three.js/src/extras/GeometryUtils.js

/**
 * @author mrdoob / http://mrdoob.com/
 * @author alteredq / http://alteredqualia.com/
 */

THREE.GeometryUtils = {

	// Merge two geometries or geometry and geometry from object (using object's transform)

	merge: function ( geometry1, object2 /* mesh | geometry */ ) {

		var matrix, matrixRotation,
		vertexOffset = geometry1.vertices.length,
		uvPosition = geometry1.faceVertexUvs[ 0 ].length,
		geometry2 = object2 instanceof THREE.Mesh ? object2.geometry : object2,
		vertices1 = geometry1.vertices,
		vertices2 = geometry2.vertices,
		faces1 = geometry1.faces,
		faces2 = geometry2.faces,
		uvs1 = geometry1.faceVertexUvs[ 0 ],
		uvs2 = geometry2.faceVertexUvs[ 0 ];

		var geo1MaterialsMap = {};

		for ( var i = 0; i < geometry1.materials.length; i ++ ) {

			var id = geometry1.materials[ i ].id;

			geo1MaterialsMap[ id ] = i;

		}

		if ( object2 instanceof THREE.Mesh ) {

			object2.matrixAutoUpdate && object2.updateMatrix();

			matrix = object2.matrix;
			matrixRotation = new THREE.Matrix4();
			matrixRotation.extractRotation( matrix, object2.scale );

		}

		// vertices

		for ( var i = 0, il = vertices2.length; i < il; i ++ ) {

			var vertex = vertices2[ i ];

			var vertexCopy = vertex.clone();

			if ( matrix ) matrix.multiplyVector3( vertexCopy );

			vertices1.push( vertexCopy );

		}

		// faces

		for ( i = 0, il = faces2.length; i < il; i ++ ) {

			var face = faces2[ i ], faceCopy, normal, color,
			faceVertexNormals = face.vertexNormals,
			faceVertexColors = face.vertexColors;

			if ( face instanceof THREE.Face3 ) {

				faceCopy = new THREE.Face3( face.a + vertexOffset, face.b + vertexOffset, face.c + vertexOffset );

			} else if ( face instanceof THREE.Face4 ) {

				faceCopy = new THREE.Face4( face.a + vertexOffset, face.b + vertexOffset, face.c + vertexOffset, face.d + vertexOffset );

			}

			faceCopy.normal.copy( face.normal );

			if ( matrixRotation ) matrixRotation.multiplyVector3( faceCopy.normal );

			for ( var j = 0, jl = faceVertexNormals.length; j < jl; j ++ ) {

				normal = faceVertexNormals[ j ].clone();

				if ( matrixRotation ) matrixRotation.multiplyVector3( normal );

				faceCopy.vertexNormals.push( normal );

			}

			faceCopy.color.copy( face.color );

			for ( var j = 0, jl = faceVertexColors.length; j < jl; j ++ ) {

				color = faceVertexColors[ j ];
				faceCopy.vertexColors.push( color.clone() );

			}

			if ( face.materialIndex !== undefined ) {

				var material2 = geometry2.materials[ face.materialIndex ];
				var materialId2 = material2.id;

				var materialIndex = geo1MaterialsMap[ materialId2 ];

				if ( materialIndex === undefined ) {

					materialIndex = geometry1.materials.length;
					geo1MaterialsMap[ materialId2 ] = materialIndex;

					geometry1.materials.push( material2 );

				}

				faceCopy.materialIndex = materialIndex;

			}

			faceCopy.centroid.copy( face.centroid );
			if ( matrix ) matrix.multiplyVector3( faceCopy.centroid );

			faces1.push( faceCopy );

		}

		// uvs

		for ( i = 0, il = uvs2.length; i < il; i ++ ) {

			var uv = uvs2[ i ], uvCopy = [];

			for ( var j = 0, jl = uv.length; j < jl; j ++ ) {

				uvCopy.push( new THREE.UV( uv[ j ].u, uv[ j ].v ) );

			}

			uvs1.push( uvCopy );

		}

	},

	clone: function ( geometry ) {

		var cloneGeo = new THREE.Geometry();

		var i, il;

		var vertices = geometry.vertices,
			faces = geometry.faces,
			uvs = geometry.faceVertexUvs[ 0 ];

		// materials

		if ( geometry.materials ) {

			cloneGeo.materials = geometry.materials.slice();

		}

		// vertices

		for ( i = 0, il = vertices.length; i < il; i ++ ) {

			var vertex = vertices[ i ];

			cloneGeo.vertices.push( vertex.clone() );

		}

		// faces

		for ( i = 0, il = faces.length; i < il; i ++ ) {

			var face = faces[ i ];

			cloneGeo.faces.push( face.clone() );

		}

		// uvs

		for ( i = 0, il = uvs.length; i < il; i ++ ) {

			var uv = uvs[ i ], uvCopy = [];

			for ( var j = 0, jl = uv.length; j < jl; j ++ ) {

				uvCopy.push( new THREE.UV( uv[ j ].u, uv[ j ].v ) );

			}

			cloneGeo.faceVertexUvs[ 0 ].push( uvCopy );

		}

		return cloneGeo;

	},

	// Get random point in triangle (via barycentric coordinates)
	// 	(uniform distribution)
	// 	http://www.cgafaq.info/wiki/Random_Point_In_Triangle

	randomPointInTriangle: function ( vectorA, vectorB, vectorC ) {

		var a, b, c,
			point = new THREE.Vector3(),
			tmp = THREE.GeometryUtils.__v1;

		a = THREE.GeometryUtils.random();
		b = THREE.GeometryUtils.random();

		if ( ( a + b ) > 1 ) {

			a = 1 - a;
			b = 1 - b;

		}

		c = 1 - a - b;

		point.copy( vectorA );
		point.multiplyScalar( a );

		tmp.copy( vectorB );
		tmp.multiplyScalar( b );

		point.addSelf( tmp );

		tmp.copy( vectorC );
		tmp.multiplyScalar( c );

		point.addSelf( tmp );

		return point;

	},

	// Get random point in face (triangle / quad)
	// (uniform distribution)

	randomPointInFace: function ( face, geometry, useCachedAreas ) {

		var vA, vB, vC, vD;

		if ( face instanceof THREE.Face3 ) {

			vA = geometry.vertices[ face.a ];
			vB = geometry.vertices[ face.b ];
			vC = geometry.vertices[ face.c ];

			return THREE.GeometryUtils.randomPointInTriangle( vA, vB, vC );

		} else if ( face instanceof THREE.Face4 ) {

			vA = geometry.vertices[ face.a ];
			vB = geometry.vertices[ face.b ];
			vC = geometry.vertices[ face.c ];
			vD = geometry.vertices[ face.d ];

			var area1, area2;

			if ( useCachedAreas ) {

				if ( face._area1 && face._area2 ) {

					area1 = face._area1;
					area2 = face._area2;

				} else {

					area1 = THREE.GeometryUtils.triangleArea( vA, vB, vD );
					area2 = THREE.GeometryUtils.triangleArea( vB, vC, vD );

					face._area1 = area1;
					face._area2 = area2;

				}

			} else {

				area1 = THREE.GeometryUtils.triangleArea( vA, vB, vD ),
				area2 = THREE.GeometryUtils.triangleArea( vB, vC, vD );

			}

			var r = THREE.GeometryUtils.random() * ( area1 + area2 );

			if ( r < area1 ) {

				return THREE.GeometryUtils.randomPointInTriangle( vA, vB, vD );

			} else {

				return THREE.GeometryUtils.randomPointInTriangle( vB, vC, vD );

			}

		}

	},

	// Get uniformly distributed random points in mesh
	// 	- create array with cumulative sums of face areas
	//  - pick random number from 0 to total area
	//  - find corresponding place in area array by binary search
	//	- get random point in face

	randomPointsInGeometry: function ( geometry, n ) {

		var face, i,
			faces = geometry.faces,
			vertices = geometry.vertices,
			il = faces.length,
			totalArea = 0,
			cumulativeAreas = [],
			vA, vB, vC, vD;

		// precompute face areas

		for ( i = 0; i < il; i ++ ) {

			face = faces[ i ];

			if ( face instanceof THREE.Face3 ) {

				vA = vertices[ face.a ];
				vB = vertices[ face.b ];
				vC = vertices[ face.c ];

				face._area = THREE.GeometryUtils.triangleArea( vA, vB, vC );

			} else if ( face instanceof THREE.Face4 ) {

				vA = vertices[ face.a ];
				vB = vertices[ face.b ];
				vC = vertices[ face.c ];
				vD = vertices[ face.d ];

				face._area1 = THREE.GeometryUtils.triangleArea( vA, vB, vD );
				face._area2 = THREE.GeometryUtils.triangleArea( vB, vC, vD );

				face._area = face._area1 + face._area2;

			}

			totalArea += face._area;

			cumulativeAreas[ i ] = totalArea;

		}

		// binary search cumulative areas array

		function binarySearchIndices( value ) {

			function binarySearch( start, end ) {

				// return closest larger index
				// if exact number is not found

				if ( end < start )
					return start;

				var mid = start + Math.floor( ( end - start ) / 2 );

				if ( cumulativeAreas[ mid ] > value ) {

					return binarySearch( start, mid - 1 );

				} else if ( cumulativeAreas[ mid ] < value ) {

					return binarySearch( mid + 1, end );

				} else {

					return mid;

				}

			}

			var result = binarySearch( 0, cumulativeAreas.length - 1 )
			return result;

		}

		// pick random face weighted by face area

		var r, index,
			result = [];

		var stats = {};

		for ( i = 0; i < n; i ++ ) {

			r = THREE.GeometryUtils.random() * totalArea;

			index = binarySearchIndices( r );

			result[ i ] = THREE.GeometryUtils.randomPointInFace( faces[ index ], geometry, true );

			if ( ! stats[ index ] ) {

				stats[ index ] = 1;

			} else {

				stats[ index ] += 1;

			}

		}

		return result;

	},

	// Get triangle area (by Heron's formula)
	// 	http://en.wikipedia.org/wiki/Heron%27s_formula

	triangleArea: function ( vectorA, vectorB, vectorC ) {

		var s, a, b, c,
			tmp = THREE.GeometryUtils.__v1;

		tmp.sub( vectorA, vectorB );
		a = tmp.length();

		tmp.sub( vectorA, vectorC );
		b = tmp.length();

		tmp.sub( vectorB, vectorC );
		c = tmp.length();

		s = 0.5 * ( a + b + c );

		return Math.sqrt( s * ( s - a ) * ( s - b ) * ( s - c ) );

	},

	// Center geometry so that 0,0,0 is in center of bounding box

	center: function ( geometry ) {

		geometry.computeBoundingBox();

		var bb = geometry.boundingBox;

		var offset = new THREE.Vector3();

		offset.add( bb.min, bb.max );
		offset.multiplyScalar( -0.5 );

		geometry.applyMatrix( new THREE.Matrix4().makeTranslation( offset.x, offset.y, offset.z ) );
		geometry.computeBoundingBox();

		return offset;

	},

	// Normalize UVs to be from <0,1>
	// (for now just the first set of UVs)

	normalizeUVs: function ( geometry ) {

		var uvSet = geometry.faceVertexUvs[ 0 ];

		for ( var i = 0, il = uvSet.length; i < il; i ++ ) {

			var uvs = uvSet[ i ];

			for ( var j = 0, jl = uvs.length; j < jl; j ++ ) {

				// texture repeat

				if( uvs[ j ].u !== 1.0 ) uvs[ j ].u = uvs[ j ].u - Math.floor( uvs[ j ].u );
				if( uvs[ j ].v !== 1.0 ) uvs[ j ].v = uvs[ j ].v - Math.floor( uvs[ j ].v );

			}

		}

	},

	triangulateQuads: function ( geometry ) {

		var i, il, j, jl;

		var faces = [];
		var faceUvs = [];
		var faceVertexUvs = [];

		for ( i = 0, il = geometry.faceUvs.length; i < il; i ++ ) {

			faceUvs[ i ] = [];

		}

		for ( i = 0, il = geometry.faceVertexUvs.length; i < il; i ++ ) {

			faceVertexUvs[ i ] = [];

		}

		for ( i = 0, il = geometry.faces.length; i < il; i ++ ) {

			var face = geometry.faces[ i ];

			if ( face instanceof THREE.Face4 ) {

				var a = face.a;
				var b = face.b;
				var c = face.c;
				var d = face.d;

				var triA = new THREE.Face3();
				var triB = new THREE.Face3();

				triA.color.copy( face.color );
				triB.color.copy( face.color );

				triA.materialIndex = face.materialIndex;
				triB.materialIndex = face.materialIndex;

				triA.a = a;
				triA.b = b;
				triA.c = d;

				triB.a = b;
				triB.b = c;
				triB.c = d;

				if ( face.vertexColors.length === 4 ) {

					triA.vertexColors[ 0 ] = face.vertexColors[ 0 ].clone();
					triA.vertexColors[ 1 ] = face.vertexColors[ 1 ].clone();
					triA.vertexColors[ 2 ] = face.vertexColors[ 3 ].clone();

					triB.vertexColors[ 0 ] = face.vertexColors[ 1 ].clone();
					triB.vertexColors[ 1 ] = face.vertexColors[ 2 ].clone();
					triB.vertexColors[ 2 ] = face.vertexColors[ 3 ].clone();

				}

				faces.push( triA, triB );

				for ( j = 0, jl = geometry.faceVertexUvs.length; j < jl; j ++ ) {

					if ( geometry.faceVertexUvs[ j ].length ) {

						var uvs = geometry.faceVertexUvs[ j ][ i ];

						var uvA = uvs[ 0 ];
						var uvB = uvs[ 1 ];
						var uvC = uvs[ 2 ];
						var uvD = uvs[ 3 ];

						var uvsTriA = [ uvA.clone(), uvB.clone(), uvD.clone() ];
						var uvsTriB = [ uvB.clone(), uvC.clone(), uvD.clone() ];

						faceVertexUvs[ j ].push( uvsTriA, uvsTriB );

					}

				}

				for ( j = 0, jl = geometry.faceUvs.length; j < jl; j ++ ) {

					if ( geometry.faceUvs[ j ].length ) {

						var faceUv = geometry.faceUvs[ j ][ i ];

						faceUvs[ j ].push( faceUv, faceUv );

					}

				}

			} else {

				faces.push( face );

				for ( j = 0, jl = geometry.faceUvs.length; j < jl; j ++ ) {

					faceUvs[ j ].push( geometry.faceUvs[ j ][ i ] );

				}

				for ( j = 0, jl = geometry.faceVertexUvs.length; j < jl; j ++ ) {

					faceVertexUvs[ j ].push( geometry.faceVertexUvs[ j ][ i ] );

				}

			}

		}

		geometry.faces = faces;
		geometry.faceUvs = faceUvs;
		geometry.faceVertexUvs = faceVertexUvs;

		geometry.computeCentroids();
		geometry.computeFaceNormals();
		geometry.computeVertexNormals();

		if ( geometry.hasTangents ) geometry.computeTangents();

	},

	// Make all faces use unique vertices
	// so that each face can be separated from others

	explode: function( geometry ) {

		var vertices = [];

		for ( var i = 0, il = geometry.faces.length; i < il; i ++ ) {

			var n = vertices.length;

			var face = geometry.faces[ i ];

			if ( face instanceof THREE.Face4 ) {

				var a = face.a;
				var b = face.b;
				var c = face.c;
				var d = face.d;

				var va = geometry.vertices[ a ];
				var vb = geometry.vertices[ b ];
				var vc = geometry.vertices[ c ];
				var vd = geometry.vertices[ d ];

				vertices.push( va.clone() );
				vertices.push( vb.clone() );
				vertices.push( vc.clone() );
				vertices.push( vd.clone() );

				face.a = n;
				face.b = n + 1;
				face.c = n + 2;
				face.d = n + 3;

			} else {

				var a = face.a;
				var b = face.b;
				var c = face.c;

				var va = geometry.vertices[ a ];
				var vb = geometry.vertices[ b ];
				var vc = geometry.vertices[ c ];

				vertices.push( va.clone() );
				vertices.push( vb.clone() );
				vertices.push( vc.clone() );

				face.a = n;
				face.b = n + 1;
				face.c = n + 2;

			}

		}

		geometry.vertices = vertices;
		delete geometry.__tmpVertices;

	},

	// Break faces with edges longer than maxEdgeLength
	// - not recursive

	tessellate: function ( geometry, maxEdgeLength ) {

		var i, il, face,
		a, b, c, d,
		va, vb, vc, vd,
		dab, dbc, dac, dcd, dad,
		m, m1, m2,
		vm, vm1, vm2,
		vnm, vnm1, vnm2,
		vcm, vcm1, vcm2,
		triA, triB,
		quadA, quadB,
		edge;

		var faces = [];
		var faceVertexUvs = [];

		for ( i = 0, il = geometry.faceVertexUvs.length; i < il; i ++ ) {

			faceVertexUvs[ i ] = [];

		}

		for ( i = 0, il = geometry.faces.length; i < il; i ++ ) {

			face = geometry.faces[ i ];

			if ( face instanceof THREE.Face3 ) {

				a = face.a;
				b = face.b;
				c = face.c;

				va = geometry.vertices[ a ];
				vb = geometry.vertices[ b ];
				vc = geometry.vertices[ c ];

				dab = va.distanceTo( vb );
				dbc = vb.distanceTo( vc );
				dac = va.distanceTo( vc );

				if ( dab > maxEdgeLength || dbc > maxEdgeLength || dac > maxEdgeLength ) {

					m = geometry.vertices.length;

					triA = face.clone();
					triB = face.clone();

					if ( dab >= dbc && dab >= dac ) {

						vm = va.clone();
						vm.lerpSelf( vb, 0.5 );

						triA.a = a;
						triA.b = m;
						triA.c = c;

						triB.a = m;
						triB.b = b;
						triB.c = c;

						if ( face.vertexNormals.length === 3 ) {

							vnm = face.vertexNormals[ 0 ].clone();
							vnm.lerpSelf( face.vertexNormals[ 1 ], 0.5 );

							triA.vertexNormals[ 1 ].copy( vnm );
							triB.vertexNormals[ 0 ].copy( vnm );

						}

						if ( face.vertexColors.length === 3 ) {

							vcm = face.vertexColors[ 0 ].clone();
							vcm.lerpSelf( face.vertexColors[ 1 ], 0.5 );

							triA.vertexColors[ 1 ].copy( vcm );
							triB.vertexColors[ 0 ].copy( vcm );

						}

						edge = 0;

					} else if ( dbc >= dab && dbc >= dac ) {

						vm = vb.clone();
						vm.lerpSelf( vc, 0.5 );

						triA.a = a;
						triA.b = b;
						triA.c = m;

						triB.a = m;
						triB.b = c;
						triB.c = a;

						if ( face.vertexNormals.length === 3 ) {

							vnm = face.vertexNormals[ 1 ].clone();
							vnm.lerpSelf( face.vertexNormals[ 2 ], 0.5 );

							triA.vertexNormals[ 2 ].copy( vnm );

							triB.vertexNormals[ 0 ].copy( vnm );
							triB.vertexNormals[ 1 ].copy( face.vertexNormals[ 2 ] );
							triB.vertexNormals[ 2 ].copy( face.vertexNormals[ 0 ] );

						}

						if ( face.vertexColors.length === 3 ) {

							vcm = face.vertexColors[ 1 ].clone();
							vcm.lerpSelf( face.vertexColors[ 2 ], 0.5 );

							triA.vertexColors[ 2 ].copy( vcm );

							triB.vertexColors[ 0 ].copy( vcm );
							triB.vertexColors[ 1 ].copy( face.vertexColors[ 2 ] );
							triB.vertexColors[ 2 ].copy( face.vertexColors[ 0 ] );

						}

						edge = 1;

					} else {

						vm = va.clone();
						vm.lerpSelf( vc, 0.5 );

						triA.a = a;
						triA.b = b;
						triA.c = m;

						triB.a = m;
						triB.b = b;
						triB.c = c;

						if ( face.vertexNormals.length === 3 ) {

							vnm = face.vertexNormals[ 0 ].clone();
							vnm.lerpSelf( face.vertexNormals[ 2 ], 0.5 );

							triA.vertexNormals[ 2 ].copy( vnm );
							triB.vertexNormals[ 0 ].copy( vnm );

						}

						if ( face.vertexColors.length === 3 ) {

							vcm = face.vertexColors[ 0 ].clone();
							vcm.lerpSelf( face.vertexColors[ 2 ], 0.5 );

							triA.vertexColors[ 2 ].copy( vcm );
							triB.vertexColors[ 0 ].copy( vcm );

						}

						edge = 2;

					}

					faces.push( triA, triB );
					geometry.vertices.push( vm );

					var j, jl, uvs, uvA, uvB, uvC, uvM, uvsTriA, uvsTriB;

					for ( j = 0, jl = geometry.faceVertexUvs.length; j < jl; j ++ ) {

						if ( geometry.faceVertexUvs[ j ].length ) {

							uvs = geometry.faceVertexUvs[ j ][ i ];

							uvA = uvs[ 0 ];
							uvB = uvs[ 1 ];
							uvC = uvs[ 2 ];

							// AB

							if ( edge === 0 ) {

								uvM = uvA.clone();
								uvM.lerpSelf( uvB, 0.5 );

								uvsTriA = [ uvA.clone(), uvM.clone(), uvC.clone() ];
								uvsTriB = [ uvM.clone(), uvB.clone(), uvC.clone() ];

							// BC

							} else if ( edge === 1 ) {

								uvM = uvB.clone();
								uvM.lerpSelf( uvC, 0.5 );

								uvsTriA = [ uvA.clone(), uvB.clone(), uvM.clone() ];
								uvsTriB = [ uvM.clone(), uvC.clone(), uvA.clone() ];

							// AC

							} else {

								uvM = uvA.clone();
								uvM.lerpSelf( uvC, 0.5 );

								uvsTriA = [ uvA.clone(), uvB.clone(), uvM.clone() ];
								uvsTriB = [ uvM.clone(), uvB.clone(), uvC.clone() ];

							}

							faceVertexUvs[ j ].push( uvsTriA, uvsTriB );

						}

					}

				} else {

					faces.push( face );

					for ( j = 0, jl = geometry.faceVertexUvs.length; j < jl; j ++ ) {

						faceVertexUvs[ j ].push( geometry.faceVertexUvs[ j ][ i ] );

					}

				}

			} else {

				a = face.a;
				b = face.b;
				c = face.c;
				d = face.d;

				va = geometry.vertices[ a ];
				vb = geometry.vertices[ b ];
				vc = geometry.vertices[ c ];
				vd = geometry.vertices[ d ];

				dab = va.distanceTo( vb );
				dbc = vb.distanceTo( vc );
				dcd = vc.distanceTo( vd );
				dad = va.distanceTo( vd );

				if ( dab > maxEdgeLength || dbc > maxEdgeLength || dcd > maxEdgeLength || dad > maxEdgeLength ) {

					m1 = geometry.vertices.length;
					m2 = geometry.vertices.length + 1;

					quadA = face.clone();
					quadB = face.clone();

					if ( ( dab >= dbc && dab >= dcd && dab >= dad ) || ( dcd >= dbc && dcd >= dab && dcd >= dad ) ) {

						vm1 = va.clone();
						vm1.lerpSelf( vb, 0.5 );

						vm2 = vc.clone();
						vm2.lerpSelf( vd, 0.5 );

						quadA.a = a;
						quadA.b = m1;
						quadA.c = m2;
						quadA.d = d;

						quadB.a = m1;
						quadB.b = b;
						quadB.c = c;
						quadB.d = m2;

						if ( face.vertexNormals.length === 4 ) {

							vnm1 = face.vertexNormals[ 0 ].clone();
							vnm1.lerpSelf( face.vertexNormals[ 1 ], 0.5 );

							vnm2 = face.vertexNormals[ 2 ].clone();
							vnm2.lerpSelf( face.vertexNormals[ 3 ], 0.5 );

							quadA.vertexNormals[ 1 ].copy( vnm1 );
							quadA.vertexNormals[ 2 ].copy( vnm2 );

							quadB.vertexNormals[ 0 ].copy( vnm1 );
							quadB.vertexNormals[ 3 ].copy( vnm2 );

						}

						if ( face.vertexColors.length === 4 ) {

							vcm1 = face.vertexColors[ 0 ].clone();
							vcm1.lerpSelf( face.vertexColors[ 1 ], 0.5 );

							vcm2 = face.vertexColors[ 2 ].clone();
							vcm2.lerpSelf( face.vertexColors[ 3 ], 0.5 );

							quadA.vertexColors[ 1 ].copy( vcm1 );
							quadA.vertexColors[ 2 ].copy( vcm2 );

							quadB.vertexColors[ 0 ].copy( vcm1 );
							quadB.vertexColors[ 3 ].copy( vcm2 );

						}

						edge = 0;

					} else {

						vm1 = vb.clone();
						vm1.lerpSelf( vc, 0.5 );

						vm2 = vd.clone();
						vm2.lerpSelf( va, 0.5 );

						quadA.a = a;
						quadA.b = b;
						quadA.c = m1;
						quadA.d = m2;

						quadB.a = m2;
						quadB.b = m1;
						quadB.c = c;
						quadB.d = d;

						if ( face.vertexNormals.length === 4 ) {

							vnm1 = face.vertexNormals[ 1 ].clone();
							vnm1.lerpSelf( face.vertexNormals[ 2 ], 0.5 );

							vnm2 = face.vertexNormals[ 3 ].clone();
							vnm2.lerpSelf( face.vertexNormals[ 0 ], 0.5 );

							quadA.vertexNormals[ 2 ].copy( vnm1 );
							quadA.vertexNormals[ 3 ].copy( vnm2 );

							quadB.vertexNormals[ 0 ].copy( vnm2 );
							quadB.vertexNormals[ 1 ].copy( vnm1 );

						}

						if ( face.vertexColors.length === 4 ) {

							vcm1 = face.vertexColors[ 1 ].clone();
							vcm1.lerpSelf( face.vertexColors[ 2 ], 0.5 );

							vcm2 = face.vertexColors[ 3 ].clone();
							vcm2.lerpSelf( face.vertexColors[ 0 ], 0.5 );

							quadA.vertexColors[ 2 ].copy( vcm1 );
							quadA.vertexColors[ 3 ].copy( vcm2 );

							quadB.vertexColors[ 0 ].copy( vcm2 );
							quadB.vertexColors[ 1 ].copy( vcm1 );

						}

						edge = 1;

					}

					faces.push( quadA, quadB );
					geometry.vertices.push( vm1, vm2 );

					var j, jl, uvs, uvA, uvB, uvC, uvD, uvM1, uvM2, uvsQuadA, uvsQuadB;

					for ( j = 0, jl = geometry.faceVertexUvs.length; j < jl; j ++ ) {

						if ( geometry.faceVertexUvs[ j ].length ) {

							uvs = geometry.faceVertexUvs[ j ][ i ];

							uvA = uvs[ 0 ];
							uvB = uvs[ 1 ];
							uvC = uvs[ 2 ];
							uvD = uvs[ 3 ];

							// AB + CD

							if ( edge === 0 ) {

								uvM1 = uvA.clone();
								uvM1.lerpSelf( uvB, 0.5 );

								uvM2 = uvC.clone();
								uvM2.lerpSelf( uvD, 0.5 );

								uvsQuadA = [ uvA.clone(), uvM1.clone(), uvM2.clone(), uvD.clone() ];
								uvsQuadB = [ uvM1.clone(), uvB.clone(), uvC.clone(), uvM2.clone() ];

							// BC + AD

							} else {

								uvM1 = uvB.clone();
								uvM1.lerpSelf( uvC, 0.5 );

								uvM2 = uvD.clone();
								uvM2.lerpSelf( uvA, 0.5 );

								uvsQuadA = [ uvA.clone(), uvB.clone(), uvM1.clone(), uvM2.clone() ];
								uvsQuadB = [ uvM2.clone(), uvM1.clone(), uvC.clone(), uvD.clone() ];

							}

							faceVertexUvs[ j ].push( uvsQuadA, uvsQuadB );

						}

					}

				} else {

					faces.push( face );

					for ( j = 0, jl = geometry.faceVertexUvs.length; j < jl; j ++ ) {

						faceVertexUvs[ j ].push( geometry.faceVertexUvs[ j ][ i ] );

					}

				}

			}

		}

		geometry.faces = faces;
		geometry.faceVertexUvs = faceVertexUvs;

	}

};

THREE.GeometryUtils.random = THREE.Math.random16;

THREE.GeometryUtils.__v1 = new THREE.Vector3();