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://en.wikipedia.org/wiki/Viviani%27s_curve
 * http://www.mi.sanu.ac.rs/vismath/taylorapril2011/Taylor.pdf
 * https://prideout.net/blog/old/blog/index.html@p=44.html
 */

	// GrannyKnot

	class GrannyKnot extends THREE.Curve {

		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			t = 2 * Math.PI * t;
			const x = - 0.22 * Math.cos( t ) - 1.28 * Math.sin( t ) - 0.44 * Math.cos( 3 * t ) - 0.78 * Math.sin( 3 * t );
			const 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 );
			const z = 0.7 * Math.cos( 3 * t ) - 0.4 * Math.sin( 3 * t );
			return point.set( x, y, z ).multiplyScalar( 20 );

		}

	}

	// HeartCurve

	class HeartCurve extends THREE.Curve {

		constructor( scale = 5 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			t *= 2 * Math.PI;
			const x = 16 * Math.pow( Math.sin( t ), 3 );
			const y = 13 * Math.cos( t ) - 5 * Math.cos( 2 * t ) - 2 * Math.cos( 3 * t ) - Math.cos( 4 * t );
			const z = 0;
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	// Viviani's THREE.Curve

	class VivianiCurve extends THREE.Curve {

		constructor( scale = 70 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			t = t * 4 * Math.PI; // normalized to 0..1
			const a = this.scale / 2;
			const x = a * ( 1 + Math.cos( t ) );
			const y = a * Math.sin( t );
			const z = 2 * a * Math.sin( t / 2 );
			return point.set( x, y, z );

		}

	}

	// KnotCurve

	class KnotCurve extends THREE.Curve {

		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			t *= 2 * Math.PI;
			const R = 10;
			const s = 50;
			const x = s * Math.sin( t );
			const y = Math.cos( t ) * ( R + s * Math.cos( t ) );
			const z = Math.sin( t ) * ( R + s * Math.cos( t ) );
			return point.set( x, y, z );

		}

	}

	// HelixCurve

	class HelixCurve extends THREE.Curve {

		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			const a = 30; // radius
			const b = 150; // height

			const t2 = 2 * Math.PI * t * b / 30;
			const x = Math.cos( t2 ) * a;
			const y = Math.sin( t2 ) * a;
			const z = b * t;
			return point.set( x, y, z );

		}

	}

	// TrefoilKnot

	class TrefoilKnot extends THREE.Curve {

		constructor( scale = 10 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			t *= Math.PI * 2;
			const x = ( 2 + Math.cos( 3 * t ) ) * Math.cos( 2 * t );
			const y = ( 2 + Math.cos( 3 * t ) ) * Math.sin( 2 * t );
			const z = Math.sin( 3 * t );
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	// TorusKnot

	class TorusKnot extends THREE.Curve {

		constructor( scale = 10 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			const p = 3;
			const q = 4;
			t *= Math.PI * 2;
			const x = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t );
			const y = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t );
			const z = Math.sin( q * t );
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	// CinquefoilKnot

	class CinquefoilKnot extends THREE.Curve {

		constructor( scale = 10 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			const p = 2;
			const q = 5;
			t *= Math.PI * 2;
			const x = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t );
			const y = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t );
			const z = Math.sin( q * t );
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	// TrefoilPolynomialKnot

	class TrefoilPolynomialKnot extends THREE.Curve {

		constructor( scale = 10 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			t = t * 4 - 2;
			const x = Math.pow( t, 3 ) - 3 * t;
			const y = Math.pow( t, 4 ) - 4 * t * t;
			const z = 1 / 5 * Math.pow( t, 5 ) - 2 * t;
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}
	function scaleTo( x, y, t ) {

		const r = y - x;
		return t * r + x;

	}

	// FigureEightPolynomialKnot

	class FigureEightPolynomialKnot extends THREE.Curve {

		constructor( scale = 1 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			t = scaleTo( - 4, 4, t );
			const x = 2 / 5 * t * ( t * t - 7 ) * ( t * t - 10 );
			const y = Math.pow( t, 4 ) - 13 * t * t;
			const z = 1 / 10 * t * ( t * t - 4 ) * ( t * t - 9 ) * ( t * t - 12 );
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	// DecoratedTorusKnot4a

	class DecoratedTorusKnot4a extends THREE.Curve {

		constructor( scale = 40 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			t *= Math.PI * 2;
			const x = Math.cos( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) );
			const y = Math.sin( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) );
			const z = 0.35 * Math.sin( 5 * t );
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	// DecoratedTorusKnot4b

	class DecoratedTorusKnot4b extends THREE.Curve {

		constructor( scale = 40 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			const fi = t * Math.PI * 2;
			const x = Math.cos( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) );
			const y = Math.sin( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) );
			const z = 0.2 * Math.sin( 9 * fi );
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	// DecoratedTorusKnot5a

	class DecoratedTorusKnot5a extends THREE.Curve {

		constructor( scale = 40 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			const fi = t * Math.PI * 2;
			const x = Math.cos( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) );
			const y = Math.sin( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) );
			const z = 0.2 * Math.sin( 20 * fi );
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	// DecoratedTorusKnot5c

	class DecoratedTorusKnot5c extends THREE.Curve {

		constructor( scale = 40 ) {

			super();
			this.scale = scale;

		}
		getPoint( t, optionalTarget = new THREE.Vector3() ) {

			const point = optionalTarget;
			const fi = t * Math.PI * 2;
			const x = Math.cos( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) );
			const y = Math.sin( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) );
			const z = 0.35 * Math.sin( 15 * fi );
			return point.set( x, y, z ).multiplyScalar( this.scale );

		}

	}

	THREE.CinquefoilKnot = CinquefoilKnot;
	THREE.DecoratedTorusKnot4a = DecoratedTorusKnot4a;
	THREE.DecoratedTorusKnot4b = DecoratedTorusKnot4b;
	THREE.DecoratedTorusKnot5a = DecoratedTorusKnot5a;
	THREE.DecoratedTorusKnot5c = DecoratedTorusKnot5c;
	THREE.FigureEightPolynomialKnot = FigureEightPolynomialKnot;
	THREE.GrannyKnot = GrannyKnot;
	THREE.HeartCurve = HeartCurve;
	THREE.HelixCurve = HelixCurve;
	THREE.KnotCurve = KnotCurve;
	THREE.TorusKnot = TorusKnot;
	THREE.TrefoilKnot = TrefoilKnot;
	THREE.TrefoilPolynomialKnot = TrefoilPolynomialKnot;
	THREE.VivianiCurve = VivianiCurve;

} )();