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