Supershapes formula

Inspired by Johan Gielis, Paul Bourke’s website deals with, among other geometry, supershapes.

THE FORMULA

see also https://www.researchgate.net/publication/282433972_Examples_of_Supershapes

Extended to 3d the formula extends as:

Daniel Schiffman excellent youTube on this, here is the code for Processing sketch taken from his gitHub:

 

Also see Reza Ali’s Website – more supershapes.

 

to do:

take the code below and convert to a Point Cloud.

// Daniel Shiffman
// http://codingtra.in
// http://patreon.com/codingtrain
// Code for: https://youtu.be/akM4wMZIBWg

import peasy.*;

PeasyCam cam;

PVector[ ][ ]  globe;
int total = 75;

float offset = 0;

float m = 0;
float mchange = 0;

void setup() {
size(600, 600, P3D);
cam = new PeasyCam(this, 500);
colorMode(HSB);
globe = new PVector[total+1][total+1];
}

float a = 1;
float b = 1;

float supershape(float theta, float m, float n1, float n2, float n3) {
float t1 = abs((1/a)*cos(m * theta / 4));
t1 = pow(t1, n2);
float t2 = abs((1/b)*sin(m * theta/4));
t2 = pow(t2, n3);
float t3 = t1 + t2;
float r = pow(t3, – 1 / n1);
return r;
}

void draw() {

m = map(sin(mchange), -1, 1, 0, 7);
mchange += 0.02;

background(0);
noStroke();
lights();
float r = 200;
for (int i = 0; i < total+1; i++) {
float lat = map(i, 0, total, -HALF_PI, HALF_PI);
float r2 = supershape(lat, m, 0.2, 1.7, 1.7);
//float r2 = supershape(lat, 2, 10, 10, 10);
for (int j = 0; j < total+1; j++) {
float lon = map(j, 0, total, -PI, PI);
float r1 = supershape(lon, m, 0.2, 1.7, 1.7);
//float r1 = supershape(lon, 8, 60, 100, 30);
float x = r * r1 * cos(lon) * r2 * cos(lat);
float y = r * r1 * sin(lon) * r2 * cos(lat);
float z = r * r2 * sin(lat);
globe[i][j] = new PVector(x, y, z);
}
}

//stroke(255);
//fill(255);
//noFill();
offset += 5;
for (int i = 0; i < total; i++) {
float hu = map(i, 0, total, 0, 255*6);
fill((hu + offset) % 255 , 255, 255);
beginShape(TRIANGLE_STRIP);
for (int j = 0; j < total+1; j++) {
PVector v1 = globe[i][j];
vertex(v1.x, v1.y, v1.z);
PVector v2 = globe[i+1][j];
vertex(v2.x, v2.y, v2.z);
}
endShape();
}
}

 

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