# I don't know if the result is the right result for a penteract( aka: 5D"cube")

Hello

First, I created a cube in a 2D engine (processing) slightly inspired by Daniel Shiffmann. Then I made I Hypercube also inspired by him. In that video he talks about the fact that you could take further and make a 5D and a 6D and so on, so I attempted to make a 5D “cube”. Now I have some code and I have a result but I don’t know if this is right. Can annyone who knows how a 5D “cube” looks like see if it is right?

Code:

``````int scale = 200;
float angle = 0;

P5Vector[] points;

void setup() {
size(1900, 1000, P3D);
ortho();
points = new P5Vector[32];
points[0] = new P5Vector(-1, -1, -1, 1, 1);
points[1] = new P5Vector(1, -1, -1, 1, 1);
points[2] = new P5Vector(1, 1, -1, 1, 1);
points[3] = new P5Vector(-1, 1, -1, 1, 1);
points[4] = new P5Vector(-1, -1, 1, 1, 1);
points[5] = new P5Vector(1, -1, 1, 1, 1);
points[6] = new P5Vector(1, 1, 1, 1, 1);
points[7] = new P5Vector(-1, 1, 1, 1, 1);
points[8] = new P5Vector(-1, -1, -1, -1, 1);
points[9] = new P5Vector(1, -1, -1, -1, 1);
points[10] = new P5Vector(1, 1, -1, -1, 1);
points[11] = new P5Vector(-1, 1, -1, -1, 1);
points[12] = new P5Vector(-1, -1, 1, -1, 1);
points[13] = new P5Vector(1, -1, 1, -1, 1);
points[14] = new P5Vector(1, 1, 1, -1, 1);
points[15] = new P5Vector(-1, 1, 1, -1, 1);
points[16] = new P5Vector(-1, -1, -1, 1, -1);
points[17] = new P5Vector(1, -1, -1, 1, -1);
points[18] = new P5Vector(1, 1, -1, 1, -1);
points[19] = new P5Vector(-1, 1, -1, 1, -1);
points[20] = new P5Vector(-1, -1, 1, 1, -1);
points[21] = new P5Vector(1, -1, 1, 1, -1);
points[22] = new P5Vector(1, 1, 1, 1, -1);
points[23] = new P5Vector(-1, 1, 1, 1, -1);
points[24] = new P5Vector(-1, -1, -1, -1, -1);
points[25] = new P5Vector(1, -1, -1, -1, -1);
points[26] = new P5Vector(1, 1, -1, -1, -1);
points[27] = new P5Vector(-1, 1, -1, -1, -1);
points[28] = new P5Vector(-1, -1, 1, -1, -1);
points[29] = new P5Vector(1, -1, 1, -1, -1);
points[30] = new P5Vector(1, 1, 1, -1, -1);
points[31] = new P5Vector(-1, 1, 1, -1, -1);
}

void draw() {
background(0);
translate(width/2, height/2);
stroke(255);
strokeWeight(10);
rotateX(-PI/9);
rotateY(-PI/3);
//rotateZ(-PI/2);

PVector[] projected3Dl = new PVector[32];
for (int i = 0; i < points.length; i++) {
P5Vector v = points[i];

//rotation matrix
float[][] rotateVXY = {
{1, 0, 0, 0, 0},
{0, 1, 0, 0, 0},
{0, 0, cos(angle), -sin(angle), 0},
{0, 0, sin(angle), cos(angle), 0},
{0, 0, 0, 0, 1}
};

float[][] rotateWVX = {
{1, 0, 0, 0, 0},
{0, cos(angle), -sin(angle), 0, 0},
{0, sin(angle), cos(angle), 0, 0},
{0, 0, 0, 1, 0},
{0, 0, 0, 0, 1}
};

//rotation
//P5Vector rotated = matMult(rotateXYZ, v, true, true);
//P5Vector rotated = matMult(rotateZWV, v, true, true);
//P5Vector rotated = matMult(rotateVXY, v, true, true);
P5Vector rotated = matMult(rotateWVX, v, true, true);

//Calculating the projection
float distance = 2;
float w = 1 / (distance - rotated.w);

float[][] projection4D = {
{w, 0, 0, 0, 0},
{0, w, 0, 0, 0},
{0, 0, w, 0, 0},
{0, 0, 0, w, 0}
};

float[][] projection3D = {
{w, 0, 0, 0},
{0, w, 0, 0},
{0, 0, w, 0}
};

P4Vector projected4D = matMult(projection4D, rotated, true);
PVector projected3D = matMult(projection3D, projected4D);
projected3D.mult(scale);

//Drawing the points
projected3Dl[i] = projected3D;
point(projected3D.x, projected3D.y, projected3D.z);
}
angle += 0.01;

connect(0, 0, 1, projected3Dl);
connect(0, 1, 2, projected3Dl);
connect(0, 2, 3, projected3Dl);
connect(0, 3, 0, projected3Dl);

connect(4, 0, 1, projected3Dl);
connect(4, 1, 2, projected3Dl);
connect(4, 2, 3, projected3Dl);
connect(4, 3, 0, projected3Dl);

connect(8, 0, 1, projected3Dl);
connect(8, 1, 2, projected3Dl);
connect(8, 2, 3, projected3Dl);
connect(8, 3, 0, projected3Dl);

connect(12, 0, 1, projected3Dl);
connect(12, 1, 2, projected3Dl);
connect(12, 2, 3, projected3Dl);
connect(12, 3, 0, projected3Dl);

connect(0, 0, 4, projected3Dl);
connect(1, 0, 4, projected3Dl);
connect(2, 0, 4, projected3Dl);
connect(3, 0, 4, projected3Dl);

connect(8, 0, 4, projected3Dl);
connect(9, 0, 4, projected3Dl);
connect(10, 0, 4, projected3Dl);
connect(11, 0, 4, projected3Dl);

connect(0, 0, 8, projected3Dl);
connect(1, 0, 8, projected3Dl);
connect(2, 0, 8, projected3Dl);
connect(3, 0, 8, projected3Dl);

connect(4, 0, 8, projected3Dl);
connect(5, 0, 8, projected3Dl);
connect(6, 0, 8, projected3Dl);
connect(7, 0, 8, projected3Dl);

//Connecting all the points

//  for (int i = 0; i < 4; i++) {
//    connect(0, i, (i+1) % 4, projected3Dl);
//    connect(0, i+4, ((i+1) % 4)+4, projected3Dl);
//    connect(0, i, i+4, projected3Dl);
//  }

//  for (int i = 0; i < 4; i++) {
//    connect(8, i, (i+1) % 4, projected3Dl);
//    connect(8, i+4, ((i+1) % 4)+4, projected3Dl);
//    connect(8, i, i+4, projected3Dl);
//  }

//  for (int i = 0; i < 8; i++) {
//    connect(0, i, i + 8, projected3Dl);
//  }
}

void connect(int offset, int i, int j, PVector[] points) {
PVector a = points[i+offset];
PVector b = points[j+offset];
strokeWeight(1);
stroke(255);
line(a.x, a.y, a.z, b.x, b.y, b.z);
}
``````

If you need the library for the matrix multiplication and P4-P5Vectors, you can find that on my github (in the folder: Coding chalanges/projection from 5D)

Thanks a lot
ExellentCoin2044