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 */, materialIndexOffset ) {

		var matrix, normalMatrix,
		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 ];

		if ( materialIndexOffset === undefined ) materialIndexOffset = 0;

		if ( object2 instanceof THREE.Mesh ) {

			object2.matrixAutoUpdate && object2.updateMatrix();

			matrix = object2.matrix;

			normalMatrix = new THREE.Matrix3().getNormalMatrix( matrix );

		}

		// vertices

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

			var vertex = vertices2[ i ];

			var vertexCopy = vertex.clone();

			if ( matrix ) vertexCopy.applyMatrix4( matrix );

			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;

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

			if ( normalMatrix ) {

				faceCopy.normal.applyMatrix3( normalMatrix ).normalize();

			}

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

				normal = faceVertexNormals[ j ].clone();

				if ( normalMatrix ) {

					normal.applyMatrix3( normalMatrix ).normalize();

				}

				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() );

			}

			faceCopy.materialIndex = face.materialIndex + materialIndexOffset;

			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.Vector2( uv[ j ].x, uv[ j ].y ) );

			}

			uvs1.push( uvCopy );

		}

	},

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

	randomPointInTriangle: function () {

		var vector = new THREE.Vector3();

		return function ( vectorA, vectorB, vectorC ) {

			var point = new THREE.Vector3();

			var a = THREE.Math.random16();
			var b = THREE.Math.random16();

			if ( ( a + b ) > 1 ) {

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

			}

			var c = 1 - a - b;

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

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

			point.add( vector );

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

			point.add( vector );

			return point;

		};

	}(),

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

	randomPointInFace: function ( face, geometry, useCachedAreas ) {

		var vA, vB, vC, vD;

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

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

	},

	// 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 ];

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

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

			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.Math.random16() * 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 (half of parallelogram)
	//	http://mathworld.wolfram.com/TriangleArea.html

	triangleArea: function () {

		var vector1 = new THREE.Vector3();
		var vector2 = new THREE.Vector3();

		return function ( vectorA, vectorB, vectorC ) {

			vector1.subVectors( vectorB, vectorA );
			vector2.subVectors( vectorC, vectorA );
			vector1.cross( vector2 );

			return 0.5 * vector1.length();

		};

	}(),

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

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

		return offset;

	}

};