gradational sphere
@author
float scale = 100;
float phi = (1 + sqrt(5)) / 2.0;
float radious = sqrt(sq(1) + sq(phi));
ArrayList<Triangle> triangles;
color[][] cols;
void mousePressed(){
cols = new color[3][2];
for(int i = 0; i < 3; i++){
for(int j = 0; j < 2; j++){
cols[i][j] = color(random(255), random(255), random(255));
}
}
}
void setup(){
size(500, 500, P3D);
mousePressed();
PVector[] vertices = {new PVector(0, 1, phi),
new PVector(0, -1, phi),
new PVector(0, -1, -phi),
new PVector(0, 1, -phi),
new PVector(phi, 0, 1),
new PVector(-phi, 0, 1),
new PVector(-phi, 0, -1),
new PVector(phi, 0, -1),
new PVector(1, phi, 0),
new PVector(-1, phi, 0),
new PVector(-1, -phi, 0),
new PVector(1, -phi, 0)};
triangles = new ArrayList<Triangle>();
triangles.add(new Triangle(vertices[0], vertices[8], vertices[9]));
triangles.add(new Triangle(vertices[0], vertices[9], vertices[5]));
triangles.add(new Triangle(vertices[0], vertices[5], vertices[1]));
triangles.add(new Triangle(vertices[0], vertices[1], vertices[4]));
triangles.add(new Triangle(vertices[0], vertices[4], vertices[8]));
triangles.add(new Triangle(vertices[1], vertices[5], vertices[10]));
triangles.add(new Triangle(vertices[1], vertices[10], vertices[11]));
triangles.add(new Triangle(vertices[1], vertices[11], vertices[4]));
triangles.add(new Triangle(vertices[2], vertices[3], vertices[7]));
triangles.add(new Triangle(vertices[2], vertices[7], vertices[11]));
triangles.add(new Triangle(vertices[2], vertices[11], vertices[10]));
triangles.add(new Triangle(vertices[2], vertices[10], vertices[6]));
triangles.add(new Triangle(vertices[2], vertices[6], vertices[3]));
triangles.add(new Triangle(vertices[3], vertices[6], vertices[9]));
triangles.add(new Triangle(vertices[3], vertices[9], vertices[8]));
triangles.add(new Triangle(vertices[3], vertices[8], vertices[7]));
triangles.add(new Triangle(vertices[4], vertices[11], vertices[7]));
triangles.add(new Triangle(vertices[4], vertices[7], vertices[8]));
triangles.add(new Triangle(vertices[5], vertices[9], vertices[6]));
triangles.add(new Triangle(vertices[5], vertices[6], vertices[10]));
for(int i = 0; i < 3; i++){
ArrayList<Triangle> nextTriangles = new ArrayList<Triangle>();
for(Triangle t: triangles){
nextTriangles.addAll(t.divide());
}
triangles = nextTriangles;
}
}
void draw(){
background(0);
translate(width / 2, height / 2);
rotateX(frameCount * 0.01);
rotateY(frameCount * 0.02);
rotateZ(frameCount * 0.03);
for(Triangle t: triangles){
t.display();
}
}
class Triangle{
PVector[] vertices;
Triangle(PVector v0, PVector v1, PVector v2){
vertices = new PVector[3];
vertices[0] = v0;
vertices[1] = v1;
vertices[2] = v2;
}
void display(){
stroke(255);
PVector center = new PVector(0, 0, 0);
for(int i = 0; i < 3; i++){
center.add(vertices[i]);
}
center.div(3);
float r = (map(center.x, -radious, radious, red(cols[0][0]), red(cols[0][1])) + map(center.y, -radious, radious, red(cols[1][0]), red(cols[1][1])) + map(center.z, -radious, radious, red(cols[2][0]), red(cols[2][1]))) / 3.0;
float g = (map(center.x, -radious, radious, green(cols[0][0]), green(cols[0][1])) + map(center.y, -radious, radious, green(cols[1][0]), green(cols[1][1])) + map(center.z, -radious, radious, green(cols[2][0]), green(cols[2][1]))) / 3.0;
float b = (map(center.x, -radious, radious, blue(cols[0][0]), blue(cols[0][1])) + map(center.y, -radious, radious, blue(cols[1][0]), blue(cols[1][1])) + map(center.z, -radious, radious, blue(cols[2][0]), blue(cols[2][1]))) / 3.0;
fill(r, g, b);
beginShape();
for(int i = 0; i < 3; i++){
vertex(vertices[i].x * scale, vertices[i].y * scale, vertices[i].z * scale);
}
endShape(CLOSE);
}
ArrayList<Triangle> divide(){
PVector[] midpoints = new PVector[3];
for(int i = 0; i < 3; i++){
int j = i != 2 ? i + 1: 0;
PVector m = PVector.lerp(vertices[i], vertices[j], 0.5);
m.normalize();
m.mult(radious);
midpoints[i] = m;
}
ArrayList<Triangle> triangles = new ArrayList<Triangle>();
triangles.add(new Triangle(vertices[0], midpoints[0], midpoints[2]));
triangles.add(new Triangle(vertices[1], midpoints[1], midpoints[0]));
triangles.add(new Triangle(vertices[2], midpoints[2], midpoints[1]));
triangles.add(new Triangle(midpoints[0], midpoints[1], midpoints[2]));
return triangles;
}
}