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

import {
	Curve,
	Vector3,
	Vector4
} from 'three';
import * as NURBSUtils from '../curves/NURBSUtils.js';

/**
 * 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.
 *
 **/

class NURBSCurve extends Curve {

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

		super();

		const knotsLength = knots ? knots.length - 1 : 0;
		const pointsLength = controlPoints ? controlPoints.length : 0;

		this.degree = degree;
		this.knots = knots;
		this.controlPoints = [];
		// Used by periodic NURBS to remove hidden spans
		this.startKnot = startKnot || 0;
		this.endKnot = endKnot || knotsLength;

		for ( let i = 0; i < pointsLength; ++ i ) {

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

		}

	}

	getPoint( t, optionalTarget = new 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 = 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 Vector3() ) {

		const tangent = optionalTarget;

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

		return tangent;

	}

	toJSON() {

		const data = super.toJSON();

		data.degree = this.degree;
		data.knots = [ ...this.knots ];
		data.controlPoints = this.controlPoints.map( p => p.toArray() );
		data.startKnot = this.startKnot;
		data.endKnot = this.endKnot;

		return data;

	}

	fromJSON( json ) {

		super.fromJSON( json );

		this.degree = json.degree;
		this.knots = [ ...json.knots ];
		this.controlPoints = json.controlPoints.map( p => new Vector4( p[ 0 ], p[ 1 ], p[ 2 ], p[ 3 ] ) );
		this.startKnot = json.startKnot;
		this.endKnot = json.endKnot;

		return this;

	}

}

export { NURBSCurve };