTTON(1)) THEN
  37.                 PointB.x = -_WIDTH / 2 + _MOUSEX
  38.                 PointB.y = _HEIGHT / 2 - _MOUSEY
  39.                 CALL SetMotion
  40.             END IF
  41.         LOOP
  42.  
  43.         Player.x = PointA.x + Displacement.x * (p) + Tangential.x * (40 * SIN(2 * pi * p))
  44.         Player.y = PointA.y + Displacement.y * (p) + Tangential.y * (40 * SIN(5 * pi * p))
  45.  
  46.         'CLS
  47.         LINE (0, 0)-(_WIDTH, _HEIGHT), _RGBA(0, 0, 0, 30), BF
  48.         LOCATE 1, 1: PRINT "Left-Click+Drag to move target point."
  49.         CALL ccircle(PointA.x, PointA.y, 20, _RGBA(255, 0, 0, 255))
  50.         CALL ccircle(Player.x, Player.y, 20, _RGBA(0, 255, 0, 255))
  51.         CALL ccircle(PointB.x, PointB.y, 20, _RGBA(0, 0, 255, 255))
  52.         _DISPLAY
  53.         _LIMIT 30
  54.     NEXT
  55.  
  57.  
  58. SUB SetMotion
  59.     DIM mag AS DOUBLE
  60.     Displacement.x = PointB.x - PointA.x
  61.     Displacement.y = PointB.y - PointA.y
  62.     Tangential.x = -Displacement.y
  63.     Tangential.y = Displacement.x
  64.     mag = SQR(Tangential.x ^ 2 + Tangential.y ^ 2)
  65.     Tangential.x = Tangential.x / mag
  66.     Tangential.y = Tangential.y / mag
  68.  
  69. SUB ccircle (x1 AS DOUBLE, y1 AS DOUBLE, rad AS DOUBLE, col AS _UNSIGNED LONG)
  70.     CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), rad, col
  72.  
  73. FUNCTION tanh (x AS DOUBLE)
  74.     tanh = (EXP(2 * x) - 1) / (EXP(2 * x) + 1)
Title: Re: How to properly move stuff
Post by: _vince on November 25, 2020, 07:44:26 pm
Nice, welcome to the "I've used tanh not for the sake of using tanh" club!

Also, people may want things moving at a constant velocity magnitude
Title: Re: How to properly move stuff
Post by: OldMoses on November 25, 2020, 09:13:26 pm
I would dearly love to get my head wrapped around parametrics, as it looks like something I'm desperately trying to do, but my Algebra I teacher spent most of his time throwing erasers at me. ;)
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