ThreeCSG.js

'use strict';
window.ThreeBSP = (function() {
	
	var ThreeBSP,
		EPSILON = 1e-5,
		COPLANAR = 0,
		FRONT = 1,
		BACK = 2,
		SPANNING = 3;
	
	ThreeBSP = function( geometry ) {
		// Convert THREE.Geometry to ThreeBSP
		var i, _length_i,
			face, vertex, faceVertexUvs, uvs,
			polygon,
			polygons = [],
			tree;
	
		if ( geometry instanceof THREE.Geometry ) {
			this.matrix = new THREE.Matrix4;
		} else if ( geometry instanceof THREE.Mesh ) {
			// #todo: add hierarchy support
			geometry.updateMatrix();
			this.matrix = geometry.matrix.clone();
			geometry = geometry.geometry;
		} else if ( geometry instanceof ThreeBSP.Node ) {
			this.tree = geometry;
			this.matrix = new THREE.Matrix4;
			return this;
		} else {
			throw 'ThreeBSP: Given geometry is unsupported';
		}
	
		for ( i = 0, _length_i = geometry.faces.length; i < _length_i; i++ ) {
			face = geometry.faces[i];
			faceVertexUvs = geometry.faceVertexUvs[0][i];
			polygon = new ThreeBSP.Polygon;
			
			if ( face instanceof THREE.Face3 ) {
				vertex = geometry.vertices[ face.a ];
                                uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[0].x, faceVertexUvs[0].y ) : null;
                                vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[0], uvs );
				vertex.applyMatrix4(this.matrix);
				polygon.vertices.push( vertex );
				
				vertex = geometry.vertices[ face.b ];
                                uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[1].x, faceVertexUvs[1].y ) : null;
                                vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[1], uvs );
				vertex.applyMatrix4(this.matrix);
				polygon.vertices.push( vertex );
				
				vertex = geometry.vertices[ face.c ];
                                uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[2].x, faceVertexUvs[2].y ) : null;
                                vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[2], uvs );
				vertex.applyMatrix4(this.matrix);
				polygon.vertices.push( vertex );
			} else if ( typeof THREE.Face4 ) {
				vertex = geometry.vertices[ face.a ];
                                uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[0].x, faceVertexUvs[0].y ) : null;
                                vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[0], uvs );
				vertex.applyMatrix4(this.matrix);
				polygon.vertices.push( vertex );
				
				vertex = geometry.vertices[ face.b ];
                                uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[1].x, faceVertexUvs[1].y ) : null;
                                vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[1], uvs );
				vertex.applyMatrix4(this.matrix);
				polygon.vertices.push( vertex );
				
				vertex = geometry.vertices[ face.c ];
                                uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[2].x, faceVertexUvs[2].y ) : null;
                                vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[2], uvs );
				vertex.applyMatrix4(this.matrix);
				polygon.vertices.push( vertex );
				
				vertex = geometry.vertices[ face.d ];
                                uvs = faceVertexUvs ? new THREE.Vector2( faceVertexUvs[3].x, faceVertexUvs[3].y ) : null;
                                vertex = new ThreeBSP.Vertex( vertex.x, vertex.y, vertex.z, face.vertexNormals[3], uvs );
				vertex.applyMatrix4(this.matrix);
				polygon.vertices.push( vertex );
			} else {
				throw 'Invalid face type at index ' + i;
			}
			
			polygon.calculateProperties();
			polygons.push( polygon );
		};
	
		this.tree = new ThreeBSP.Node( polygons );
	};
	ThreeBSP.prototype.subtract = function( other_tree ) {
		var a = this.tree.clone(),
			b = other_tree.tree.clone();
		
		a.invert();
		a.clipTo( b );
		b.clipTo( a );
		b.invert();
		b.clipTo( a );
		b.invert();
		a.build( b.allPolygons() );
		a.invert();
		a = new ThreeBSP( a );
		a.matrix = this.matrix;
		return a;
	};
	ThreeBSP.prototype.union = function( other_tree ) {
		var a = this.tree.clone(),
			b = other_tree.tree.clone();
		
		a.clipTo( b );
		b.clipTo( a );
		b.invert();
		b.clipTo( a );
		b.invert();
		a.build( b.allPolygons() );
		a = new ThreeBSP( a );
		a.matrix = this.matrix;
		return a;
	};
	ThreeBSP.prototype.intersect = function( other_tree ) {
		var a = this.tree.clone(),
			b = other_tree.tree.clone();
		
		a.invert();
		b.clipTo( a );
		b.invert();
		a.clipTo( b );
		b.clipTo( a );
		a.build( b.allPolygons() );
		a.invert();
		a = new ThreeBSP( a );
		a.matrix = this.matrix;
		return a;
	};
	ThreeBSP.prototype.toGeometry = function() {
		var i, j,
			matrix = new THREE.Matrix4().getInverse( this.matrix ),
			geometry = new THREE.Geometry(),
			polygons = this.tree.allPolygons(),
			polygon_count = polygons.length,
			polygon, polygon_vertice_count,
			vertice_dict = {},
			vertex_idx_a, vertex_idx_b, vertex_idx_c,
			vertex, face,
			verticeUvs;
	
		for ( i = 0; i < polygon_count; i++ ) {
			polygon = polygons[i];
			polygon_vertice_count = polygon.vertices.length;
			
			for ( j = 2; j < polygon_vertice_count; j++ ) {
				verticeUvs = [];
				
				vertex = polygon.vertices[0];
				verticeUvs.push( new THREE.Vector2( vertex.uv.x, vertex.uv.y ) );
				vertex = new THREE.Vector3( vertex.x, vertex.y, vertex.z );
				vertex.applyMatrix4(matrix);
				
				if ( typeof vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] !== 'undefined' ) {
					vertex_idx_a = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ];
				} else {
					geometry.vertices.push( vertex );
					vertex_idx_a = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] = geometry.vertices.length - 1;
				}
				
				vertex = polygon.vertices[j-1];
				verticeUvs.push( new THREE.Vector2( vertex.uv.x, vertex.uv.y ) );
				vertex = new THREE.Vector3( vertex.x, vertex.y, vertex.z );
				vertex.applyMatrix4(matrix);
				if ( typeof vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] !== 'undefined' ) {
					vertex_idx_b = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ];
				} else {
					geometry.vertices.push( vertex );
					vertex_idx_b = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] = geometry.vertices.length - 1;
				}
				
				vertex = polygon.vertices[j];
				verticeUvs.push( new THREE.Vector2( vertex.uv.x, vertex.uv.y ) );
				vertex = new THREE.Vector3( vertex.x, vertex.y, vertex.z );
				vertex.applyMatrix4(matrix);
				if ( typeof vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] !== 'undefined' ) {
					vertex_idx_c = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ];
				} else {
					geometry.vertices.push( vertex );
					vertex_idx_c = vertice_dict[ vertex.x + ',' + vertex.y + ',' + vertex.z ] = geometry.vertices.length - 1;
				}
				
				face = new THREE.Face3(
					vertex_idx_a,
					vertex_idx_b,
					vertex_idx_c,
					new THREE.Vector3( polygon.normal.x, polygon.normal.y, polygon.normal.z )
				);
				
				geometry.faces.push( face );
				geometry.faceVertexUvs[0].push( verticeUvs );
			}
			
		}
		return geometry;
	};
	ThreeBSP.prototype.toMesh = function( material ) {
		var geometry = this.toGeometry(),
			mesh = new THREE.Mesh( geometry, material );
		
		mesh.position.setFromMatrixPosition( this.matrix );
		mesh.rotation.setFromRotationMatrix( this.matrix );
		
		return mesh;
	};
	
	
	ThreeBSP.Polygon = function( vertices, normal, w ) {
		if ( !( vertices instanceof Array ) ) {
			vertices = [];
		}
		
		this.vertices = vertices;
		if ( vertices.length > 0 ) {
			this.calculateProperties();
		} else {
			this.normal = this.w = undefined;
		}
	};
	ThreeBSP.Polygon.prototype.calculateProperties = function() {
		var a = this.vertices[0],
			b = this.vertices[1],
			c = this.vertices[2];
			
		this.normal = b.clone().subtract( a ).cross(
			c.clone().subtract( a )
		).normalize();
		
		this.w = this.normal.clone().dot( a );
		
		return this;
	};
	ThreeBSP.Polygon.prototype.clone = function() {
		var i, vertice_count,
			polygon = new ThreeBSP.Polygon;
		
		for ( i = 0, vertice_count = this.vertices.length; i < vertice_count; i++ ) {
			polygon.vertices.push( this.vertices[i].clone() );
		};
		polygon.calculateProperties();
		
		return polygon;
	};
	
	ThreeBSP.Polygon.prototype.flip = function() {
		var i, vertices = [];
		
		this.normal.multiplyScalar( -1 );
		this.w *= -1;
		
		for ( i = this.vertices.length - 1; i >= 0; i-- ) {
			vertices.push( this.vertices[i] );
		};
		this.vertices = vertices;
		
		return this;
	};
	ThreeBSP.Polygon.prototype.classifyVertex = function( vertex ) {  
		var side_value = this.normal.dot( vertex ) - this.w;
		
		if ( side_value < -EPSILON ) {
			return BACK;
		} else if ( side_value > EPSILON ) {
			return FRONT;
		} else {
			return COPLANAR;
		}
	};
	ThreeBSP.Polygon.prototype.classifySide = function( polygon ) {
		var i, vertex, classification,
			num_positive = 0,
			num_negative = 0,
			vertice_count = polygon.vertices.length;
		
		for ( i = 0; i < vertice_count; i++ ) {
			vertex = polygon.vertices[i];
			classification = this.classifyVertex( vertex );
			if ( classification === FRONT ) {
				num_positive++;
			} else if ( classification === BACK ) {
				num_negative++;
			}
		}
		
        if ( num_positive === vertice_count && num_negative === 0 ) {
            return FRONT;
        } else if ( num_positive === 0 && num_negative === vertice_count ) {
            return BACK;
        } else if ( num_positive > 0 && num_negative > 0 ) {
            return SPANNING;
        } else {
            return COPLANAR;
        }
	};
	ThreeBSP.Polygon.prototype.splitPolygon = function( polygon, coplanar_front, coplanar_back, front, back ) {
		var classification = this.classifySide( polygon );
		
		if ( classification === COPLANAR ) {
			
			( this.normal.dot( polygon.normal ) > 0 ? coplanar_front : coplanar_back ).push( polygon );
			
		} else if ( classification === FRONT ) {
			
			front.push( polygon );
			
		} else if ( classification === BACK ) {
			
			back.push( polygon );
			
		} else {
			
			var vertice_count,
				i, j, ti, tj, vi, vj,
				t, v,
				f = [],
				b = [];
			
			for ( i = 0, vertice_count = polygon.vertices.length; i < vertice_count; i++ ) {
				
				j = (i + 1) % vertice_count;
				vi = polygon.vertices[i];
				vj = polygon.vertices[j];
				ti = this.classifyVertex( vi );
				tj = this.classifyVertex( vj );
				
				if ( ti != BACK ) f.push( vi );
				if ( ti != FRONT ) b.push( vi );
				if ( (ti | tj) === SPANNING ) {
					t = ( this.w - this.normal.dot( vi ) ) / this.normal.dot( vj.clone().subtract( vi ) );
					v = vi.interpolate( vj, t );
					f.push( v );
					b.push( v );
				}
			}
			
			
			if ( f.length >= 3 ) front.push( new ThreeBSP.Polygon( f ).calculateProperties() );
			if ( b.length >= 3 ) back.push( new ThreeBSP.Polygon( b ).calculateProperties() );
		}
	};
	
	ThreeBSP.Vertex = function( x, y, z, normal, uv ) {
		this.x = x;
		this.y = y;
		this.z = z;
		this.normal = normal || new THREE.Vector3;
		this.uv = uv || new THREE.Vector2;
	};
	ThreeBSP.Vertex.prototype.clone = function() {
		return new ThreeBSP.Vertex( this.x, this.y, this.z, this.normal.clone(), this.uv.clone() );
	};
	ThreeBSP.Vertex.prototype.add = function( vertex ) {
		this.x += vertex.x;
		this.y += vertex.y;
		this.z += vertex.z;
		return this;
	};
	ThreeBSP.Vertex.prototype.subtract = function( vertex ) {
		this.x -= vertex.x;
		this.y -= vertex.y;
		this.z -= vertex.z;
		return this;
	};
	ThreeBSP.Vertex.prototype.multiplyScalar = function( scalar ) {
		this.x *= scalar;
		this.y *= scalar;
		this.z *= scalar;
		return this;
	};
	ThreeBSP.Vertex.prototype.cross = function( vertex ) {
		var x = this.x,
			y = this.y,
			z = this.z;

		this.x = y * vertex.z - z * vertex.y;
		this.y = z * vertex.x - x * vertex.z;
		this.z = x * vertex.y - y * vertex.x;
		
		return this;
	};
	ThreeBSP.Vertex.prototype.normalize = function() {
		var length = Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z );
		
		this.x /= length;
		this.y /= length;
		this.z /= length;
		
		return this;
	};
	ThreeBSP.Vertex.prototype.dot = function( vertex ) {
		return this.x * vertex.x + this.y * vertex.y + this.z * vertex.z;
	};
	ThreeBSP.Vertex.prototype.lerp = function( a, t ) {
		this.add(
			a.clone().subtract( this ).multiplyScalar( t )
		);
		
		this.normal.add(
			a.normal.clone().sub( this.normal ).multiplyScalar( t )
		);
		
		this.uv.add(
			a.uv.clone().sub( this.uv ).multiplyScalar( t )
		);
		
		return this;
	};
	ThreeBSP.Vertex.prototype.interpolate = function( other, t ) {
		return this.clone().lerp( other, t );
	};
	ThreeBSP.Vertex.prototype.applyMatrix4 = function ( m ) {

		// input: THREE.Matrix4 affine matrix

		var x = this.x, y = this.y, z = this.z;

		var e = m.elements;

		this.x = e[0] * x + e[4] * y + e[8]  * z + e[12];
		this.y = e[1] * x + e[5] * y + e[9]  * z + e[13];
		this.z = e[2] * x + e[6] * y + e[10] * z + e[14];

		return this;

	}
	
	
	ThreeBSP.Node = function( polygons ) {
		var i, polygon_count,
			front = [],
			back = [];

		this.polygons = [];
		this.front = this.back = undefined;
		
		if ( !(polygons instanceof Array) || polygons.length === 0 ) return;

		this.divider = polygons[0].clone();
		
		for ( i = 0, polygon_count = polygons.length; i < polygon_count; i++ ) {
			this.divider.splitPolygon( polygons[i], this.polygons, this.polygons, front, back );
		}   
		
		if ( front.length > 0 ) {
			this.front = new ThreeBSP.Node( front );
		}
		
		if ( back.length > 0 ) {
			this.back = new ThreeBSP.Node( back );
		}
	};
	ThreeBSP.Node.isConvex = function( polygons ) {
		var i, j;
		for ( i = 0; i < polygons.length; i++ ) {
			for ( j = 0; j < polygons.length; j++ ) {
				if ( i !== j && polygons[i].classifySide( polygons[j] ) !== BACK ) {
					return false;
				}
			}
		}
		return true;
	};
	ThreeBSP.Node.prototype.build = function( polygons ) {
		var i, polygon_count,
			front = [],
			back = [];
		
		if ( !this.divider ) {
			this.divider = polygons[0].clone();
		}

		for ( i = 0, polygon_count = polygons.length; i < polygon_count; i++ ) {
			this.divider.splitPolygon( polygons[i], this.polygons, this.polygons, front, back );
		}   
		
		if ( front.length > 0 ) {
			if ( !this.front ) this.front = new ThreeBSP.Node();
			this.front.build( front );
		}
		
		if ( back.length > 0 ) {
			if ( !this.back ) this.back = new ThreeBSP.Node();
			this.back.build( back );
		}
	};
	ThreeBSP.Node.prototype.allPolygons = function() {
		var polygons = this.polygons.slice();
		if ( this.front ) polygons = polygons.concat( this.front.allPolygons() );
		if ( this.back ) polygons = polygons.concat( this.back.allPolygons() );
		return polygons;
	};
	ThreeBSP.Node.prototype.clone = function() {
		var node = new ThreeBSP.Node();
		
		node.divider = this.divider.clone();
		node.polygons = this.polygons.map( function( polygon ) { return polygon.clone(); } );
		node.front = this.front && this.front.clone();
		node.back = this.back && this.back.clone();
		
		return node;
	};
	ThreeBSP.Node.prototype.invert = function() {
		var i, polygon_count, temp;
		
		for ( i = 0, polygon_count = this.polygons.length; i < polygon_count; i++ ) {
			this.polygons[i].flip();
		}
		
		this.divider.flip();
		if ( this.front ) this.front.invert();
		if ( this.back ) this.back.invert();
		
		temp = this.front;
		this.front = this.back;
		this.back = temp;
		
		return this;
	};
	ThreeBSP.Node.prototype.clipPolygons = function( polygons ) {
		var i, polygon_count,
			front, back;

		if ( !this.divider ) return polygons.slice();
		
		front = [], back = [];
		
		for ( i = 0, polygon_count = polygons.length; i < polygon_count; i++ ) {
			this.divider.splitPolygon( polygons[i], front, back, front, back );
		}

		if ( this.front ) front = this.front.clipPolygons( front );
		if ( this.back ) back = this.back.clipPolygons( back );
		else back = [];

		return front.concat( back );
	};
	
	ThreeBSP.Node.prototype.clipTo = function( node ) {
		this.polygons = node.clipPolygons( this.polygons );
		if ( this.front ) this.front.clipTo( node );
		if ( this.back ) this.back.clipTo( node );
	};
	
	
	return ThreeBSP;
})();