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355 lines
7.9 KiB
355 lines
7.9 KiB
2 years ago
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( function () {
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/**
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* A bunch of parametric curves
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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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* https://prideout.net/blog/old/blog/index.html@p=44.html
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*/
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// GrannyKnot
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class GrannyKnot extends THREE.Curve {
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t = 2 * Math.PI * t;
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const 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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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 );
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const 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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class HeartCurve extends THREE.Curve {
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constructor( scale = 5 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t *= 2 * Math.PI;
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const x = 16 * Math.pow( Math.sin( t ), 3 );
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const y = 13 * Math.cos( t ) - 5 * Math.cos( 2 * t ) - 2 * Math.cos( 3 * t ) - Math.cos( 4 * t );
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const 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 THREE.Curve
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class VivianiCurve extends THREE.Curve {
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constructor( scale = 70 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t = t * 4 * Math.PI; // normalized to 0..1
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const a = this.scale / 2;
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const x = a * ( 1 + Math.cos( t ) );
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const y = a * Math.sin( t );
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const 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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class KnotCurve extends THREE.Curve {
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t *= 2 * Math.PI;
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const R = 10;
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const s = 50;
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const x = s * Math.sin( t );
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const y = Math.cos( t ) * ( R + s * Math.cos( t ) );
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const 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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class HelixCurve extends THREE.Curve {
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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const a = 30; // radius
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const b = 150; // height
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const t2 = 2 * Math.PI * t * b / 30;
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const x = Math.cos( t2 ) * a;
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const y = Math.sin( t2 ) * a;
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const 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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class TrefoilKnot extends THREE.Curve {
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constructor( scale = 10 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t *= Math.PI * 2;
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const x = ( 2 + Math.cos( 3 * t ) ) * Math.cos( 2 * t );
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const y = ( 2 + Math.cos( 3 * t ) ) * Math.sin( 2 * t );
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const 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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class TorusKnot extends THREE.Curve {
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constructor( scale = 10 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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const p = 3;
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const q = 4;
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t *= Math.PI * 2;
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const x = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t );
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const y = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t );
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const 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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class CinquefoilKnot extends THREE.Curve {
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constructor( scale = 10 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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const p = 2;
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const q = 5;
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t *= Math.PI * 2;
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const x = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t );
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const y = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t );
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const 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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class TrefoilPolynomialKnot extends THREE.Curve {
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constructor( scale = 10 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t = t * 4 - 2;
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const x = Math.pow( t, 3 ) - 3 * t;
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const y = Math.pow( t, 4 ) - 4 * t * t;
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const 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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}
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function scaleTo( x, y, t ) {
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const r = y - x;
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return t * r + x;
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} // FigureEightPolynomialKnot
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class FigureEightPolynomialKnot extends THREE.Curve {
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constructor( scale = 1 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t = scaleTo( - 4, 4, t );
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const x = 2 / 5 * t * ( t * t - 7 ) * ( t * t - 10 );
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const y = Math.pow( t, 4 ) - 13 * t * t;
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const 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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class DecoratedTorusKnot4a extends THREE.Curve {
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constructor( scale = 40 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t *= Math.PI * 2;
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const x = Math.cos( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) );
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const y = Math.sin( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) );
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const 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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class DecoratedTorusKnot4b extends THREE.Curve {
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constructor( scale = 40 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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const fi = t * Math.PI * 2;
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const x = Math.cos( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) );
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const y = Math.sin( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) );
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const 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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class DecoratedTorusKnot5a extends THREE.Curve {
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constructor( scale = 40 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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const fi = t * Math.PI * 2;
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const x = Math.cos( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) );
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const y = Math.sin( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) );
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const 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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class DecoratedTorusKnot5c extends THREE.Curve {
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constructor( scale = 40 ) {
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super();
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this.scale = scale;
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}
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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const fi = t * Math.PI * 2;
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const x = Math.cos( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) );
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const y = Math.sin( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) );
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const 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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}
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const Curves = {
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GrannyKnot: GrannyKnot,
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HeartCurve: HeartCurve,
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VivianiCurve: VivianiCurve,
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KnotCurve: KnotCurve,
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HelixCurve: HelixCurve,
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TrefoilKnot: TrefoilKnot,
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TorusKnot: TorusKnot,
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CinquefoilKnot: CinquefoilKnot,
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TrefoilPolynomialKnot: TrefoilPolynomialKnot,
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FigureEightPolynomialKnot: FigureEightPolynomialKnot,
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DecoratedTorusKnot4a: DecoratedTorusKnot4a,
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DecoratedTorusKnot4b: DecoratedTorusKnot4b,
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DecoratedTorusKnot5a: DecoratedTorusKnot5a,
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DecoratedTorusKnot5c: DecoratedTorusKnot5c
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};
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THREE.Curves = Curves;
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} )();
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