three.js/examples/js/curves/NURBSCurve.js

/**
 * @author renej
 * NURBS curve object
 *
 * Derives from Curve, overriding getPoint and getTangent.
 *
 * Implementation is based on (x, y [, z=0 [, w=1]]) control points with w=weight.
 *
 **/


/**************************************************************
 *	NURBS curve
 **************************************************************/

THREE.NURBSCurve = function ( degree, knots /* array of reals */, controlPoints /* array of Vector(2|3|4) */) {

	this.degree = degree;
	this.knots = knots;
	this.controlPoints = [];
	for (var i = 0; i < controlPoints.length; ++i) { // ensure Vector4 for control points
		var point = controlPoints[i];
		this.controlPoints[i] = new THREE.Vector4(point.x, point.y, point.z, point.w);
	}

};


THREE.NURBSCurve.prototype = Object.create( THREE.Curve.prototype );
THREE.NURBSCurve.prototype.constructor = THREE.NURBSCurve;


THREE.NURBSCurve.prototype.getPoint = function ( t ) {

	var u = this.knots[0] + t * (this.knots[this.knots.length - 1] - this.knots[0]); // linear mapping t->u

	// following results in (wx, wy, wz, w) homogeneous point
	var hpoint = THREE.NURBSUtils.calcBSplinePoint(this.degree, this.knots, this.controlPoints, u);

	if (hpoint.w != 1.0) { // project to 3D space: (wx, wy, wz, w) -> (x, y, z, 1)
		hpoint.divideScalar(hpoint.w);
	}

	return new THREE.Vector3(hpoint.x, hpoint.y, hpoint.z);
};


THREE.NURBSCurve.prototype.getTangent = function ( t ) {

	var u = this.knots[0] + t * (this.knots[this.knots.length - 1] - this.knots[0]);
	var ders = THREE.NURBSUtils.calcNURBSDerivatives(this.degree, this.knots, this.controlPoints, u, 1);
	var tangent = ders[1].clone();
	tangent.normalize();

	return tangent;
};