/* * 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 * http://prideout.net/blog/?p=44 */ // Lets define some curves THREE.Curves = {}; THREE.Curves.GrannyKnot = THREE.Curve.create( function() {}, function( t ) { 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 new THREE.Vector3( x, y, z ).multiplyScalar( 20 ); } ); THREE.Curves.HeartCurve = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 5 : s; }, function( t ) { t *= 2 * Math.PI; var tx = 16 * Math.pow( Math.sin( t ), 3 ); var ty = 13 * Math.cos( t ) - 5 * Math.cos( 2 * t ) - 2 * Math.cos( 3 * t ) - Math.cos( 4 * t ), tz = 0; return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale ); } ); // Viviani's Curve THREE.Curves.VivianiCurve = THREE.Curve.create( function( radius ) { this.radius = radius; }, function( t ) { t = t * 4 * Math.PI; // Normalized to 0..1 var a = this.radius / 2; var tx = a * ( 1 + Math.cos( t ) ), ty = a * Math.sin( t ), tz = 2 * a * Math.sin( t / 2 ); return new THREE.Vector3( tx, ty, tz ); } ); THREE.Curves.KnotCurve = THREE.Curve.create( function() { }, function( t ) { t *= 2 * Math.PI; var R = 10; var s = 50; var tx = s * Math.sin( t ), ty = Math.cos( t ) * ( R + s * Math.cos( t ) ), tz = Math.sin( t ) * ( R + s * Math.cos( t ) ); return new THREE.Vector3( tx, ty, tz ); } ); THREE.Curves.HelixCurve = THREE.Curve.create( function() { }, function( t ) { var a = 30; // radius var b = 150; //height var t2 = 2 * Math.PI * t * b / 30; var tx = Math.cos( t2 ) * a, ty = Math.sin( t2 ) * a, tz = b * t; return new THREE.Vector3( tx, ty, tz ); } ); THREE.Curves.TrefoilKnot = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 10 : s; }, function( t ) { t *= Math.PI * 2; var tx = ( 2 + Math.cos( 3 * t ) ) * Math.cos( 2 * t ), ty = ( 2 + Math.cos( 3 * t ) ) * Math.sin( 2 * t ), tz = Math.sin( 3 * t ); return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale ); } ); THREE.Curves.TorusKnot = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 10 : s; }, function( t ) { var p = 3, q = 4; t *= Math.PI * 2; var tx = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t ), ty = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t ), tz = Math.sin( q * t ); return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale ); } ); THREE.Curves.CinquefoilKnot = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 10 : s; }, function( t ) { var p = 2, q = 5; t *= Math.PI * 2; var tx = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t ), ty = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t ), tz = Math.sin( q * t ); return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale ); } ); THREE.Curves.TrefoilPolynomialKnot = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 10 : s; }, function( t ) { t = t * 4 - 2; var tx = Math.pow( t, 3 ) - 3 * t, ty = Math.pow( t, 4 ) - 4 * t * t, tz = 1 / 5 * Math.pow( t, 5 ) - 2 * t; return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale ); } ); // var scaleTo = function(x, y) { // var r = y - x; // return function(t) { // t * r + x; // }; // } var scaleTo = function( x, y, t ) { var r = y - x; return t * r + x; }; THREE.Curves.FigureEightPolynomialKnot = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 1 : s; }, function( t ) { t = scaleTo( - 4, 4, t ); var tx = 2 / 5 * t * ( t * t - 7 ) * ( t * t - 10 ), ty = Math.pow( t, 4 ) - 13 * t * t, tz = 1 / 10 * t * ( t * t - 4 ) * ( t * t - 9 ) * ( t * t - 12 ); return new THREE.Vector3( tx, ty, tz ).multiplyScalar( this.scale ); } ); THREE.Curves.DecoratedTorusKnot4a = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 40 : s; }, function( t ) { t *= Math.PI * 2; var x = Math.cos( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) ), y = Math.sin( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) ), z = 0.35 * Math.sin( 5 * t ); return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale ); } ); THREE.Curves.DecoratedTorusKnot4b = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 40 : s; }, function( t ) { 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 ) ), y = Math.sin( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) ), z = 0.2 * Math.sin( 9 * fi ); return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale ); } ); THREE.Curves.DecoratedTorusKnot5a = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 40 : s; }, function( t ) { 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 ) ), y = Math.sin( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) ), z = 0.2 * Math.sin( 20 * fi ); return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale ); } ); THREE.Curves.DecoratedTorusKnot5c = THREE.Curve.create( function( s ) { this.scale = ( s === undefined ) ? 40 : s; }, function( t ) { 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 ) ) ), y = Math.sin( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) ), z = 0.35 * Math.sin( 15 * fi ); return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale ); } );