The Hyperbolic Paraboloid (z=x²-y²). T… by rodrigo.siqueira

function u(t) {

c.width=1920 // clear the canvas
for(i=0;i<9;i++)
x.fillRect(400+i*100+S(t)*300,400,50,200) // draw 50x200 rects

} // 122/140

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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.

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rodrigo.siqueira

function u(t) {

for(c.width=w=i=2e3;i--;)
X=S(i*i),Y=S(i),ℵ=C(Math.atan2(X,Y)-t)*Math.hypot(X,Y),
K=w/2,x.fillRect(w*ℵ/(Z=4+C(t)+X*X-Y*Y)+K,w+K*(ℵ-6)/Z,7,8)

Jun 26 2019 7:01 PM UTC

}// 140/140

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The Hyperbolic Paraboloid (z=x²-y²). The S(i*i) and S(i) are random number generators between -1 and +1. The atan2 and hypot are used to calculate 3d object rotation (Euler equations could also be used, as seen on /d/12086). Thanks to u/cantelope for the Tiny 3D Engine Tutorials: https://cantelope.org/tiny_3D/ and https://cantelope.org/3D/ #math #hypot #D3 #hyperbolic #surface

u/cantelope

:D
u/rodrigo.siqueira

There is an interesting fact that the Pringles potato chips are a truncated hyperbolic paraboloid. The strength of the shape helps to prevent them from breaking while stacked. The curvature of the shape improves resistance to tension and compression forces. Remember this next time you eat a hyperbolic paraboloid.


      u(t) is called 60 times per second.
      t: elapsed time in seconds.
      c: A 1920x1080 canvas.
      x: A 2D context for that canvas.
      S: Math.sin
      C: Math.cos
      T: Math.tan
      R: Generates rgba-strings, ex.: R(255, 255, 255, 0.5)

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