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Shapes3D.pde
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import pallav.Matrix.Matrix;
static class Shapes3D {
//https://www.mathsisfun.com/geometry/common-3d-shapes.html
// http://eusebeia.dyndns.org/4d/platonic
static float[][] rotX;
static float[][] rotY;
static float[][] rotZ;
static void calcRot(PVector r) {
rotX = new float[][]{
{1, 0, 0},
{0, cos(r.x), -sin(r.x)},
{0, sin(r.x), cos(r.x)}
};
rotY = new float[][]{
{cos(r.y), 0, sin(r.y)},
{0, 1, 0},
{-sin(r.y), 0, cos(r.y)}
};
rotZ = new float[][]{
{cos(r.z), -sin(r.z), 0},
{sin(r.z), cos(r.z), 0},
{0, 0, 1}
};
}
static float[][] toArray(PVector p) {
return new float[][]{
{p.x},
{p.y},
{p.z}
};
}
static PVector toPVector(float[][] m) {
return new PVector(m[0][0], m[1][0], m[2][0]);
}
// http://eusebeia.dyndns.org/4d/icosahedron
public static ArrayList<PVector> icosahedron() {
ArrayList<PVector> points = new ArrayList<PVector>();
PVector p0 = new PVector(0, 0, 0);
float phi = (1+sqrt(5))/2;
PVector p1 = new PVector(0, 1, phi);
PVector p2 = new PVector(0, 1, -phi);
PVector p3 = new PVector(0, -1, -phi);
PVector p4 = new PVector(0, -1, phi);
PVector p5= new PVector(1, phi, 0);
PVector p6 = new PVector(1, -phi, 0);
PVector p7 = new PVector(-1, -phi, 0);
PVector p8 = new PVector(-1, phi, 0);
PVector p9 = new PVector(phi, 0, 1);
PVector p10 = new PVector(-phi, 0, 1);
PVector p11 = new PVector(-phi, 0, -1);
PVector p12 = new PVector(phi, 0, -1);
points.add(p0);
points.add(p1);
points.add(p2);
points.add(p3);
points.add(p4);
points.add(p5);
points.add(p6);
points.add(p7);
points.add(p8);
points.add(p9);
points.add(p10);
points.add(p11);
points.add(p12);
return points;
}
// https://en.wikipedia.org/wiki/Regular_icosahedron
public static DefaultUndirectedGraph<PVector, DefaultEdge> icosahedronGraph(int s, PVector t, PVector r) {
ArrayList<PVector> p = icosahedron();
DefaultUndirectedGraph<PVector, DefaultEdge> g = new DefaultUndirectedGraph<PVector, DefaultEdge>(DefaultEdge.class);
calcRot(r);
for (PVector ps : p) {
ps.set(toPVector(Matrix.Multiply(rotX, toArray(ps))));
ps.set(toPVector(Matrix.Multiply(rotY, toArray(ps))));
ps.set(toPVector(Matrix.Multiply(rotZ, toArray(ps))));
ps.mult(s/2).add(t);
g.addVertex(ps);
}
g.addEdge(p.get(0), p.get(1));
g.addEdge(p.get(0), p.get(2));
g.addEdge(p.get(0), p.get(3));
g.addEdge(p.get(0), p.get(4));
g.addEdge(p.get(0), p.get(5));
g.addEdge(p.get(0), p.get(6));
g.addEdge(p.get(0), p.get(7));
g.addEdge(p.get(0), p.get(8));
g.addEdge(p.get(0), p.get(9));
g.addEdge(p.get(0), p.get(10));
g.addEdge(p.get(0), p.get(11));
g.addEdge(p.get(0), p.get(12));
g.addEdge(p.get(1), p.get(4));
g.addEdge(p.get(1), p.get(4));
g.addEdge(p.get(1), p.get(4));
g.addEdge(p.get(1), p.get(4));
g.addEdge(p.get(1), p.get(5));
g.addEdge(p.get(1), p.get(8));
g.addEdge(p.get(1), p.get(9));
g.addEdge(p.get(1), p.get(10));
g.addEdge(p.get(2), p.get(3));
g.addEdge(p.get(2), p.get(5));
g.addEdge(p.get(2), p.get(8));
g.addEdge(p.get(2), p.get(11));
g.addEdge(p.get(2), p.get(12));
g.addEdge(p.get(3), p.get(2));
g.addEdge(p.get(3), p.get(6));
g.addEdge(p.get(3), p.get(7));
g.addEdge(p.get(3), p.get(11));
g.addEdge(p.get(3), p.get(12));
g.addEdge(p.get(4), p.get(1));
g.addEdge(p.get(4), p.get(6));
g.addEdge(p.get(4), p.get(7));
g.addEdge(p.get(4), p.get(9));
g.addEdge(p.get(4), p.get(10));
g.addEdge(p.get(5), p.get(1));
g.addEdge(p.get(5), p.get(2));
g.addEdge(p.get(5), p.get(8));
g.addEdge(p.get(5), p.get(9));
g.addEdge(p.get(5), p.get(12));
g.addEdge(p.get(6), p.get(3));
g.addEdge(p.get(6), p.get(4));
g.addEdge(p.get(6), p.get(7));
g.addEdge(p.get(6), p.get(9));
g.addEdge(p.get(6), p.get(12));
g.addEdge(p.get(7), p.get(3));
g.addEdge(p.get(7), p.get(4));
g.addEdge(p.get(7), p.get(6));
g.addEdge(p.get(7), p.get(10));
g.addEdge(p.get(7), p.get(11));
g.addEdge(p.get(8), p.get(1));
g.addEdge(p.get(8), p.get(2));
g.addEdge(p.get(8), p.get(5));
g.addEdge(p.get(8), p.get(10));
g.addEdge(p.get(8), p.get(11));
g.addEdge(p.get(9), p.get(1));
g.addEdge(p.get(9), p.get(4));
g.addEdge(p.get(9), p.get(5));
g.addEdge(p.get(9), p.get(6));
g.addEdge(p.get(9), p.get(12));
g.addEdge(p.get(10), p.get(1));
g.addEdge(p.get(10), p.get(4));
g.addEdge(p.get(10), p.get(7));
g.addEdge(p.get(10), p.get(8));
g.addEdge(p.get(10), p.get(11));
g.addEdge(p.get(11), p.get(2));
g.addEdge(p.get(11), p.get(3));
g.addEdge(p.get(11), p.get(7));
g.addEdge(p.get(11), p.get(8));
g.addEdge(p.get(11), p.get(10));
g.addEdge(p.get(12), p.get(2));
g.addEdge(p.get(12), p.get(3));
g.addEdge(p.get(12), p.get(5));
g.addEdge(p.get(12), p.get(6));
g.addEdge(p.get(12), p.get(9));
return g;
}
public static ArrayList<PVector> cube() {
ArrayList<PVector> points = new ArrayList<PVector>();
PVector p0 = new PVector(0, 0, 0);
PVector p1 = new PVector(-1, -1, 1);
PVector p2 = new PVector(1, -1, 1);
PVector p3 = new PVector(1, 1, 1);
PVector p4 = new PVector(-1, 1, 1);
PVector p5 = new PVector(-1, -1, -1);
PVector p6 = new PVector(1, -1, -1);
PVector p7 = new PVector(1, 1, -1);
PVector p8 = new PVector(-1, 1, -1);
points.add(p0);
points.add(p1);
points.add(p2);
points.add(p3);
points.add(p4);
points.add(p5);
points.add(p6);
points.add(p7);
points.add(p8);
return points;
}
public static DefaultUndirectedGraph<PVector, DefaultEdge> cubeGraph(int s, PVector t, PVector r) {
ArrayList<PVector> p = cube();
DefaultUndirectedGraph<PVector, DefaultEdge> g = new DefaultUndirectedGraph<PVector, DefaultEdge>(DefaultEdge.class);
calcRot(r);
for (PVector ps : p) {
ps.set(toPVector(Matrix.Multiply(rotX, toArray(ps))));
ps.set(toPVector(Matrix.Multiply(rotY, toArray(ps))));
ps.set(toPVector(Matrix.Multiply(rotZ, toArray(ps))));
ps.mult(s/2).add(t);
g.addVertex(ps);
}
g.addEdge(p.get(0), p.get(1));
g.addEdge(p.get(0), p.get(2));
g.addEdge(p.get(0), p.get(3));
g.addEdge(p.get(0), p.get(4));
g.addEdge(p.get(0), p.get(5));
g.addEdge(p.get(0), p.get(6));
g.addEdge(p.get(0), p.get(7));
g.addEdge(p.get(0), p.get(8));
g.addEdge(p.get(1), p.get(2));
g.addEdge(p.get(2), p.get(3));
g.addEdge(p.get(3), p.get(4));
g.addEdge(p.get(4), p.get(1));
g.addEdge(p.get(5), p.get(6));
g.addEdge(p.get(6), p.get(7));
g.addEdge(p.get(7), p.get(8));
g.addEdge(p.get(8), p.get(5));
g.addEdge(p.get(1), p.get(5));
g.addEdge(p.get(2), p.get(6));
g.addEdge(p.get(3), p.get(7));
g.addEdge(p.get(4), p.get(8));
return g;
}
public static ArrayList<PVector> tetrahydron() {
ArrayList<PVector> points = new ArrayList<PVector>();
PVector p1 = new PVector(1, -1/sqrt(3), -1/sqrt(6));
PVector p2 = new PVector(-1, -1/sqrt(3), -1/sqrt(6));
PVector p3 = new PVector(0, 2/sqrt(3), -1/sqrt(6));
PVector p4 = new PVector(0, 0, 3/sqrt(6));
PVector p0 = new PVector(0, 0, 0);
points.add(p0);
points.add(p1);
points.add(p2);
points.add(p3);
points.add(p4);
return points;
}
public static DefaultUndirectedGraph<PVector, DefaultEdge> tetrahydronGraph(int s, PVector t, PVector r) {
ArrayList<PVector> p = tetrahydron();
DefaultUndirectedGraph<PVector, DefaultEdge> g = new DefaultUndirectedGraph<PVector, DefaultEdge>(DefaultEdge.class);
calcRot(r);
for (PVector ps : p) {
ps.set(toPVector(Matrix.Multiply(rotX, toArray(ps))));
ps.set(toPVector(Matrix.Multiply(rotY, toArray(ps))));
ps.set(toPVector(Matrix.Multiply(rotZ, toArray(ps))));
ps.mult(s/2).add(t);
g.addVertex(ps);
}
g.addEdge(p.get(1), p.get(2));
g.addEdge(p.get(2), p.get(3));
g.addEdge(p.get(3), p.get(1));
g.addEdge(p.get(1), p.get(4));
g.addEdge(p.get(2), p.get(4));
g.addEdge(p.get(3), p.get(4));
g.addEdge(p.get(0), p.get(1));
g.addEdge(p.get(0), p.get(2));
g.addEdge(p.get(0), p.get(3));
g.addEdge(p.get(0), p.get(4));
return g;
}
//http://eusebeia.dyndns.org/4d/prism3
//void generatePrism() {
// PVector p1 = new PVector(-1, -1/sqrt(3), 1);
// PVector p2 = new PVector(1, -1/sqrt(3), 1);
// PVector p3 = new PVector(0, 2/sqrt(3), 1);
// PVector p4 = new PVector(-1, -1/sqrt(3), -1);
// PVector p5 = new PVector(1, -1/sqrt(3), -1);
// PVector p6 = new PVector(0, 2/sqrt(3), -1);
// g.addVertex(p1);
// g.addVertex(p2);
// g.addVertex(p3);
// g.addVertex(p4);
// g.addVertex(p5);
// g.addVertex(p6);
// g.addEdge(p1, p2);
// g.addEdge(p2, p3);
// g.addEdge(p3, p1);
// g.addEdge(p4, p5);
// g.addEdge(p5, p6);
// g.addEdge(p6, p4);
// g.addEdge(p1, p4);
// g.addEdge(p2, p5);
// g.addEdge(p3, p6);
// startingNodes.add(p1);
// startingNodes.add(p2);
// startingNodes.add(p3);
// startingNodes.add(p4);
// startingNodes.add(p5);
// startingNodes.add(p6);
// planeRadius = w/3.5;
// forceMultiplier = .1;
//}
}