Added Convex Geometry

src/extras/geometries/ConvexGeometry.js

@@ -0,0 +1,204 @@
+/**
+ * @author qiao / https://github.com/qiao
+ * @fileoverview This is a convex hull generator using the incremental method. 
+ * The complexity is O(n^2) where n is the number of vertices.
+ * O(nlogn) algorithms do exist, but they are much more complicated.
+ *
+ * Benchmark: 
+ *
+ *  Platform: CPU: P7350 @2.00GHz Engine: V8
+ *		
+ *  Num Vertices	Time(ms)
+ *		
+ *     10           1
+ *     20           3
+ *     30           19
+ *     40           48
+ *     50           107
+ */
+
+THREE.ConvexGeometry = function( vertices ) {
+
+	THREE.Geometry.call( this );
+
+	var faces = [ [ 0, 1, 2 ], [ 0, 2, 1 ] ]; 
+
+	for ( var i = 3; i < vertices.length; i++ ) {
+
+		addPoint( i );
+
+	}
+
+
+	function addPoint( vertexId ) {
+
+		var vertex = vertices[ vertexId ].clone();
+
+		var mag = vertex.length();
+		vertex.x += mag * randomOffset();
+		vertex.y += mag * randomOffset();
+		vertex.z += mag * randomOffset();
+
+		var hole = [];
+
+		for ( var f = 0; f < faces.length; ) {
+
+			var face = faces[ f ];
+			
+			// for each face, if the vertex can see it,
+			// then we try to add the face's edges into the hole.
+			if ( visible( face, vertex ) ) {
+
+				for ( var e = 0; e < 3; e++ ) {
+					
+					var edge = [ face[ e ], face[ ( e + 1 ) % 3 ] ];
+					var boundary = true;
+
+					// remove duplicated edges.
+					for ( var h = 0; h < hole.length; h++ ) {
+					
+						if ( equalEdge( hole[ h ], edge ) ) {
+						
+							hole[ h ] = hole[ hole.length - 1 ];
+							hole.pop();
+							boundary = false;
+							break;
+
+						}
+
+					}
+
+					if ( boundary ) {
+
+						hole.push( edge );
+
+					}
+
+				}
+
+				// remove faces[ f ]
+				faces[ f ] = faces[ faces.length - 1 ];
+				faces.pop();
+			
+			} else { // not visible
+			
+				f++;
+
+			}
+		}
+
+		// construct the new faces formed by the edges of the hole and the vertex
+		for ( var h = 0; h < hole.length; h++ ) {
+
+			faces.push( [ 
+				hole[ h ][ 0 ],
+				hole[ h ][ 1 ],
+				vertexId
+			] );
+
+		}
+	}
+
+	/**
+	 * Whether the face is visible from the vertex
+	 */
+	function visible( face, vertex ) {
+
+		var va = vertices[ face[ 0 ] ];
+		var vb = vertices[ face[ 1 ] ];
+		var vc = vertices[ face[ 2 ] ];
+
+		var n = normal( va, vb, vc );
+
+		// distance from face to origin
+		var dist = n.dot( va );
+
+		return n.dot( vertex ) >= dist; 
+
+	}
+
+	/**
+	 * Face normal
+	 */
+	function normal( va, vb, vc ) {
+	
+		var cb = new THREE.Vector3();
+		var ab = new THREE.Vector3();
+
+		cb.sub( vc, vb );
+		ab.sub( va, vb );
+		cb.crossSelf( ab );
+
+		if ( !cb.isZero() ) {
+			
+			cb.normalize(); 
+
+		}
+
+		return cb;
+
+	}
+
+	/**
+	 * Detect whether two edges are equal.
+	 * Note that when constructing the convex hull, two same edges can only
+	 * be of the negative direction.
+	 */
+	function equalEdge( ea, eb ) {
+	
+		return ea[ 0 ] === eb[ 1 ] && ea[ 1 ] === eb[ 0 ]; 
+
+	}
+
+	/**
+	 * Create a random offset between -1e-6 and 1e-6.
+	 */
+	function randomOffset() {
+
+		return ( Math.random() - 0.5 ) * 2 * 1e-6;
+
+	}
+
+	// Push vertices into `this.vertices`, skipping those inside the hull
+	var id = 0;
+	var newId = new Array( vertices.length ); // map from old vertex id to new id
+
+	for ( var i = 0; i < faces.length; i++ ) {
+
+		 var face = faces[ i ];
+		
+		 for ( var j = 0; j < 3; j++ ) {
+		 
+				if ( newId[ face[ j ] ] === undefined ) {
+				
+						newId[ face[ j ] ] = id++;
+						this.vertices.push( vertices[ face[ j ] ] );
+				
+				}
+
+				face[ j ] = newId[ face[ j ] ];
+
+		 } 
+		
+	}
+
+	// Convert faces into instances of THREE.Face3
+	for ( var i = 0; i < faces.length; i++ ) {
+
+		this.faces.push( new THREE.Face3( 
+				faces[ i ][ 0 ],
+				faces[ i ][ 1 ],
+				faces[ i ][ 2 ]
+		) );
+
+	}
+	
+
+	this.computeCentroids();
+	this.computeFaceNormals();
+	this.computeVertexNormals();
+
+};
+
+THREE.ConvexGeometry.prototype = new THREE.Geometry();
+THREE.ConvexGeometry.prototype.constructor = THREE.ConvexGeometry;