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426 lines
10 KiB
426 lines
10 KiB
/*
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* A bunch of parametric curves
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* @author zz85
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*
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* Formulas collected from various sources
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* http://mathworld.wolfram.com/HeartCurve.html
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* http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page6.html
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* http://en.wikipedia.org/wiki/Viviani%27s_curve
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* http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page4.html
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* http://www.mi.sanu.ac.rs/vismath/taylorapril2011/Taylor.pdf
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* http://prideout.net/blog/?p=44
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*/
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( function ( Curves ) {
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// GrannyKnot
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function GrannyKnot() {
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THREE.Curve.call( this );
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}
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GrannyKnot.prototype = Object.create( THREE.Curve.prototype );
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GrannyKnot.prototype.constructor = GrannyKnot;
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GrannyKnot.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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t = 2 * Math.PI * t;
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var x = - 0.22 * Math.cos( t ) - 1.28 * Math.sin( t ) - 0.44 * Math.cos( 3 * t ) - 0.78 * Math.sin( 3 * t );
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var y = - 0.1 * Math.cos( 2 * t ) - 0.27 * Math.sin( 2 * t ) + 0.38 * Math.cos( 4 * t ) + 0.46 * Math.sin( 4 * t );
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var z = 0.7 * Math.cos( 3 * t ) - 0.4 * Math.sin( 3 * t );
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return point.set( x, y, z ).multiplyScalar( 20 );
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};
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// HeartCurve
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function HeartCurve( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 5 : scale;
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}
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HeartCurve.prototype = Object.create( THREE.Curve.prototype );
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HeartCurve.prototype.constructor = HeartCurve;
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HeartCurve.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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t *= 2 * Math.PI;
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var x = 16 * Math.pow( Math.sin( t ), 3 );
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var y = 13 * Math.cos( t ) - 5 * Math.cos( 2 * t ) - 2 * Math.cos( 3 * t ) - Math.cos( 4 * t );
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var z = 0;
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// Viviani's Curve
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function VivianiCurve( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 70 : scale;
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}
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VivianiCurve.prototype = Object.create( THREE.Curve.prototype );
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VivianiCurve.prototype.constructor = VivianiCurve;
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VivianiCurve.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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t = t * 4 * Math.PI; // normalized to 0..1
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var a = this.scale / 2;
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var x = a * ( 1 + Math.cos( t ) );
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var y = a * Math.sin( t );
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var z = 2 * a * Math.sin( t / 2 );
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return point.set( x, y, z );
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};
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// KnotCurve
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function KnotCurve() {
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THREE.Curve.call( this );
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}
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KnotCurve.prototype = Object.create( THREE.Curve.prototype );
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KnotCurve.prototype.constructor = KnotCurve;
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KnotCurve.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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t *= 2 * Math.PI;
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var R = 10;
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var s = 50;
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var x = s * Math.sin( t );
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var y = Math.cos( t ) * ( R + s * Math.cos( t ) );
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var z = Math.sin( t ) * ( R + s * Math.cos( t ) );
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return point.set( x, y, z );
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};
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// HelixCurve
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function HelixCurve() {
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THREE.Curve.call( this );
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}
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HelixCurve.prototype = Object.create( THREE.Curve.prototype );
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HelixCurve.prototype.constructor = HelixCurve;
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HelixCurve.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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var a = 30; // radius
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var b = 150; // height
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var t2 = 2 * Math.PI * t * b / 30;
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var x = Math.cos( t2 ) * a;
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var y = Math.sin( t2 ) * a;
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var z = b * t;
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return point.set( x, y, z );
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};
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// TrefoilKnot
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function TrefoilKnot( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 10 : scale;
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}
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TrefoilKnot.prototype = Object.create( THREE.Curve.prototype );
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TrefoilKnot.prototype.constructor = TrefoilKnot;
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TrefoilKnot.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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t *= Math.PI * 2;
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var x = ( 2 + Math.cos( 3 * t ) ) * Math.cos( 2 * t );
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var y = ( 2 + Math.cos( 3 * t ) ) * Math.sin( 2 * t );
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var z = Math.sin( 3 * t );
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// TorusKnot
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function TorusKnot( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 10 : scale;
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}
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TorusKnot.prototype = Object.create( THREE.Curve.prototype );
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TorusKnot.prototype.constructor = TorusKnot;
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TorusKnot.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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var p = 3;
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var q = 4;
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t *= Math.PI * 2;
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var x = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t );
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var y = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t );
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var z = Math.sin( q * t );
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// CinquefoilKnot
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function CinquefoilKnot( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 10 : scale;
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}
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CinquefoilKnot.prototype = Object.create( THREE.Curve.prototype );
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CinquefoilKnot.prototype.constructor = CinquefoilKnot;
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CinquefoilKnot.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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var p = 2;
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var q = 5;
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t *= Math.PI * 2;
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var x = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t );
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var y = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t );
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var z = Math.sin( q * t );
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// TrefoilPolynomialKnot
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function TrefoilPolynomialKnot( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 10 : scale;
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}
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TrefoilPolynomialKnot.prototype = Object.create( THREE.Curve.prototype );
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TrefoilPolynomialKnot.prototype.constructor = TrefoilPolynomialKnot;
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TrefoilPolynomialKnot.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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t = t * 4 - 2;
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var x = Math.pow( t, 3 ) - 3 * t;
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var y = Math.pow( t, 4 ) - 4 * t * t;
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var z = 1 / 5 * Math.pow( t, 5 ) - 2 * t;
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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var scaleTo = function ( x, y, t ) {
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var r = y - x;
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return t * r + x;
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};
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// FigureEightPolynomialKnot
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function FigureEightPolynomialKnot( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 1 : scale;
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}
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FigureEightPolynomialKnot.prototype = Object.create( THREE.Curve.prototype );
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FigureEightPolynomialKnot.prototype.constructor = FigureEightPolynomialKnot;
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FigureEightPolynomialKnot.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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t = scaleTo( - 4, 4, t );
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var x = 2 / 5 * t * ( t * t - 7 ) * ( t * t - 10 );
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var y = Math.pow( t, 4 ) - 13 * t * t;
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var z = 1 / 10 * t * ( t * t - 4 ) * ( t * t - 9 ) * ( t * t - 12 );
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// DecoratedTorusKnot4a
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function DecoratedTorusKnot4a( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 40 : scale;
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}
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DecoratedTorusKnot4a.prototype = Object.create( THREE.Curve.prototype );
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DecoratedTorusKnot4a.prototype.constructor = DecoratedTorusKnot4a;
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DecoratedTorusKnot4a.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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t *= Math.PI * 2;
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var x = Math.cos( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) );
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var y = Math.sin( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) );
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var z = 0.35 * Math.sin( 5 * t );
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// DecoratedTorusKnot4b
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function DecoratedTorusKnot4b( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 40 : scale;
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}
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DecoratedTorusKnot4b.prototype = Object.create( THREE.Curve.prototype );
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DecoratedTorusKnot4b.prototype.constructor = DecoratedTorusKnot4b;
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DecoratedTorusKnot4b.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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var fi = t * Math.PI * 2;
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var x = Math.cos( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) );
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var y = Math.sin( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) );
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var z = 0.2 * Math.sin( 9 * fi );
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// DecoratedTorusKnot5a
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function DecoratedTorusKnot5a( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 40 : scale;
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}
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DecoratedTorusKnot5a.prototype = Object.create( THREE.Curve.prototype );
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DecoratedTorusKnot5a.prototype.constructor = DecoratedTorusKnot5a;
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DecoratedTorusKnot5a.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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var fi = t * Math.PI * 2;
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var x = Math.cos( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) );
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var y = Math.sin( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) );
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var z = 0.2 * Math.sin( 20 * fi );
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// DecoratedTorusKnot5c
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function DecoratedTorusKnot5c( scale ) {
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THREE.Curve.call( this );
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this.scale = ( scale === undefined ) ? 40 : scale;
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}
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DecoratedTorusKnot5c.prototype = Object.create( THREE.Curve.prototype );
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DecoratedTorusKnot5c.prototype.constructor = DecoratedTorusKnot5c;
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DecoratedTorusKnot5c.prototype.getPoint = function ( t, optionalTarget ) {
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var point = optionalTarget || new THREE.Vector3();
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var fi = t * Math.PI * 2;
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var x = Math.cos( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) );
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var y = Math.sin( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) );
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var z = 0.35 * Math.sin( 15 * fi );
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return point.set( x, y, z ).multiplyScalar( this.scale );
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};
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// export
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Curves.GrannyKnot = GrannyKnot;
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Curves.HeartCurve = HeartCurve;
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Curves.VivianiCurve = VivianiCurve;
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Curves.KnotCurve = KnotCurve;
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Curves.HelixCurve = HelixCurve;
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Curves.TrefoilKnot = TrefoilKnot;
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Curves.TorusKnot = TorusKnot;
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Curves.CinquefoilKnot = CinquefoilKnot;
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Curves.TrefoilPolynomialKnot = TrefoilPolynomialKnot;
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Curves.FigureEightPolynomialKnot = FigureEightPolynomialKnot;
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Curves.DecoratedTorusKnot4a = DecoratedTorusKnot4a;
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Curves.DecoratedTorusKnot4b = DecoratedTorusKnot4b;
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Curves.DecoratedTorusKnot5a = DecoratedTorusKnot5a;
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Curves.DecoratedTorusKnot5c = DecoratedTorusKnot5c;
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} )( THREE.Curves = THREE.Curves || {} );
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