Creating a Necker Cube in Three.js

To achieve the Necker cube optical illusion effect as shown in your image, you're on the right track by using an OrthographicCamera. This camera type is perfect for this illusion because it renders objects with parallel projection rather than perspective projection.

Key Considerations

1. The OrthographicCamera is ideal because it doesn't have perspective distortion, which is essential for the Necker cube illusion.
2. You'll need to position the camera at a specific angle to get the isometric-like view.
3. The cube should be rendered as wireframe or with thin cylinders for edges.

Implementation Approach

Here's how you can achieve this effect:

JAVASCRIPTCopied
// Set up the scene
const scene = new THREE.Scene();
scene.background = new THREE.Color(0xffffff);

// Create an orthographic camera
// Parameters: left, right, top, bottom, near, far
const aspectRatio = window.innerWidth / window.innerHeight;
const cameraSize = 10;
const camera = new THREE.OrthographicCamera(
  -cameraSize * aspectRatio, 
  cameraSize * aspectRatio, 
  cameraSize, 
  -cameraSize, 
  0.1, 
  1000
);

// Position the camera for isometric-like view
camera.position.set(10, 10, 10);
camera.lookAt(0, 0, 0);

// Create the cube edges using cylinders
function createCubeEdges(size, edgeRadius) {
  const group = new THREE.Group();
  const halfSize = size / 2;
  const positions = [
    // Bottom square
    [-halfSize, -halfSize, -halfSize], [halfSize, -halfSize, -halfSize],
    [halfSize, -halfSize, -halfSize], [halfSize, -halfSize, halfSize],
    [halfSize, -halfSize, halfSize], [-halfSize, -halfSize, halfSize],
    [-halfSize, -halfSize, halfSize], [-halfSize, -halfSize, -halfSize],
    
    // Top square
    [-halfSize, halfSize, -halfSize], [halfSize, halfSize, -halfSize],
    [halfSize, halfSize, -halfSize], [halfSize, halfSize, halfSize],
    [halfSize, halfSize, halfSize], [-halfSize, halfSize, halfSize],
    [-halfSize, halfSize, halfSize], [-halfSize, halfSize, -halfSize],
    
    // Connecting edges
    [-halfSize, -halfSize, -halfSize], [-halfSize, halfSize, -halfSize],
    [halfSize, -halfSize, -halfSize], [halfSize, halfSize, -halfSize],
    [halfSize, -halfSize, halfSize], [halfSize, halfSize, halfSize],
    [-halfSize, -halfSize, halfSize], [-halfSize, halfSize, halfSize]
  ];
  
  // Create cylinders for each edge
  for (let i = 0; i < positions.length; i += 2) {
    const start = new THREE.Vector3(...positions[i]);
    const end = new THREE.Vector3(...positions[i + 1]);
    
    const direction = new THREE.Vector3().subVectors(end, start);
    const length = direction.length();
    
    const cylinder = new THREE.CylinderGeometry(
      edgeRadius, edgeRadius, length, 8, 1
    );
    
    // Rotate and position the cylinder to align with the edge
    cylinder.translate(0, length / 2, 0);
    cylinder.rotateX(Math.PI / 2);
    
    const mesh = new THREE.Mesh(
      cylinder, 
      new THREE.MeshBasicMaterial({ color: 0x000000 })
    );
    
    // Position and orient the cylinder
    mesh.position.copy(start);
    mesh.lookAt(end);
    
    group.add(mesh);
  }
  
  return group;
}

// Add the cube to the scene
const cubeEdges = createCubeEdges(5, 0.05);
scene.add(cubeEdges);

// Set up renderer
const renderer = new THREE.WebGLRenderer({ antialias: true });
renderer.setSize(window.innerWidth, window.innerHeight);
document.body.appendChild(renderer.domElement);

// Animation loop
function animate() {
  requestAnimationFrame(animate);
  renderer.render(scene, camera);
}
animate();

Fine-tuning Tips

1. Camera Position: Adjust the camera position to get the exact angle you want. The isometric-like view is crucial for the illusion.

2. Edge Thickness: Make the cylinder radius small enough to create thin lines.

3. Rotation: You might want to rotate the entire cube slightly to match the exact orientation in your reference image.

4. No Shading: Use MeshBasicMaterial to avoid shading that might give depth cues and break the illusion.

This approach should help you create the Necker cube illusion with the parallel projection effect you're looking for.