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) */, startKnot /* index in knots */, endKnot /* index in knots */ ) {

	THREE.Curve.call( this );

	this.degree = degree;
	this.knots = knots;
	this.controlPoints = [];
	// Used by periodic NURBS to remove hidden spans
	this.startKnot = startKnot || 0;
	this.endKnot = endKnot || ( this.knots.length - 1 );
	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, optionalTarget ) {

	var point = optionalTarget || new THREE.Vector3();

	var u = this.knots[ this.startKnot ] + t * ( this.knots[ this.endKnot ] - this.knots[ this.startKnot ] ); // 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 point.set( hpoint.x, hpoint.y, hpoint.z );

};


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

	var tangent = optionalTarget || new THREE.Vector3();

	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 );
	tangent.copy( ders[ 1 ] ).normalize();

	return tangent;

};