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Algorithmic

Last update: 8 June 2021

Square

createPath

square
vertices = [[0,0], [100,0], [100,100], [0,100]];
inTangents=[]
outTangents=[]
closed = true;
createPath(vertices,inTangents, outTangents, closed);

Triangle

createPath

l = 100;
w = 50;
vertices = [[0,0], [-w,l], [w,l]]
inTangents=[]
outTangents=[]
closed = true;
createPath(vertices,inTangents, outTangents, closed);

Circle

x=radius∗sin(theta)y=radius∗cos(theta)x = radius*sin(theta)\\ y = radius*cos(theta)

createPath

no tangent
w/ tangent
var pts = 50;
var a = 500; //radius
var completion = 100 / 100;
​
var t, x, y;
var vertices = [];
​
for (i = 0; i < pts; i++) {
t = i / pts * Math.PI * 2 * completion; // element num/ num of elements ;
x = a * Math.cos(t);
y = a * Math.sin(t);
vertices[i] = [x, y]
}
createPath(vertices, [], [], 1)
w = 500; // width
r = w/2;
ratio = .5523;
t = r*ratio;
vertices = [[r,0],[0,r],[r,2*r],[2*r,r]];
inTangents = [[t,0],[0,-t],[-t,0],[0,t]];
outTangents = [[-t,0],[0,t],[t,0],[0,-t]];
createPath(vertices,inTangents,outTangents,1);
x=a∗sin(t)y=asin(t)cos(t)x= a *sin(t)\\y=asin(t)cos(t)

Position

// source: Dan Ebbert
​
center = [thisComp.width,thisComp.height]/2;
radius = 200;
period = 3;
angle = 2*Math.PI*time/period;
x = 2*radius*Math.cos(angle)*Math.sqrt(Math.cos(angle)*Math.cos(angle));
y = 2*radius*Math.cos(angle)*Math.sin(angle);
center + [x,y]

Torus

x=(a+bcosu)cosvy=(a+bcosu)sinvz=bsinux=(a+bcosu)cosv \\ y=(a+bcosu)sinv\\ z=bsinu

Position

u = 1
v = 2
a = 540;
​
x = a*Math.cos(v*time)*Math.sin(u*time);
y = a*Math.cos(v*time)*Math.cos(u*time);
[x,y]+[thisComp.width/2,thisComp.height/2]

createPath

var pts = 50;
var u = 1
var v = 10;
var a = 75 // inner radius
var c = 450 // outer radius
var completion = 100 / 100;
​
var t, x, y;
var vertices = [];
​
for (i = 0; i < pts; i++) {
t = i / pts * Math.PI * 2 * completion; // element num/ num of elements ;
x = (c + a * Math.cos(v * t)) * Math.cos(u * t);
y = (c + a * Math.cos(v * t)) * Math.sin(u * t);
vertices[i] = [x, y]
}
createPath(vertices, [], [], 1)

Wavy Circle

Position

u = 1
v = 10;
a = 75 // inner radius
c = 450 // outer radius
phase = 10; // animate this
​
​
x = (c+a*Math.cos(v*phase))*Math.cos(u*phase);
y = (c+a*Math.cos(v*phase))*Math.sin(u*phase);
[x,y]+[thisComp.width/2,thisComp.height/2]

Conical spiral (equidistant)

Position

freq = 60;
mul = 500;
radius = 90;
​
x = radius*Math.sin(time*freq)
y = radius*Math.cos(time*freq)
z = time*mul
value + [x,y,z]

Archimedes Spiral

createPath

path property
// connect to sliders
let w = 1000;
let points = 200;
let steps = 20;
let angle = 0;
​
let r = w / 2;
let step = (Math.PI * 2) / steps;
let radius = 0;
let vertices = [];
​
//main
for (i = 0; i < points; i++) {
angle += step;
radius = i / points * r;
x = Math.cos(angle) * radius;
y = Math.sin(angle) * radius;
vertices[i] = [x, y];
}
​
createPath(vertices, [], [], 0)

Phyllotaxis

Position

var a = 137.508;
var r = 25;
​
var theta = degreesToRadians(myIndex * a);
var myIndex = index - thisComp.layer("controls").index;
​
x = r * Math.sqrt(myIndex) * Math.cos(theta);
y = r * Math.sqrt(myIndex) * Math.sin(theta);
​
[x, y] + [thisComp.width, thisComp.height] / 2;

Harmonic Motion

createPath

sine
squiggly
// var ctrl = thisLayer;
var inc = 1500;
var amp = 300;
var n = 30;
var freq = .5
var seed = 185;
​
var vertices = [];
var x, y, pt, phase;
seedRandom(seed, true)
var offset = random() * Math.PI * 2
​
for (i = 0; i < n; i++) {
pt = i / (n - 1);
x = inc * pt
​
phase = time * freq * Math.PI * 2 + pt * Math.PI
//phase += offset;
​
y = amp * Math.sin(phase);
//y *= Math.sin(phase / 2);
//y *= Math.sin(phase / 3);
//y += noise(time + pt) * 100;
​
// create point
vertices[i] = [x, y]
}
​
createPath(vertices, [], [], 0)
// var ctrl = thisLayer;
var inc = 1500;
var amp = 300;
var n = 50;
var freq = .5
var seed = 185;
var r = 0.25;
​
​
var vertices = [];
var x, y, pt, phase;
seedRandom(seed, true)
var offset = random() * Math.PI * 2
​
for (i = 0; i < n; i++) {
pt = i / (n - 1);
x = inc * pt
​
phase = time * freq * Math.PI * 2 + (pt * Math.PI /r)
// phase += offset;
​
w1 = Math.sin(phase);
y = amp * w1;
​
// create point
vertices[i] = [x, y]
}
​
createPath(vertices, [], [], 0)
​
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