import { Vector3 } from '../../math/Vector3.js'; import { Curve } from '../core/Curve.js'; /** * @author zz85 https://github.com/zz85 * * 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() { var 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] var t1 = ( x1 - x0 ) / dt0 - ( x2 - x0 ) / ( dt0 + dt1 ) + ( x2 - x1 ) / dt1; var 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 ) { var t2 = t * t; var t3 = t2 * t; return c0 + c1 * t + c2 * t2 + c3 * t3; } }; } // var tmp = new Vector3(); var 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 || 0.5; } CatmullRomCurve3.prototype = Object.create( Curve.prototype ); CatmullRomCurve3.prototype.constructor = CatmullRomCurve3; CatmullRomCurve3.prototype.isCatmullRomCurve3 = true; CatmullRomCurve3.prototype.getPoint = function ( t, optionalTarget ) { var point = optionalTarget || new Vector3(); var points = this.points; var l = points.length; var p = ( l - ( this.closed ? 0 : 1 ) ) * t; var intPoint = Math.floor( p ); var 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; } var p0, p1, p2, p3; // 4 points 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; } p1 = points[ intPoint % l ]; 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 var pow = this.curveType === 'chordal' ? 0.5 : 0.25; var dt0 = Math.pow( p0.distanceToSquared( p1 ), pow ); var dt1 = Math.pow( p1.distanceToSquared( p2 ), pow ); var 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 ( var i = 0, l = source.points.length; i < l; i ++ ) { var 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 () { var data = Curve.prototype.toJSON.call( this ); data.points = []; for ( var i = 0, l = this.points.length; i < l; i ++ ) { var 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 ( var i = 0, l = json.points.length; i < l; i ++ ) { var 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 };