three.js/src/extras/curves/CatmullRomCurve3.js

import { Vector3 } from '../../math/Vector3.js';
import { Curve } from '../core/Curve.js';

/**
 * Centripetal CatmullRom Curve - which is useful for avoiding
 * cusps and self-intersections in non-uniform catmull rom curves.
 * http://www.cemyuksel.com/research/catmullrom_param/catmullrom.pdf
 *
 * curve.type accepts centripetal(default), chordal and catmullrom
 * curve.tension is used for catmullrom which defaults to 0.5
 */


/*
Based on an optimized c++ solution in
 - http://stackoverflow.com/questions/9489736/catmull-rom-curve-with-no-cusps-and-no-self-intersections/
 - http://ideone.com/NoEbVM

This CubicPoly class could be used for reusing some variables and calculations,
but for three.js curve use, it could be possible inlined and flatten into a single function call
which can be placed in CurveUtils.
*/

function CubicPoly() {

	let c0 = 0, c1 = 0, c2 = 0, c3 = 0;

	/*
	 * Compute coefficients for a cubic polynomial
	 *   p(s) = c0 + c1*s + c2*s^2 + c3*s^3
	 * such that
	 *   p(0) = x0, p(1) = x1
	 *  and
	 *   p'(0) = t0, p'(1) = t1.
	 */
	function init( x0, x1, t0, t1 ) {

		c0 = x0;
		c1 = t0;
		c2 = - 3 * x0 + 3 * x1 - 2 * t0 - t1;
		c3 = 2 * x0 - 2 * x1 + t0 + t1;

	}

	return {

		initCatmullRom: function ( x0, x1, x2, x3, tension ) {

			init( x1, x2, tension * ( x2 - x0 ), tension * ( x3 - x1 ) );

		},

		initNonuniformCatmullRom: function ( x0, x1, x2, x3, dt0, dt1, dt2 ) {

			// compute tangents when parameterized in [t1,t2]
			let t1 = ( x1 - x0 ) / dt0 - ( x2 - x0 ) / ( dt0 + dt1 ) + ( x2 - x1 ) / dt1;
			let t2 = ( x2 - x1 ) / dt1 - ( x3 - x1 ) / ( dt1 + dt2 ) + ( x3 - x2 ) / dt2;

			// rescale tangents for parametrization in [0,1]
			t1 *= dt1;
			t2 *= dt1;

			init( x1, x2, t1, t2 );

		},

		calc: function ( t ) {

			const t2 = t * t;
			const t3 = t2 * t;
			return c0 + c1 * t + c2 * t2 + c3 * t3;

		}

	};

}

//

const tmp = new Vector3();
const px = new CubicPoly(), py = new CubicPoly(), pz = new CubicPoly();

function CatmullRomCurve3( points, closed, curveType, tension ) {

	Curve.call( this );

	this.type = 'CatmullRomCurve3';

	this.points = points || [];
	this.closed = closed || false;
	this.curveType = curveType || 'centripetal';
	this.tension = ( tension !== undefined ) ? tension : 0.5;

}

CatmullRomCurve3.prototype = Object.create( Curve.prototype );
CatmullRomCurve3.prototype.constructor = CatmullRomCurve3;

CatmullRomCurve3.prototype.isCatmullRomCurve3 = true;

CatmullRomCurve3.prototype.getPoint = function ( t, optionalTarget ) {

	const point = optionalTarget || new Vector3();

	const points = this.points;
	const l = points.length;

	const p = ( l - ( this.closed ? 0 : 1 ) ) * t;
	let intPoint = Math.floor( p );
	let weight = p - intPoint;

	if ( this.closed ) {

		intPoint += intPoint > 0 ? 0 : ( Math.floor( Math.abs( intPoint ) / l ) + 1 ) * l;

	} else if ( weight === 0 && intPoint === l - 1 ) {

		intPoint = l - 2;
		weight = 1;

	}

	let p0, p3; // 4 points (p1 & p2 defined below)

	if ( this.closed || intPoint > 0 ) {

		p0 = points[ ( intPoint - 1 ) % l ];

	} else {

		// extrapolate first point
		tmp.subVectors( points[ 0 ], points[ 1 ] ).add( points[ 0 ] );
		p0 = tmp;

	}

	const p1 = points[ intPoint % l ];
	const p2 = points[ ( intPoint + 1 ) % l ];

	if ( this.closed || intPoint + 2 < l ) {

		p3 = points[ ( intPoint + 2 ) % l ];

	} else {

		// extrapolate last point
		tmp.subVectors( points[ l - 1 ], points[ l - 2 ] ).add( points[ l - 1 ] );
		p3 = tmp;

	}

	if ( this.curveType === 'centripetal' || this.curveType === 'chordal' ) {

		// init Centripetal / Chordal Catmull-Rom
		const pow = this.curveType === 'chordal' ? 0.5 : 0.25;
		let dt0 = Math.pow( p0.distanceToSquared( p1 ), pow );
		let dt1 = Math.pow( p1.distanceToSquared( p2 ), pow );
		let dt2 = Math.pow( p2.distanceToSquared( p3 ), pow );

		// safety check for repeated points
		if ( dt1 < 1e-4 ) dt1 = 1.0;
		if ( dt0 < 1e-4 ) dt0 = dt1;
		if ( dt2 < 1e-4 ) dt2 = dt1;

		px.initNonuniformCatmullRom( p0.x, p1.x, p2.x, p3.x, dt0, dt1, dt2 );
		py.initNonuniformCatmullRom( p0.y, p1.y, p2.y, p3.y, dt0, dt1, dt2 );
		pz.initNonuniformCatmullRom( p0.z, p1.z, p2.z, p3.z, dt0, dt1, dt2 );

	} else if ( this.curveType === 'catmullrom' ) {

		px.initCatmullRom( p0.x, p1.x, p2.x, p3.x, this.tension );
		py.initCatmullRom( p0.y, p1.y, p2.y, p3.y, this.tension );
		pz.initCatmullRom( p0.z, p1.z, p2.z, p3.z, this.tension );

	}

	point.set(
		px.calc( weight ),
		py.calc( weight ),
		pz.calc( weight )
	);

	return point;

};

CatmullRomCurve3.prototype.copy = function ( source ) {

	Curve.prototype.copy.call( this, source );

	this.points = [];

	for ( let i = 0, l = source.points.length; i < l; i ++ ) {

		const point = source.points[ i ];

		this.points.push( point.clone() );

	}

	this.closed = source.closed;
	this.curveType = source.curveType;
	this.tension = source.tension;

	return this;

};

CatmullRomCurve3.prototype.toJSON = function () {

	const data = Curve.prototype.toJSON.call( this );

	data.points = [];

	for ( let i = 0, l = this.points.length; i < l; i ++ ) {

		const point = this.points[ i ];
		data.points.push( point.toArray() );

	}

	data.closed = this.closed;
	data.curveType = this.curveType;
	data.tension = this.tension;

	return data;

};

CatmullRomCurve3.prototype.fromJSON = function ( json ) {

	Curve.prototype.fromJSON.call( this, json );

	this.points = [];

	for ( let i = 0, l = json.points.length; i < l; i ++ ) {

		const point = json.points[ i ];
		this.points.push( new Vector3().fromArray( point ) );

	}

	this.closed = json.closed;
	this.curveType = json.curveType;
	this.tension = json.tension;

	return this;

};


export { CatmullRomCurve3 };