Galaxy by pavel

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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pavel

function u(t) {

for(c.width|=p=300;e=p--**.9%1;x.fillRect(960+r(0)/z,200+99/z,s=9*e/z,s))r=d=>p/(1+e*C(a=t/4+p))*C(a+p+d)+2*p/(1/e-e)*C(p+d),z=.5+r(1.6)/800

Feb 28 2019 6:54 AM UTC

}// 140/140

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Galaxy

u/pavel

300 bodies which individually only interact with an infinite mass at the center
u/pavel

Each body moves around an ellipse, the orbits are accurate. However, the movement speed is a very rough approximation.
u/pavel

Naively drawing an ellipse centers it around one of the focal points, however moving a body on this path slows the body down near this focal point and speeds it up near the other one.
u/pavel

The opposite effect is needed. So this code still moves a body around an ellipse but it re-centers the ellipse on the 'other' focal point.
u/pavel

In polar coordinates the difference between the x and y coordinates is a phase shift of pi/2 ~ 1.6


      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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