three.js/examples/js/modifiers/SubdivisionModifier.js

/*
 *	@author zz85 / http://twitter.com/blurspline / http://www.lab4games.net/zz85/blog 
 *
 *	Subdivision Geometry Modifier 
 *		using Loop Subdivision Scheme
 *
 *	References:
 *		http://graphics.stanford.edu/~mdfisher/subdivision.html
 *		http://www.holmes3d.net/graphics/subdivision/
 *		http://www.cs.rutgers.edu/~decarlo/readings/subdiv-sg00c.pdf
 *
 *	Known Issues:
 *		- currently doesn't handle UVs
 *		- currently doesn't handle "Sharp Edges"
 *
 */

THREE.SubdivisionModifier = function ( subdivisions ) {

	this.subdivisions = (subdivisions === undefined ) ? 1 : subdivisions;

};

// Applies the "modify" pattern
THREE.SubdivisionModifier.prototype.modify = function ( geometry ) {

	var repeats = this.subdivisions;

	while ( repeats-- > 0 ) {
		this.smooth( geometry );
	}

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

};

(function() {

	// Some constants
	var WARNINGS = !true; // Set to true for development
	var ABC = ['a', 'b', 'c'];
	

	function getEdge( a, b, map ) {

		var vertexIndexA = Math.min( a, b );
		var vertexIndexB = Math.max( a, b );

		var key = vertexIndexA + "_" + vertexIndexB;

		return map[ key ];

	}


	function processEdge( a, b, vertices, map, face, metaVertices ) {

		var vertexIndexA = Math.min( a, b );
		var vertexIndexB = Math.max( a, b );

		var key = vertexIndexA + "_" + vertexIndexB;

		var edge;

		if ( key in map ) {

			edge = map[ key ];

		} else {
			
			var vertexA = vertices[ vertexIndexA ];
			var vertexB = vertices[ vertexIndexB ];

			edge = {

				a: vertexA, // pointer reference
				b: vertexB,
				newEdge: null,
				// aIndex: a, // numbered reference
				// bIndex: b,
				faces: [] // pointers to face

			};

			map[ key ] = edge;

		}

		edge.faces.push( face );

		metaVertices[ a ].edges.push( edge );
		metaVertices[ b ].edges.push( edge );
		

	}

	function generateLookups( vertices, faces, metaVertices, edges ) {

		var i, il, face, edge;

		for (i=0, il=vertices.length; i < il; i++) {
			metaVertices[ i ] = { edges: [] };
		}
		
		for (i=0, il=faces.length; i < il; i++) {
			face = faces[i];

			processEdge( face.a, face.b, vertices, edges, face, metaVertices );
			processEdge( face.b, face.c, vertices, edges, face, metaVertices );
			processEdge( face.c, face.a, vertices, edges, face, metaVertices );

		}
	}

	function newFace( newFaces, a, b, c ) {

		newFaces.push( new THREE.Face3( a, b, c ) );

	}


	/////////////////////////////

	// Performs one iteration of Subdivision
	THREE.SubdivisionModifier.prototype.smooth = function ( geometry ) {

		var tmp = new THREE.Vector3();

		var oldVertices, oldFaces;
		var newVertices, newFaces; // newUVs = [];

		var n, l, i, il, j, k;
		var metaVertices, sourceEdges;

		// new stuff.
		var sourceEdges, newEdgeVertices, newSourceVertices

		oldVertices = geometry.vertices; // { x, y, z}
		oldFaces = geometry.faces; // { a: oldVertex1, b: oldVertex2, c: oldVertex3 }

		/******************************************************
		 *
		 * Step 0: Preprocess Geometry to Generate edges Lookup
		 *
		 *******************************************************/

		metaVertices = new Array( oldVertices.length );
		sourceEdges = {}; // Edge => { oldVertex1, oldVertex2, faces[]  }

		generateLookups(oldVertices, oldFaces, metaVertices, sourceEdges);


		/******************************************************
		 *
		 *	Step 1. 
		 *	For each edge, create a new Edge Vertex,
		 *	then position it.
		 *
		 *******************************************************/

		newEdgeVertices = [];
		var other, currentEdge, newEdge, face;
		var edgeVertexWeight, adjacentVertexWeight, connectedFaces;

		for (i in sourceEdges) {
			currentEdge = sourceEdges[i];
			newEdge = new THREE.Vector3();

			edgeVertexWeight = 3 / 8;
			adjacentVertexWeight = 1 / 8;

			connectedFaces = currentEdge.faces.length;

			// check how many linked faces. 2 should be correct.
			if (connectedFaces != 2) {

				// if length is not 2, handle condition
				edgeVertexWeight = 0.5;
				adjacentVertexWeight = 0;

				if (connectedFaces != 1 ) {
					
					if (WARNINGS) console.warn('Subdivision Modifier: Number of connected faces != 2, is: ', connectedFaces, currentEdge);
			
				}

			}

			newEdge.addVectors( currentEdge.a, currentEdge.b ).multiplyScalar( edgeVertexWeight );

			tmp.set( 0, 0, 0 );

			for (j = 0; j < connectedFaces; j++ ) {

				face = currentEdge.faces[ j ];
				
				for (k = 0; k < 3; k++) {

					other = oldVertices[ face[ ABC[k] ] ];
					if (other !== currentEdge.a && other !== currentEdge.b ) break;

				}

				tmp.add( other );

			}

			tmp.multiplyScalar( adjacentVertexWeight );
			newEdge.add( tmp );

			currentEdge.newEdge = newEdgeVertices.length;
			newEdgeVertices.push(newEdge);

			// console.log(currentEdge, newEdge);
		}

		/******************************************************
		 *
		 *	Step 2. 
		 *	Reposition each source vertices.
		 *
		 *******************************************************/

		var beta, sourceVertexWeight, connectingVertexWeight;
		var connectingEdge, connectingEdges, oldVertex, newSourceVertex;
		newSourceVertices = [];

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

			oldVertex = oldVertices[i];

			// find all connecting edges (using lookupTable)
			connectingEdges = metaVertices[ i ].edges;
			n = connectingEdges.length;
			beta;

			if (n == 3) {

				beta = 3 / 16;

			} else if (n > 3) {

				beta = 3 / ( 8 * n ); // Warren's modified formula

			}

			// Loop's original beta formula
			// beta = 1 / n * ( 5/8 - Math.pow( 3/8 + 1/4 * Math.cos( 2 * Math. PI / n ), 2) );

			sourceVertexWeight = 1 - n * beta;
			connectingVertexWeight = beta;

			if (n <= 2) {
				
				// crease and boundary rules
				// console.warn('crease and boundary rules');

				if (n == 2) {

					if (WARNINGS) console.warn('2 connecting edges', connectingEdges);
					sourceVertexWeight = 3 / 4;
					connectingVertexWeight = 1 / 8;

					// sourceVertexWeight = 1;
					// connectingVertexWeight = 0;

				} else if (n == 1) {

					if (WARNINGS) console.warn('only 1 connecting edge');

				} else if (n == 0) {

					if (WARNINGS) console.warn('0 connecting edges');
			
				}
			
			}

			newSourceVertex = oldVertex.clone().multiplyScalar( sourceVertexWeight );

			tmp.set(0, 0, 0);

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

				connectingEdge = connectingEdges[ j ];
				other = connectingEdge.a !== oldVertex ? connectingEdge.a : connectingEdge.b;
				tmp.add( other );

			}

			tmp.multiplyScalar( connectingVertexWeight );
			newSourceVertex.add( tmp );
			
			newSourceVertices.push( newSourceVertex );

		}

							   
		/******************************************************
		 *
		 *	Step 3. 
		 *	Generate Faces between source vertecies
		 *	and edge vertices.
		 *
		 *******************************************************/

		newVertices = newSourceVertices.concat( newEdgeVertices );
		var sl = newSourceVertices.length, edge1, edge2, edge3;
		newFaces = [];

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

			face = oldFaces[i];

			// find the 3 new edges vertex of each old face

			edge1 = getEdge( face.a, face.b, sourceEdges ).newEdge + sl;
			edge2 = getEdge( face.b, face.c, sourceEdges ).newEdge + sl;
			edge3 = getEdge( face.c, face.a, sourceEdges ).newEdge + sl;

			// create 4 faces.

			newFace( newFaces, edge1, edge2, edge3 );
			newFace( newFaces, face.a, edge1, edge3 );
			newFace( newFaces, face.b, edge2, edge1 );
			newFace( newFaces, face.c, edge3, edge2 );

		}

		// Overwrite old arrays
		geometry.vertices = newVertices;
		geometry.faces = newFaces;

		// console.log('done');

	};


})();