# Algorithmic

Last update: 8 June 2021

## Square

### createPath

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

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

### createPath

no tangent
w/ tangent
var pts = 50;
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);

## ​Eight curve​

$x= a *sin(t)\\y=asin(t)cos(t)$

### Position

// source: Dan Ebbert
center = [thisComp.width,thisComp.height]/2;
period = 3;
angle = 2*Math.PI*time/period;
center + [x,y]

## Torus

$x=(a+bcosu)cosv \\ y=(a+bcosu)sinv\\ z=bsinu$

### 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]

freq = 60;
mul = 500;
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 vertices = [];
//main
for (i = 0; i < points; i++) {
angle += step;
radius = i / points * r;
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)