systemsplanet.github.io/tesseract.html at main · Systemsplanet/systemsplanet.github.io · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>3D Spinning Tesseract</title>
  <style>
    body {
      margin: 0;
      overflow: hidden;
      background: white;
    }
    canvas {
      display: block;
    }
  </style>
</head>
<body>
  generate code in pure javascript
  to make a 3d spinning tesseract
</p>
<canvas id="tesseractCanvas"></canvas>

<script>
  const canvas = document.getElementById("tesseractCanvas");
  const ctx = canvas.getContext("2d");

  // Resize canvas to fit the screen
  canvas.width = window.innerWidth;
  canvas.height = window.innerHeight;

  const width = canvas.width;
  const height = canvas.height;

  // Define the vertices of the tesseract in 4D space
  const vertices = [
    [-1, -1, -1, -1],
    [-1, -1, -1, 1],
    [-1, -1, 1, -1],
    [-1, -1, 1, 1],
    [-1, 1, -1, -1],
    [-1, 1, -1, 1],
    [-1, 1, 1, -1],
    [-1, 1, 1, 1],
    [1, -1, -1, -1],
    [1, -1, -1, 1],
    [1, -1, 1, -1],
    [1, -1, 1, 1],
    [1, 1, -1, -1],
    [1, 1, -1, 1],
    [1, 1, 1, -1],
    [1, 1, 1, 1]
  ];

  // Define the edges connecting the vertices
  const edges = [
  [0, 1], [0, 2], [0, 4], [0, 8],
  [1, 3], [1, 5], [1, 9],
  [2, 3], [2, 6], [2, 10],
  [3, 7], [3, 11],
  [4, 5], [4, 6], [4, 12],
  [5, 7], [5, 13],
  [6, 7], [6, 14],
  [7, 15],
  [8, 9], [8, 10], [8, 12],
  [9, 11], [9, 13],
  [10, 11], [10, 14],
  [11, 15],
  [12, 13], [12, 14],
  [13, 15],
  [14, 15]
];

// Rotation angles
let angleXY = 0;
let angleXZ = 0;
let angleXW = 0;
let angleYW = 0;

// Project a point from 4D to a lower dimension
function project(point) {
  // Rotate in XY plane
  let x = point[0] * Math.cos(angleXY) - point[1] * Math.sin(angleXY);
  let y = point[0] * Math.sin(angleXY) + point[1] * Math.cos(angleXY);

  // Rotate in XZ plane
  let z = point[2] * Math.cos(angleXZ) - x * Math.sin(angleXZ);
  x = point[2] * Math.sin(angleXZ) + x * Math.cos(angleXZ);

  // Rotate in XW plane
  let w = point[3] * Math.cos(angleXW) - x * Math.sin(angleXW);
  x = point[3] * Math.sin(angleXW) + x * Math.cos(angleXW);

  // Rotate in YW plane
  w = w * Math.cos(angleYW) - y * Math.sin(angleYW);
  y = w * Math.sin(angleYW) + y * Math.cos(angleYW);

  // Perspective projection (4D to 3D to screen)
  const perspective = w !== -2 ? (1 / (w + 3)) : (1 / (w + Number.EPSILON));

  return [
    x * perspective * width / height,
    y * perspective,
    z * perspective
];
}

// Draw the tesseract
function draw() {
  ctx.clearRect(0, 0, canvas.width, canvas.height);
  ctx.fillStyle = "red";
  ctx.strokeStyle = "red";
  ctx.lineWidth = 2;

  // Project all vertices to 2D screen space
  const projectedVertices = vertices.map(project);

  // Center the tesseract on the screen
  const scale = Math.min(width, height) / 4; /// 8;
  const offsetX = width / 2;
  const offsetY = height / 2;

  // Draw edges
  for (const edge of edges) {
    const [startIdx, endIdx] = edge;
    const start = projectedVertices[startIdx];
    const end = projectedVertices[endIdx];

    ctx.beginPath();
    ctx.moveTo(start[0] * scale + offsetX, start[1] * scale + offsetY);
    ctx.lineTo(end[0] * scale + offsetX, end[1] * scale + offsetY);
    ctx.stroke();
  }

  // Draw vertices as small circles
  for (const vertex of projectedVertices) {
    ctx.beginPath();
    ctx.arc(
      vertex[0] * scale + offsetX,
      vertex[1] * scale + offsetY,
      3,
      0,
      Math.PI * 2
    );
    ctx.fill();
  }
}

// Animation loop
function animate() {
  angleXY += 0.01; // Rotate in XY plane
  angleXZ += 0.01; // Rotate in XZ plane
  angleXW += 0.01; // Rotate in XW plane
  angleYW += 0.01; // Rotate in YW plane

  draw();
  requestAnimationFrame(animate);
}

// Start the animation
animate();

</script>
</body>
</html>