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331 lines
6.2 KiB
331 lines
6.2 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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// Lets define some curves
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THREE.Curves = {};
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THREE.Curves.GrannyKnot = THREE.Curve.create( function() {},
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function( t ) {
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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 new THREE.Vector3( x, y, z ).multiplyScalar( 20 );
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}
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);
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THREE.Curves.HeartCurve = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 5 : s;
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},
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function( t ) {
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t *= 2 * Math.PI;
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var tx = 16 * Math.pow( Math.sin( t ), 3 );
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var ty = 13 * Math.cos( t ) - 5 * Math.cos( 2 * t ) - 2 * Math.cos( 3 * t ) - Math.cos( 4 * t ), tz = 0;
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return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale );
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}
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);
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// Viviani's Curve
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THREE.Curves.VivianiCurve = THREE.Curve.create(
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function( radius ) {
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this.radius = radius;
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},
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function( t ) {
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t = t * 4 * Math.PI; // Normalized to 0..1
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var a = this.radius / 2;
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var tx = a * ( 1 + Math.cos( t ) ),
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ty = a * Math.sin( t ),
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tz = 2 * a * Math.sin( t / 2 );
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return new THREE.Vector3( tx, ty, tz );
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}
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);
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THREE.Curves.KnotCurve = THREE.Curve.create(
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function() {
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},
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function( t ) {
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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 tx = s * Math.sin( t ),
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ty = Math.cos( t ) * ( R + s * Math.cos( t ) ),
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tz = Math.sin( t ) * ( R + s * Math.cos( t ) );
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return new THREE.Vector3( tx, ty, tz );
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}
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);
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THREE.Curves.HelixCurve = THREE.Curve.create(
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function() {
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},
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function( t ) {
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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 tx = Math.cos( t2 ) * a,
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ty = Math.sin( t2 ) * a,
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tz = b * t;
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return new THREE.Vector3( tx, ty, tz );
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}
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);
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THREE.Curves.TrefoilKnot = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 10 : s;
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},
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function( t ) {
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t *= Math.PI * 2;
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var tx = ( 2 + Math.cos( 3 * t ) ) * Math.cos( 2 * t ),
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ty = ( 2 + Math.cos( 3 * t ) ) * Math.sin( 2 * t ),
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tz = Math.sin( 3 * t );
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return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale );
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}
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);
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THREE.Curves.TorusKnot = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 10 : s;
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},
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function( t ) {
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var p = 3,
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q = 4;
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t *= Math.PI * 2;
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var tx = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t ),
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ty = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t ),
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tz = Math.sin( q * t );
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return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale );
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}
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);
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THREE.Curves.CinquefoilKnot = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 10 : s;
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},
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function( t ) {
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var p = 2,
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q = 5;
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t *= Math.PI * 2;
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var tx = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t ),
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ty = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t ),
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tz = Math.sin( q * t );
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return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale );
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}
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);
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THREE.Curves.TrefoilPolynomialKnot = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 10 : s;
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},
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function( t ) {
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t = t * 4 - 2;
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var tx = Math.pow( t, 3 ) - 3 * t,
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ty = Math.pow( t, 4 ) - 4 * t * t,
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tz = 1 / 5 * Math.pow( t, 5 ) - 2 * t;
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return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale );
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}
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);
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// var scaleTo = function(x, y) {
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// var r = y - x;
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// return function(t) {
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// t * r + x;
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// };
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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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THREE.Curves.FigureEightPolynomialKnot = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 1 : s;
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},
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function( t ) {
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t = scaleTo( - 4, 4, t );
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var tx = 2 / 5 * t * ( t * t - 7 ) * ( t * t - 10 ),
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ty = Math.pow( t, 4 ) - 13 * t * t,
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tz = 1 / 10 * t * ( t * t - 4 ) * ( t * t - 9 ) * ( t * t - 12 );
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return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale );
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}
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);
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THREE.Curves.DecoratedTorusKnot4a = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 40 : s;
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},
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function( t ) {
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t *= Math.PI * 2;
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var
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x = Math.cos( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) ),
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y = Math.sin( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) ),
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z = 0.35 * Math.sin( 5 * t );
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return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
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}
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);
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THREE.Curves.DecoratedTorusKnot4b = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 40 : s;
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},
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function( t ) {
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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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y = Math.sin( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) ),
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z = 0.2 * Math.sin( 9 * fi );
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return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
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}
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);
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THREE.Curves.DecoratedTorusKnot5a = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 40 : s;
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},
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function( t ) {
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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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y = Math.sin( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) ),
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z = 0.2 * Math.sin( 20 * fi );
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return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
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}
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);
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THREE.Curves.DecoratedTorusKnot5c = THREE.Curve.create(
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function( s ) {
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this.scale = ( s === undefined ) ? 40 : s;
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},
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function( t ) {
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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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y = Math.sin( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) ),
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z = 0.35 * Math.sin( 15 * fi );
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return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
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}
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);
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