added nurbs surface

examples/webgl_geometry_nurbs.html

@@ -28,6 +28,7 @@
 
 		<script src="../build/three.min.js"></script>
 		<script src="../src/extras/core/NURBSCurve.js"></script>
+		<script src="../src/extras/core/NURBSSurface.js"></script>
 
 		<script src="js/libs/stats.min.js"></script>
 
@@ -70,6 +71,8 @@
 
 				scene = new THREE.Scene();
 
+				scene.add( new THREE.AmbientLight( 0x404040 ) );
+
 				var light = new THREE.DirectionalLight( 0xffffff );
 				light.position.set( 0, 0, 1 );
 				scene.add( light );
@@ -121,6 +124,53 @@
 				parent.add( nurbsLine );
 				parent.add( nurbsControlPointsLine );
 
+				// NURBS Surface
+
+				var nsControlPoints = [
+					[
+						new THREE.Vector4 ( -200, -200, 100, 1 ),
+						new THREE.Vector4 ( -200, -100, -200, 1 ),
+						new THREE.Vector4 ( -200, 100, 250, 1 ),
+						new THREE.Vector4 ( -200, 200, -100, 1 )
+					],
+					[
+						new THREE.Vector4 ( 0, -200, 0, 1 ),
+						new THREE.Vector4 ( 0, -100, -100, 1 ),
+						new THREE.Vector4 ( 0, 100, 150, 1 ),
+						new THREE.Vector4 ( 0, 200, 0, 1 )
+					],
+					[
+						new THREE.Vector4 ( 200, -200, -100, 1 ),
+						new THREE.Vector4 ( 200, -100, 200, 1 ),
+						new THREE.Vector4 ( 200, 100, -250, 1 ),
+						new THREE.Vector4 ( 200, 200, 100, 1 )
+					]
+				];
+				var degree1 = 2;
+				var degree2 = 3;
+				var knots1 = [0, 0, 0, 1, 1, 1];
+				var knots2 = [0, 0, 0, 0, 1, 1, 1, 1];
+				var nurbsSurface = new THREE.NURBSSurface(degree1, degree2, knots1, knots2, nsControlPoints);
+
+				var map = THREE.ImageUtils.loadTexture( 'textures/ash_uvgrid01.jpg' );
+				map.wrapS = map.wrapT = THREE.RepeatWrapping;
+				map.anisotropy = 16;
+
+				var materials = [
+					new THREE.MeshLambertMaterial( { ambient: 0xbbbbbb, map: map, side: THREE.DoubleSide } ),
+					new THREE.MeshBasicMaterial( { color: 0xffffff, wireframe: true, transparent: true, opacity: 0.1, side: THREE.DoubleSide } )
+				];
+
+				getSurfacePoint = function(u, v) {
+					return nurbsSurface.getPoint(u, v);
+				};
+
+				var geo = new THREE.ParametricGeometry( getSurfacePoint, 50, 50 );
+				var object = THREE.SceneUtils.createMultiMaterialObject( geo, materials );
+				object.position.set( 0, 100, 0 );
+				object.scale.multiplyScalar( 1 );
+				parent.add( object );
+
 				//
 
 				renderer = new THREE.WebGLRenderer( { antialias: true } );

src/extras/core/NURBSSurface.js

@@ -0,0 +1,106 @@
+/**
+ * @author renej
+ * NURBS surface object
+ *
+ * Derives from Curve, overriding getPoint and getTangent.
+ *
+ * Implementation is based on (x, y [, z=0 [, w=1]]) control points with w=weight.
+ *
+ **/
+
+
+/**************************************************************
+ *	NURBS surface
+ **************************************************************/
+
+THREE.NURBSSurface = function ( degree1, degree2, knots1, knots2 /* arrays of reals */, controlPoints /* array^2 of Vector(2|3|4) */) {
+
+	this.degree1 = degree1;
+	this.degree2 = degree2;
+	this.knots1 = knots1;
+	this.knots2 = knots2;
+	this.controlPoints = [];
+
+	var len1 = knots1.length - degree1 - 1;
+	var len2 = knots2.length - degree2 - 1;
+
+	//console.log("controlPoints: " + controlPoints);
+	//console.log("controlPoints[0][0].x: " + controlPoints[0][0].x);
+
+	// ensure Vector4 for control points
+	for (var i = 0; i < len1; ++i) {
+		this.controlPoints[i] = []
+		for (var j = 0; j < len2; ++j) {
+			//console.log("i=" + i + " j=" + j);
+			var point = controlPoints[i][j];
+			this.controlPoints[i][j] = new THREE.Vector4(point.x, point.y, point.z, point.w);
+		}
+	}
+};
+
+
+THREE.NURBSSurface.prototype = {
+
+	constructor: THREE.NURBSSurface,
+
+	getPoint: function ( t1, t2 ) {
+
+		//console.log("this.knots1=" + this.knots1);
+		//console.log("this.knots2=" + this.knots2);
+		//console.log("this.controlPoints=" + this.controlPoints);
+		var u = this.knots1[0] + t1 * (this.knots1[this.knots1.length - 1] - this.knots1[0]); // linear mapping t1->u
+		var v = this.knots2[0] + t2 * (this.knots2[this.knots2.length - 1] - this.knots2[0]); // linear mapping t2->u
+
+		var point = THREE.NURBSSurface.Utils.calcSurfacePoint(this.degree1, this.degree2, this.knots1, this.knots2, this.controlPoints, u, v);
+		//console.log("u=" + u + " v=" + v + " point=" + point.x + ", " + point.y + ", " + point.z);
+		return point;
+	}
+};
+
+
+/**************************************************************
+ *	Utils
+ **************************************************************/
+
+THREE.NURBSSurface.Utils = {
+
+	/*
+	Calculate rational B-Spline surface point. See The NURBS Book, page 134, algorithm A4.3.
+ 
+	p1, p2 : degrees of B-Spline surface
+	U1, U2 : knot vectors
+	P      : control points (x, y, z, w)
+	u, v   : parametric values
+
+	returns point for given (u, v)
+	*/
+	calcSurfacePoint: function( p, q, U, V, P, u, v ) {
+		var uspan = THREE.NURBSCurve.Utils.findSpan(p, u, U);
+		var vspan = THREE.NURBSCurve.Utils.findSpan(q, v, V);
+		var Nu = THREE.NURBSCurve.Utils.calcBasisFunctions(uspan, u, p, U);
+		var Nv = THREE.NURBSCurve.Utils.calcBasisFunctions(vspan, v, q, V);
+		var temp = [];
+
+		for (var l = 0; l <= q; ++l) {
+			temp[l] = new THREE.Vector4(0, 0, 0, 0);
+			for (var k = 0; k <= p; ++k) {
+				var point = P[uspan - p + k][vspan - q + l].clone();
+				var w = point.w;
+				point.x *= w;
+				point.y *= w;
+				point.z *= w;
+				temp[l].add(point.multiplyScalar(Nu[k]));
+			}
+		}
+
+		var Sw = new THREE.Vector4(0, 0, 0, 0);
+		for (var l = 0; l <= q; ++l) {
+			Sw.add(temp[l].multiplyScalar(Nv[l]));
+		}
+
+		Sw.divideScalar(Sw.w);
+		return new THREE.Vector3(Sw.x, Sw.y, Sw.z);
+	}
+
+};
+