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

( function () {

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

	class NURBSCurve extends THREE.Curve {

		constructor( degree, knots /* array of reals */, controlPoints /* array of Vector(2|3|4) */, startKnot /* index in knots */, endKnot /* index in knots */ ) {

			super();
			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 ( let i = 0; i < controlPoints.length; ++ i ) {

				// ensure THREE.Vector4 for control points
				const point = controlPoints[ i ];
				this.controlPoints[ i ] = new THREE.Vector4( point.x, point.y, point.z, point.w );

			}

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			const 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
			const 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 );

		}
		getTangent( t, optionalTarget = new THREE.Vector3() ) {

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

		}

	}

	THREE.NURBSCurve = NURBSCurve;

} )();