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CurveExtras: Format

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examples/js/CurveExtras.js
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......@@ -3,361 +3,361 @@
* @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
* 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
*/
( function( Curves ) {
// GrannyKnot
// GrannyKnot
function GrannyKnot() {}
function GrannyKnot() {}
GrannyKnot.prototype = Object.create( THREE.Curve.prototype );
GrannyKnot.prototype.constructor = GrannyKnot;
GrannyKnot.prototype = Object.create( THREE.Curve.prototype );
GrannyKnot.prototype.constructor = GrannyKnot;
GrannyKnot.prototype.getPoint = function( t ) {
GrannyKnot.prototype.getPoint = function( t ) {
t = 2 * Math.PI * 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 );
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 );
return new THREE.Vector3( x, y, z ).multiplyScalar( 20 );
};
};
// HeartCurve
// HeartCurve
function HeartCurve( s ) {
function HeartCurve( s ) {
this.scale = ( s === undefined ) ? 5 : s;
this.scale = ( s === undefined ) ? 5 : s;
}
}
HeartCurve.prototype = Object.create( THREE.Curve.prototype );
HeartCurve.prototype.constructor = HeartCurve;
HeartCurve.prototype = Object.create( THREE.Curve.prototype );
HeartCurve.prototype.constructor = HeartCurve;
HeartCurve.prototype.getPoint = function( t ) {
HeartCurve.prototype.getPoint = function( t ) {
t *= 2 * Math.PI;
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;
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
}
}
// Viviani's Curve
// Viviani's Curve
function VivianiCurve( radius ) {
function VivianiCurve( radius ) {
this.radius = radius;
this.radius = radius;
}
}
VivianiCurve.prototype = Object.create( THREE.Curve.prototype );
VivianiCurve.prototype.constructor = VivianiCurve;
VivianiCurve.prototype = Object.create( THREE.Curve.prototype );
VivianiCurve.prototype.constructor = VivianiCurve;
VivianiCurve.prototype.getPoint = function( t ) {
VivianiCurve.prototype.getPoint = function( t ) {
t = t * 4 * Math.PI; // normalized to 0..1
var a = this.radius / 2;
t = t * 4 * Math.PI; // normalized to 0..1
var a = this.radius / 2;
var x = a * ( 1 + Math.cos( t ) );
var y = a * Math.sin( t );
var z = 2 * a * Math.sin( t / 2 );
var x = a * ( 1 + Math.cos( t ) );
var y = a * Math.sin( t );
var z = 2 * a * Math.sin( t / 2 );
return new THREE.Vector3( x, y, z );
return new THREE.Vector3( x, y, z );
};
};
// KnotCurve
// KnotCurve
function KnotCurve() {}
function KnotCurve() {}
KnotCurve.prototype = Object.create( THREE.Curve.prototype );
KnotCurve.prototype.constructor = KnotCurve;
KnotCurve.prototype = Object.create( THREE.Curve.prototype );
KnotCurve.prototype.constructor = KnotCurve;
KnotCurve.prototype.getPoint = function( t ) {
KnotCurve.prototype.getPoint = function( t ) {
t *= 2 * Math.PI;
t *= 2 * Math.PI;
var R = 10;
var s = 50;
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 ) );
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 new THREE.Vector3( x, y, z );
return new THREE.Vector3( x, y, z );
};
};
// HelixCurve
// HelixCurve
function HelixCurve() {}
function HelixCurve() {}
HelixCurve.prototype = Object.create( THREE.Curve.prototype );
HelixCurve.prototype.constructor = HelixCurve;
HelixCurve.prototype = Object.create( THREE.Curve.prototype );
HelixCurve.prototype.constructor = HelixCurve;
HelixCurve.prototype.getPoint = function( t ) {
HelixCurve.prototype.getPoint = function( t ) {
var a = 30; // radius
var b = 150; // height
var a = 30; // radius
var b = 150; // height
var t2 = 2 * Math.PI * t * b / 30;
var t2 = 2 * Math.PI * t * b / 30;
var x = Math.cos( t2 ) * a;
var y = Math.sin( t2 ) * a;
var z = b * t;
var x = Math.cos( t2 ) * a;
var y = Math.sin( t2 ) * a;
var z = b * t;
return new THREE.Vector3( x, y, z );
return new THREE.Vector3( x, y, z );
};
};
// TrefoilKnot
// TrefoilKnot
function TrefoilKnot( s ) {
function TrefoilKnot( s ) {
this.scale = ( s === undefined ) ? 10 : s;
this.scale = ( s === undefined ) ? 10 : s;
};
};
TrefoilKnot.prototype = Object.create( THREE.Curve.prototype );
TrefoilKnot.prototype.constructor = TrefoilKnot;
TrefoilKnot.prototype = Object.create( THREE.Curve.prototype );
TrefoilKnot.prototype.constructor = TrefoilKnot;
TrefoilKnot.prototype.getPoint = function( t ) {
TrefoilKnot.prototype.getPoint = function( t ) {
t *= Math.PI * 2;
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 );
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
// TorusKnot
// TorusKnot
function TorusKnot( s ) {
function TorusKnot( s ) {
this.scale = ( s === undefined ) ? 10 : s;
this.scale = ( s === undefined ) ? 10 : s;
};
};
TorusKnot.prototype = Object.create( THREE.Curve.prototype );
TorusKnot.prototype.constructor = TorusKnot;
TorusKnot.prototype = Object.create( THREE.Curve.prototype );
TorusKnot.prototype.constructor = TorusKnot;
TorusKnot.prototype.getPoint = function( t ) {
TorusKnot.prototype.getPoint = function( t ) {
var p = 3;
var q = 4;
var p = 3;
var q = 4;
t *= Math.PI * 2;
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 );
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
// CinquefoilKnot
// CinquefoilKnot
function CinquefoilKnot( s ) {
function CinquefoilKnot( s ) {
this.scale = ( s === undefined ) ? 10 : s;
this.scale = ( s === undefined ) ? 10 : s;
};
};
CinquefoilKnot.prototype = Object.create( THREE.Curve.prototype );
CinquefoilKnot.prototype.constructor = CinquefoilKnot;
CinquefoilKnot.prototype = Object.create( THREE.Curve.prototype );
CinquefoilKnot.prototype.constructor = CinquefoilKnot;
CinquefoilKnot.prototype.getPoint = function( t ) {
CinquefoilKnot.prototype.getPoint = function( t ) {
var p = 2;
var q = 5;
var p = 2;
var q = 5;
t *= Math.PI * 2;
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 );
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
// TrefoilPolynomialKnot
// TrefoilPolynomialKnot
function TrefoilPolynomialKnot( s ) {
function TrefoilPolynomialKnot( s ) {
this.scale = ( s === undefined ) ? 10 : s;
this.scale = ( s === undefined ) ? 10 : s;
};
};
TrefoilPolynomialKnot.prototype = Object.create( THREE.Curve.prototype );
TrefoilPolynomialKnot.prototype.constructor = TrefoilPolynomialKnot;
TrefoilPolynomialKnot.prototype = Object.create( THREE.Curve.prototype );
TrefoilPolynomialKnot.prototype.constructor = TrefoilPolynomialKnot;
TrefoilPolynomialKnot.prototype.getPoint = function( t ) {
TrefoilPolynomialKnot.prototype.getPoint = function( t ) {
t = t * 4 - 2;
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;
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
var scaleTo = function( x, y, t ) {
var scaleTo = function( x, y, t ) {
var r = y - x;
return t * r + x;
var r = y - x;
return t * r + x;
};
};
// FigureEightPolynomialKnot
// FigureEightPolynomialKnot
function FigureEightPolynomialKnot( s ) {
function FigureEightPolynomialKnot( s ) {
this.scale = ( s === undefined ) ? 1 : s;
this.scale = ( s === undefined ) ? 1 : s;
};
};
FigureEightPolynomialKnot.prototype = Object.create( THREE.Curve.prototype );
FigureEightPolynomialKnot.prototype.constructor = FigureEightPolynomialKnot;
FigureEightPolynomialKnot.prototype = Object.create( THREE.Curve.prototype );
FigureEightPolynomialKnot.prototype.constructor = FigureEightPolynomialKnot;
FigureEightPolynomialKnot.prototype.getPoint = function( t ) {
FigureEightPolynomialKnot.prototype.getPoint = function( t ) {
t = scaleTo( - 4, 4, t );
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 );
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
// DecoratedTorusKnot4a
// DecoratedTorusKnot4a
function DecoratedTorusKnot4a( s ) {
function DecoratedTorusKnot4a( s ) {
this.scale = ( s === undefined ) ? 40 : s;
this.scale = ( s === undefined ) ? 40 : s;
};
};
DecoratedTorusKnot4a.prototype = Object.create( THREE.Curve.prototype );
DecoratedTorusKnot4a.prototype.constructor = DecoratedTorusKnot4a;
DecoratedTorusKnot4a.prototype = Object.create( THREE.Curve.prototype );
DecoratedTorusKnot4a.prototype.constructor = DecoratedTorusKnot4a;
DecoratedTorusKnot4a.prototype.getPoint = function( t ) {
DecoratedTorusKnot4a.prototype.getPoint = function( t ) {
t *= Math.PI * 2;
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 );
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
// DecoratedTorusKnot4b
// DecoratedTorusKnot4b
function DecoratedTorusKnot4b( s ) {
function DecoratedTorusKnot4b( s ) {
this.scale = ( s === undefined ) ? 40 : s;
this.scale = ( s === undefined ) ? 40 : s;
};
};
DecoratedTorusKnot4b.prototype = Object.create( THREE.Curve.prototype );
DecoratedTorusKnot4b.prototype.constructor = DecoratedTorusKnot4b;
DecoratedTorusKnot4b.prototype = Object.create( THREE.Curve.prototype );
DecoratedTorusKnot4b.prototype.constructor = DecoratedTorusKnot4b;
DecoratedTorusKnot4b.prototype.getPoint = function( t ) {
DecoratedTorusKnot4b.prototype.getPoint = function( t ) {
var fi = t * Math.PI * 2;
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 );
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
// DecoratedTorusKnot5a
// DecoratedTorusKnot5a
function DecoratedTorusKnot5a( s ) {
function DecoratedTorusKnot5a( s ) {
this.scale = ( s === undefined ) ? 40 : s;
this.scale = ( s === undefined ) ? 40 : s;
};
};
DecoratedTorusKnot5a.prototype = Object.create( THREE.Curve.prototype );
DecoratedTorusKnot5a.prototype.constructor = DecoratedTorusKnot5a;
DecoratedTorusKnot5a.prototype = Object.create( THREE.Curve.prototype );
DecoratedTorusKnot5a.prototype.constructor = DecoratedTorusKnot5a;
DecoratedTorusKnot5a.prototype.getPoint = function( t ) {
DecoratedTorusKnot5a.prototype.getPoint = function( t ) {
var fi = t * Math.PI * 2;
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 );
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
// DecoratedTorusKnot5c
// DecoratedTorusKnot5c
function DecoratedTorusKnot5c( s ) {
function DecoratedTorusKnot5c( s ) {
this.scale = ( s === undefined ) ? 40 : s;
this.scale = ( s === undefined ) ? 40 : s;
};
};
DecoratedTorusKnot5c.prototype = Object.create( THREE.Curve.prototype );
DecoratedTorusKnot5c.prototype.constructor = DecoratedTorusKnot5c;
DecoratedTorusKnot5c.prototype = Object.create( THREE.Curve.prototype );
DecoratedTorusKnot5c.prototype.constructor = DecoratedTorusKnot5c;
DecoratedTorusKnot5c.prototype.getPoint = function( t ) {
DecoratedTorusKnot5c.prototype.getPoint = function( t ) {
var fi = t * Math.PI * 2;
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 );
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 new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
return new THREE.Vector3( x, y, z ).multiplyScalar( this.scale );
};
};
// export
// export
Curves.GrannyKnot = GrannyKnot;
Curves.HeartCurve = HeartCurve;
Curves.VivianiCurve = VivianiCurve;
Curves.KnotCurve = KnotCurve;
Curves.HelixCurve = HelixCurve;
Curves.TrefoilKnot = TrefoilKnot;
Curves.TorusKnot = TorusKnot;
Curves.CinquefoilKnot = CinquefoilKnot;
Curves.TrefoilPolynomialKnot = TrefoilPolynomialKnot;
Curves.FigureEightPolynomialKnot = FigureEightPolynomialKnot;
Curves.DecoratedTorusKnot4a = DecoratedTorusKnot4a;
Curves.DecoratedTorusKnot4b = DecoratedTorusKnot4b;
Curves.DecoratedTorusKnot5a = DecoratedTorusKnot5a;
Curves.DecoratedTorusKnot5c = DecoratedTorusKnot5c;
Curves.GrannyKnot = GrannyKnot;
Curves.HeartCurve = HeartCurve;
Curves.VivianiCurve = VivianiCurve;
Curves.KnotCurve = KnotCurve;
Curves.HelixCurve = HelixCurve;
Curves.TrefoilKnot = TrefoilKnot;
Curves.TorusKnot = TorusKnot;
Curves.CinquefoilKnot = CinquefoilKnot;
Curves.TrefoilPolynomialKnot = TrefoilPolynomialKnot;
Curves.FigureEightPolynomialKnot = FigureEightPolynomialKnot;
Curves.DecoratedTorusKnot4a = DecoratedTorusKnot4a;
Curves.DecoratedTorusKnot4b = DecoratedTorusKnot4b;
Curves.DecoratedTorusKnot5a = DecoratedTorusKnot5a;
Curves.DecoratedTorusKnot5c = DecoratedTorusKnot5c;
} ) ( THREE.Curves = THREE.Curves || {} );
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