three
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JavaScript 3D library
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JavaScript
import { Vector3 } from '../../math/Vector3.js';
import { Curve } from '../core/Curve.js';
function CubicPoly() {
/**
* 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.
*/
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 = /*@__PURE__*/ new Vector3();
const px = /*@__PURE__*/ new CubicPoly();
const py = /*@__PURE__*/ new CubicPoly();
const pz = /*@__PURE__*/ new CubicPoly();
/**
* A curve representing a Catmull-Rom spline.
*
* ```js
* //Create a closed wavey loop
* const curve = new THREE.CatmullRomCurve3( [
* new THREE.Vector3( -10, 0, 10 ),
* new THREE.Vector3( -5, 5, 5 ),
* new THREE.Vector3( 0, 0, 0 ),
* new THREE.Vector3( 5, -5, 5 ),
* new THREE.Vector3( 10, 0, 10 )
* ] );
*
* const points = curve.getPoints( 50 );
* const geometry = new THREE.BufferGeometry().setFromPoints( points );
*
* const material = new THREE.LineBasicMaterial( { color: 0xff0000 } );
*
* // Create the final object to add to the scene
* const curveObject = new THREE.Line( geometry, material );
* ```
*
* @augments Curve
*/
class CatmullRomCurve3 extends Curve {
/**
* Constructs a new Catmull-Rom curve.
*
* @param {Array<Vector3>} [points] - An array of 3D points defining the curve.
* @param {boolean} [closed=false] - Whether the curve is closed or not.
* @param {('centripetal'|'chordal'|'catmullrom')} [curveType='centripetal'] - The curve type.
* @param {number} [tension=0.5] - Tension of the curve.
*/
constructor( points = [], closed = false, curveType = 'centripetal', tension = 0.5 ) {
super();
/**
* This flag can be used for type testing.
*
* @type {boolean}
* @readonly
* @default true
*/
this.isCatmullRomCurve3 = true;
this.type = 'CatmullRomCurve3';
/**
* An array of 3D points defining the curve.
*
* @type {Array<Vector3>}
*/
this.points = points;
/**
* Whether the curve is closed or not.
*
* @type {boolean}
* @default false
*/
this.closed = closed;
/**
* The curve type.
*
* @type {('centripetal'|'chordal'|'catmullrom')}
* @default 'centripetal'
*/
this.curveType = curveType;
/**
* Tension of the curve.
*
* @type {number}
* @default 0.5
*/
this.tension = tension;
}
/**
* Returns a point on the curve.
*
* @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
* @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
* @return {Vector3} The position on the curve.
*/
getPoint( t, optionalTarget = new Vector3() ) {
const point = optionalTarget;
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;
}
copy( source ) {
super.copy( 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;
}
toJSON() {
const data = super.toJSON();
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;
}
fromJSON( json ) {
super.fromJSON( 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 };