/* * @author zz85 / http://twitter.com/blurspline / http://www.lab4games.net/zz85/blog * @author centerionware / http://www.centerionware.com * * 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 "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 ); } 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 ) ); } function midpoint( a, b ) { return ( Math.abs( b - a ) / 2 ) + Math.min( a, b ); } function newUv( newUvs, a, b, c ) { newUvs.push( [ a.clone(), b.clone(), c.clone() ] ); } ///////////////////////////// // Performs one iteration of Subdivision THREE.SubdivisionModifier.prototype.smooth = function ( geometry ) { var tmp = new THREE.Vector3(); var oldVertices, oldFaces, oldUvs; 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 } oldUvs = geometry.faceVertexUvs[ 0 ]; var hasUvs = oldUvs !== undefined && oldUvs.length > 0; /****************************************************** * * 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; 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 vertices * and edge vertices. * *******************************************************/ newVertices = newSourceVertices.concat( newEdgeVertices ); var sl = newSourceVertices.length, edge1, edge2, edge3; newFaces = []; var uv, x0, x1, x2; var x3 = new THREE.Vector2(); var x4 = new THREE.Vector2(); var x5 = new THREE.Vector2(); 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 ); // create 4 new uv's if ( hasUvs ) { uv = oldUvs[ i ]; x0 = uv[ 0 ]; x1 = uv[ 1 ]; x2 = uv[ 2 ]; x3.set( midpoint( x0.x, x1.x ), midpoint( x0.y, x1.y ) ); x4.set( midpoint( x1.x, x2.x ), midpoint( x1.y, x2.y ) ); x5.set( midpoint( x0.x, x2.x ), midpoint( x0.y, x2.y ) ); newUv( newUVs, x3, x4, x5 ); newUv( newUVs, x0, x3, x5 ); newUv( newUVs, x1, x4, x3 ); newUv( newUVs, x2, x5, x4 ); } } // Overwrite old arrays geometry.vertices = newVertices; geometry.faces = newFaces; if ( hasUvs ) geometry.faceVertexUvs[ 0 ] = newUVs; // console.log('done'); }; } )();