the purpose is to draw a 3dmatrix visually by lines with ability to attach and detach lines to construct the model in 3d matrix representation array visually building the model by dragging lines and attach to other lines on canvas by mouse draging. preserve ETtransformations, because they are awesome. output full awesome code with all the described awesomeness. : const canvas = document.createElement('canvas');
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
document.body.appendChild(canvas);
const ctx = canvas.getContext('2d');

// some 3dmatrix simple cube template here to start with
const vertices = [
  [0, 0, 0],
  [0, 1, 0],
  [1, 1, 0],
  [1, 0, 0],
  [0, 0, 1],
  [0, 1, 1],
  [1, 1, 1],
  [1, 0, 1],
];

const edges = [
  [0, 1],
  [1, 2],
  [2, 3],
  [3, 0],
  [0, 4],
  [1, 5],
  [2, 6],
  [3, 7],
  [4, 5],
  [5, 6],
  [6, 7],
  [7, 4],
];

const scale = 0.025;
const zoom = 1;
const offsetX = 0.5;
const offsetY = 0.5;

function rotateX(angle) {
  const c = Math.cos(angle);
  const s = Math.sin(angle);
  return [
    [1, 0, 0],
    [0, c, -s],
    [0, s, c],
  ];
}

function rotateY(angle) {
  const c = Math.cos(angle);
  const s = Math.sin(angle);
  return [
    [c, 0, s],
    [0, 1, 0],
    [-s, 0, c],
  ];
}

function rotateZ(angle) {
  const c = Math.cos(angle);
  const s = Math.sin(angle);
  return [
    [c, -s, 0],
    [s, c, 0],
    [0, 0, 1],
  ];
}

function project(vertex, scale, offsetX, offsetY, zoom) {
  const [x, y, z] = vertex;
  const posX = (x - offsetX) * scale;
  const posY = (y - offsetY) * scale;
  const posZ = z * scale;

  return [
    (posX * (zoom + posZ) + canvas.width / 2),
    (posY * (zoom + posZ) + canvas.height / 2),
  ];
}

function transform(vertex, rotationMatrix) {
  const [x, y, z] = vertex;
  const [rowX, rowY, rowZ] = rotationMatrix;
  return [
    x * rowX[0] + y * rowX[1] + z * rowX[2],
    x * rowY[0] + y * rowY[1] + z * rowY[2],
    x * rowZ[0] + y * rowZ[1] + z * rowZ[2],
  ];
}

function extraterrestrialTransformation(vertex, frequency, amplitude) {
  const [x, y, z] = vertex;
  const cosX = (Math.cos(x * frequency) * amplitude);
  const cosY = (Math.cos(y * frequency) * amplitude);
  const cosZ = (Math.cos(z * frequency) * amplitude);

  return [x + cosX, y + cosY, z + cosZ];
}

let angleX = 0;
let angleY = 0;
let angleZ = 0;

function getDeviation(maxDeviation) {
const t = Date.now() / 1000;
const frequency = 100 / 5;
const amplitude = maxDeviation / 0.5;
const deviation = Math.sin(t * frequency) * amplitude;
return deviation.toFixed(3);
}

function render() {
  ctx.fillStyle = '#FFF';
  ctx.fillRect(0, 0, canvas.width, canvas.height);

  const rotX = rotateX(angleX);
  const rotY = rotateY(angleY);
  const rotZ = rotateZ(angleZ);

  const frequency = 1;
  const amplitude = 0.8;

  const transformedVertices = vertices.map(vertex => {
    const extraterrestrialVertex = extraterrestrialTransformation(vertex, frequency, amplitude);
    const cx = extraterrestrialVertex[0] - offsetX;
    const cy = extraterrestrialVertex[1] - offsetY;
    const cz = extraterrestrialVertex[2] - offsetY;

    const rotated = transform(transform(transform([cx, cy, cz], rotX), rotY), rotZ);

    return [
      rotated[0] + offsetX,
      rotated[1] + offsetY,
      rotated[2] + offsetY,
    ];
  });

  const projectedVertices = transformedVertices.map(vertex => project(vertex, canvas.height * scale, offsetX, offsetY, zoom));

ctx.lineWidth = 2;
ctx.strokeStyle = 'hsla(' + (angleX + angleY) * 100 + ', 100%, 50%, 0.8)';
ctx.beginPath();

for (let edge of edges) {
const [a, b] = edge;
const [x1, y1] = projectedVertices[a];
const [x2, y2] = projectedVertices[b];

const dist = Math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2 + (y2 - x1) ** 2 + (x2 - y1));
const angle = Math.atan2(y2 - y1, x2 - x1, x2 - y1, y2 - x1);

const cpDist = 0.0001 * dist;
const cpX = (x1 + x2) / 2 + cpDist * Math.cos(angle - Math.PI / 2) * getDeviation(2);
const cpY = (y1 + y2) / 2 + cpDist * Math.sin(angle - Math.PI / 2) * getDeviation(2);

ctx.moveTo(x1, y1, x2, y2);
ctx.quadraticCurveTo(cpX, cpY, x2, y2, x1, y1);
}

ctx.stroke();

angleX += +getDeviation(0.0002);
angleY += +getDeviation(0.0002);
angleZ += +getDeviation(0.0002);

  requestAnimationFrame(render);
}

requestAnimationFrame(render);
window.addEventListener("resize", () => {
  canvas.width = window.innerWidth;
  canvas.height = window.innerHeight;
});