three.js/examples/js/curves/CurveExtras.js

( function () {

	/**
 * A bunch of parametric curves
 *
 * 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
 */

	var Curves = function () {

		// GrannyKnot
		function GrannyKnot() {

			THREE.Curve.call( this );

		}

		GrannyKnot.prototype = Object.create( THREE.Curve.prototype );
		GrannyKnot.prototype.constructor = GrannyKnot;

		GrannyKnot.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 5 : scale;

		}

		HeartCurve.prototype = Object.create( THREE.Curve.prototype );
		HeartCurve.prototype.constructor = HeartCurve;

		HeartCurve.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 THREE.Curve


		function VivianiCurve( scale ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 70 : scale;

		}

		VivianiCurve.prototype = Object.create( THREE.Curve.prototype );
		VivianiCurve.prototype.constructor = VivianiCurve;

		VivianiCurve.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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() {

			THREE.Curve.call( this );

		}

		KnotCurve.prototype = Object.create( THREE.Curve.prototype );
		KnotCurve.prototype.constructor = KnotCurve;

		KnotCurve.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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() {

			THREE.Curve.call( this );

		}

		HelixCurve.prototype = Object.create( THREE.Curve.prototype );
		HelixCurve.prototype.constructor = HelixCurve;

		HelixCurve.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 10 : scale;

		}

		TrefoilKnot.prototype = Object.create( THREE.Curve.prototype );
		TrefoilKnot.prototype.constructor = TrefoilKnot;

		TrefoilKnot.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 10 : scale;

		}

		TorusKnot.prototype = Object.create( THREE.Curve.prototype );
		TorusKnot.prototype.constructor = TorusKnot;

		TorusKnot.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 10 : scale;

		}

		CinquefoilKnot.prototype = Object.create( THREE.Curve.prototype );
		CinquefoilKnot.prototype.constructor = CinquefoilKnot;

		CinquefoilKnot.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 10 : scale;

		}

		TrefoilPolynomialKnot.prototype = Object.create( THREE.Curve.prototype );
		TrefoilPolynomialKnot.prototype.constructor = TrefoilPolynomialKnot;

		TrefoilPolynomialKnot.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 1 : scale;

		}

		FigureEightPolynomialKnot.prototype = Object.create( THREE.Curve.prototype );
		FigureEightPolynomialKnot.prototype.constructor = FigureEightPolynomialKnot;

		FigureEightPolynomialKnot.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 40 : scale;

		}

		DecoratedTorusKnot4a.prototype = Object.create( THREE.Curve.prototype );
		DecoratedTorusKnot4a.prototype.constructor = DecoratedTorusKnot4a;

		DecoratedTorusKnot4a.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 40 : scale;

		}

		DecoratedTorusKnot4b.prototype = Object.create( THREE.Curve.prototype );
		DecoratedTorusKnot4b.prototype.constructor = DecoratedTorusKnot4b;

		DecoratedTorusKnot4b.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 40 : scale;

		}

		DecoratedTorusKnot5a.prototype = Object.create( THREE.Curve.prototype );
		DecoratedTorusKnot5a.prototype.constructor = DecoratedTorusKnot5a;

		DecoratedTorusKnot5a.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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 ) {

			THREE.Curve.call( this );
			this.scale = scale === undefined ? 40 : scale;

		}

		DecoratedTorusKnot5c.prototype = Object.create( THREE.Curve.prototype );
		DecoratedTorusKnot5c.prototype.constructor = DecoratedTorusKnot5c;

		DecoratedTorusKnot5c.prototype.getPoint = function ( t, optionalTarget ) {

			var point = optionalTarget || new THREE.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
		};

	}();

	THREE.Curves = Curves;

} )();