make some attachment points on which new edges-vertices can be snapped. spread all these attachment points all over canvas through the center of 3d matrix model. make this mvc menu appear and disappear when pointing throughou these attachmen point grid, to be able to press that addedge button and draw a new line to extend the actual wireframe. output only full properre modified and optimized code, without any shortages and cutoffs. analyze all possible functions extremely careful and if need optimize or adapt them appropriately and accordingly, by not ruinning the transformation animations and deviations. (if need make your own version of absolutely new code but with the same similar functionalities.): <!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Visual Matrix Constructor</title>
  <style>
    body {
      margin: 0;
      overflow: hidden;
    }
    canvas {
      display: block;
    }
    .vmc-menu {
      display: none;
      position: absolute;
      background-color: rgba(0,0,0,0.1);
      border-radius: 5px;
      padding: 10px;
      box-shadow: 0 2px 5px rgba(0,0,0,0.1);
      z-index:1;
    }
    .vmc-menu label {
      display: block;
      margin-bottom: 10px;
    }
    .red-dot {
      position: absolute;
      width: 5px;
      height: 5px;
      background-color: red;
      border-radius: 50%;
      pointer-events: none;
      color:red;
      z-index:0;

    }
  </style>
</head>
<body>
  <div class="vmc-menu" id="vmc-menu">
    <label>Vertex X: <input type="number" id="vmc-vertex-x" step="0.1"></label>
    <label>Vertex Y: <input type="number" id="vmc-vertex-y" step="0.1"></label>
    <label>Vertex Z: <input type="number" id="vmc-vertex-z" step="0.1"></label>
    <button id="add-edge">Add Edge</button>
    <button id="remove-edge">Remove Edge</button>
  </div>
  <div class="red-dot" id="red-dot"></div>
  <script>
  const canvas = document.createElement('canvas');
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
document.body.appendChild(canvas);

const ctx = canvas.getContext('2d');
const vmcMenu = document.getElementById('vmc-menu');

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;

let angleX = 0;
let angleY = 0;
let angleZ = 0;
  let bestIndex = -1;
  let bestDistance = Infinity;
let startNewEdgeIndex = -1;
let isMouseDown = false;
let prevMousePos = null;

// Red Dot
const redDot = document.getElementById('red-dot');

// Add Edge
document.getElementById('add-edge').addEventListener('click', () => {
  if (bestIndex === -1) return;
  if (startNewEdgeIndex === -1) {
    startNewEdgeIndex = bestIndex;
  } else {
    edges.push([startNewEdgeIndex, bestIndex]);
    startNewEdgeIndex = -1;
  }
});

// Remove Edge
document.getElementById('remove-edge').addEventListener('click', () => {
  if (bestIndex === -1) return;
  edges.forEach((edge, index) => {
    if (edge.includes(bestIndex)) {
      edges.splice(index, 1);
    }
  });
});

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];
}

function getDeviation(maxDeviation) {
const t = Date.now() / 1000;
const frequency = 100 / 50;
const amplitude = maxDeviation / 10;
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);

  // Extraterrestrial transformation parameters
  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 + offsetX + angleY + offsetY) * 55 + ', 100%, 30%, 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);

// Calculate control point for curved edge
const cpDist = 0.005 * dist;
const cpX = (x1 + x2) / 2 + cpDist * Math.cos(angle - Math.PI / 2) * getDeviation(0.2);
const cpY = (y1 + y2) / 2 + cpDist * Math.sin(angle - Math.PI / 2) * getDeviation(0.2);

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

ctx.stroke();

canvas.addEventListener('mousedown', (event) => {
  isMouseDown = true;
  prevMousePos = { x: event.clientX, y: event.clientY };
});

canvas.addEventListener('mouseup', () => {
  isMouseDown = false;
  prevMousePos = null;
});

canvas.addEventListener('mousemove', (event) => {
  const mousePos = {
    x: event.clientX - canvas.getBoundingClientRect().left,
    y: event.clientY - canvas.getBoundingClientRect().top
  };
  
  bestIndex = -1;
  bestDistance = Infinity;

  projectedVertices.forEach((currVertex, index) => {
    const distance = Math.hypot(
      currVertex[0] - mousePos.x,
      currVertex[1] - mousePos.y
    );
    if (distance < bestDistance) {
      bestIndex = index;
      bestDistance = distance;
    }
  });
  
  if (bestDistance < 10 && bestIndex !== -1) {
    vmcMenu.style.display = 'block';
    vmcMenu.style.left = mousePos.x + 'px';
    vmcMenu.style.top = mousePos.y + 'px';

    document.getElementById('vmc-vertex-x').value = vertices[bestIndex][0];
    document.getElementById('vmc-vertex-y').value = vertices[bestIndex][1];
    document.getElementById('vmc-vertex-z').value = vertices[bestIndex][2];

    document.getElementById('vmc-vertex-x').dataset.vertexIndex = bestIndex;
    document.getElementById('vmc-vertex-y').dataset.vertexIndex = bestIndex;
    document.getElementById('vmc-vertex-z').dataset.vertexIndex = bestIndex;

    redDot.style.display = 'block';
    redDot.style.left = projectedVertices[bestIndex][0] - 3 + 'px';
    redDot.style.top = projectedVertices[bestIndex][1] - 3 + 'px';
  } else {
    vmcMenu.style.display = 'none';
    redDot.style.display = 'none';
  }

  if (isMouseDown && prevMousePos) {
    const deltaX = event.clientX - prevMousePos.x;
    const deltaY = event.clientY - prevMousePos.y;

    angleY += deltaX * 0.01;
    angleX += deltaY * 0.01;

    prevMousePos = { x: event.clientX, y: event.clientY };
  }
});

function updateVertexValue(event, indexToUpdate) {
  const newValue = parseFloat(event.target.value);
  const vertexIndex = parseInt(event.target.dataset.vertexIndex);

  if (!isNaN(newValue) && vertexIndex >= 0) {
    vertices[vertexIndex][indexToUpdate] = newValue;
  }
}

document.getElementById('vmc-vertex-x').addEventListener('input', (event) => {
  updateVertexValue(event, 0);
});
document.getElementById('vmc-vertex-y').addEventListener('input', (event) => {
  updateVertexValue(event, 1);
});
document.getElementById('vmc-vertex-z').addEventListener('input', (event) => {
  updateVertexValue(event, 2);
});

angleX += +getDeviation(0.0005);
angleY += +getDeviation(0.0005);
angleZ += +getDeviation(0.0005);

  requestAnimationFrame(render);
}

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