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u(t) is called 60 times per second. t: Elapsed time in seconds. S: Shorthand for Math.sin. C: Shorthand for Math.cos. T: Shorthand for Math.tan. R: Function that generates rgba-strings, usage ex.: R(255, 255, 255, 0.5) c: A 1920x1080 canvas. x: A 2D context for that canvas.
Theme challenge of the month: #time
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  • u/taupelink
    Correction: I'm talking about X=8, not X=5. The sin(X*.6) term hits -1 around where X*.6=1.5*pi, which is around X=8.
  • u/taupelink
    So, if a rectangle is plotted with upper left-hand corner near X=8, Y=5 (i.e., bottom center), then there will be little to no green or blue in it.
  • u/taupelink
    If you're following along, then you may be looking at that spot in the picture and wondering why there's some green, yellow, orange in that location. That's due to overlap with other rectangles, ones whose upper left-hand corners are elsewhere...
  • u/taupelink
    ....The overlap is partly due to how I defined the rectangle width parameter, i/t. The "/t" means that rectangle widths shrink over time....but when t is very small, the rectangles are very wide! Part of the green/orange near X=8,Y=5 is due to rectangles that were drawn during the first half-second or so of the animation.

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  • u/taupelink
    briefly: Y ranges from -2 to 2. Below the middle line, Y is positive and there's more green than average. In the large top and bottom areas, Y is between -1 and 1, and there is more blue than average.
  • u/taupelink
    Note the formula for the top of the rectangle, 540+k/Y. This breaks the window up into four horizontal bands. From top to bottom, they are: -2<Y<-1, -1<Y<0, 1<Y<2, and 0<Y<1 respectively.
  • u/taupelink
    Correction: -1<Y<0 is the top band, -2<Y<-1 the second from the top.
  • u/taupelink
    The green component formula is k+k*Y/2. This is greater than k when Y>0.
  • u/taupelink
    The blue formula is k+k*C(Y*1.57). This is greater than k when C(Y*1.57)>0, i.e., when -1<Y<1.

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