Identifying Logical Faces in Three.js After Rotation

This is an interesting challenge that requires a systematic approach to identify logical faces of 3D shapes after arbitrary rotations. Here's a solution that should work for your current shapes and be extensible for future ones:

Approach: Face Group Tagging

The key is to tag or mark the faces during geometry creation, before any rotations are applied. Here's how you can implement this:

1. Create a Face Mapping System

JAVASCRIPTCopied
class LogicalFaceMapper {
  constructor(geometry, faceDefinitions) {
    this.geometry = geometry;
    this.faceGroups = new Map(); // Maps face indices to logical face names
    
    // Apply the face definitions to the geometry
    this.applyFaceDefinitions(faceDefinitions);
  }
  
  applyFaceDefinitions(faceDefinitions) {
    // Extend the geometry's attributes to store face group information
    if (!this.geometry.hasAttribute('faceGroup')) {
      const faceCount = this.geometry.index ? this.geometry.index.count / 3 : this.geometry.attributes.position.count / 3;
      const faceGroupAttr = new Float32Array(faceCount);
      this.geometry.setAttribute('faceGroup', new THREE.BufferAttribute(faceGroupAttr, 1));
    }
    
    // Apply each face definition
    for (const [faceName, definitionFunc] of Object.entries(faceDefinitions)) {
      const faceIndices = definitionFunc(this.geometry);
      
      // Store the mapping
      for (const index of faceIndices) {
        this.faceGroups.set(index, faceName);
        
        // Also store in the geometry attribute for shader-based approaches
        this.geometry.attributes.faceGroup.array[index] = 
          Object.keys(faceDefinitions).indexOf(faceName);
      }
    }
    
    this.geometry.attributes.faceGroup.needsUpdate = true;
  }
  
  getFaceNameFromIntersection(intersection) {
    // Get the face index from the intersection
    const faceIndex = intersection.faceIndex;
    return this.faceGroups.get(faceIndex) || 'unknown';
  }
}

2. Define Face Groups for Different Shapes

For each shape type, you'll need to define how to identify its logical faces:

JAVASCRIPTCopied
// Example for a cube
function createCubeFaceDefinitions() {
  return {
    'Front': (geometry) => {
      // Identify faces that make up the front face
      // This could be based on vertex positions, normals, etc.
      return [0, 1]; // Example indices
    },
    'Back': (geometry) => {
      return [2, 3]; // Example indices
    },
    // ... other face definitions
  };
}

// Example for a cylinder
function createCylinderFaceDefinitions() {
  return {
    'Top': (geometry) => {
      // For a cylinder, the top face might be all triangles where y is at maximum
      const indices = [];
      const positions = geometry.attributes.position.array;
      const indexArray = geometry.index ? geometry.index.array : null;
      
      // Logic to find top face triangles
      // For example, triangles where all vertices have y = maxY
      
      return indices;
    },
    'Curve': (geometry) => {
      // Side faces might be identified by having normals with non-zero x and z components
      // ...
    },
    'Bottom': (geometry) => {
      // Similar to top but with minimum y
      // ...
    }
  };
}

3. Implementation for Specific Geometries

For a PolyhedronGeometry (which can be used to create many of your shapes), you could use the vertex indices directly:

JAVASCRIPTCopied
// For a cube using PolyhedronGeometry
const verticesOfCube = [
  -1,-1,-1,    1,-1,-1,    1, 1,-1,    -1, 1,-1,
  -1,-1, 1,    1,-1, 1,    1, 1, 1,    -1, 1, 1,
];

const indicesOfFaces = [
  2,1,0,    0,3,2,  // Front face (z = -1)
  0,4,7,    7,3,0,  // Left face (x = -1)
  0,1,5,    5,4,0,  // Bottom face (y = -1)
  1,2,6,    6,5,1,  // Right face (x = 1)
  2,3,7,    7,6,2,  // Top face (y = 1)
  4,5,6,    6,7,4   // Back face (z = 1)
];

const geometry = new THREE.PolyhedronGeometry(verticesOfCube, indicesOfFaces, 6, 2);

// Define face groups based on the indices
const cubeFaceDefinitions = {
  'Front': () => [0, 1],
  'Left': () => [2, 3],
  'Bottom': () => [4, 5],
  'Right': () => [6, 7],
  'Top': () => [8, 9],
  'Back': () => [10, 11]
};

const faceMapper = new LogicalFaceMapper(geometry, cubeFaceDefinitions);

4. Using with Raycaster

JAVASCRIPTCopied
// When you get an intersection from the raycaster
raycaster.setFromCamera(mouse, camera);
const intersects = raycaster.intersectObjects(scene.children);

if (intersects.length > 0) {
  const intersection = intersects[0];
  const object = intersection.object;
  
  // Get the face mapper for this object
  const faceMapper = objectToFaceMapperMap.get(object);
  
  if (faceMapper) {
    const faceName = faceMapper.getFaceNameFromIntersection(intersection);
    console.log(`Hit the ${faceName} face`);
  }
}

Alternative Approach: Normal-Based Identification

For simpler shapes, you could use face normals to identify logical faces:

JAVASCRIPTCopied
function getFaceNameFromNormal(normal, originalOrientation) {
  // Transform the normal back to the original orientation
  const originalNormal = normal.clone().applyQuaternion(originalOrientation.inverse());
  
  // Now check which primary direction this normal points
  if (Math.abs(originalNormal.x) > Math.abs(originalNormal.y) && 
      Math.abs(originalNormal.x) > Math.abs(originalNormal.z)) {
    return originalNormal.x > 0 ? 'Right' : 'Left';
  } else if (Math.abs(originalNormal.y) > Math.abs(originalNormal.z)) {
    return originalNormal.y > 0 ? 'Top' : 'Bottom';
  } else {
    return originalNormal.z > 0 ? 'Back' : 'Front';
  }
}

This approach is simpler but may not work for all shapes, especially those with curved surfaces.

By implementing one of these approaches, you should be able to identify logical faces of your 3D shapes even after arbitrary rotations, in a way that's extensible to new shapes.