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

Processing Libraries
1

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

2

Can you post a screenshot, since we can’t run your code without downloading external libraries? Better yet, can you post a MCVE?

I think it’s going to be up to you whether it looks right or not. I’m not sure there’s a “correct” 2D representation of a 5-dimensional shape. There are a bunch of different ways to visualize it, so which one you want is up to you.

You might also try searching for images of visualizations done by other people to compare what you have with what others have done before.

3

I am sorry but I can’t. I can post a video of my screen running the program?

4

How are you able to post a video but not an image?