/**
* 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
*/
import {
Curve,
Vector3
} from "../../../build/three.module.js";
var Curves = ( function () {
// GrannyKnot
function GrannyKnot() {
Curve.call( this );
}
GrannyKnot.prototype = Object.create( Curve.prototype );
GrannyKnot.prototype.constructor = GrannyKnot;
GrannyKnot.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 5 : scale;
}
HeartCurve.prototype = Object.create( Curve.prototype );
HeartCurve.prototype.constructor = HeartCurve;
HeartCurve.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 Curve
function VivianiCurve( scale ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 70 : scale;
}
VivianiCurve.prototype = Object.create( Curve.prototype );
VivianiCurve.prototype.constructor = VivianiCurve;
VivianiCurve.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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() {
Curve.call( this );
}
KnotCurve.prototype = Object.create( Curve.prototype );
KnotCurve.prototype.constructor = KnotCurve;
KnotCurve.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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() {
Curve.call( this );
}
HelixCurve.prototype = Object.create( Curve.prototype );
HelixCurve.prototype.constructor = HelixCurve;
HelixCurve.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 10 : scale;
}
TrefoilKnot.prototype = Object.create( Curve.prototype );
TrefoilKnot.prototype.constructor = TrefoilKnot;
TrefoilKnot.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 10 : scale;
}
TorusKnot.prototype = Object.create( Curve.prototype );
TorusKnot.prototype.constructor = TorusKnot;
TorusKnot.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 10 : scale;
}
CinquefoilKnot.prototype = Object.create( Curve.prototype );
CinquefoilKnot.prototype.constructor = CinquefoilKnot;
CinquefoilKnot.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 10 : scale;
}
TrefoilPolynomialKnot.prototype = Object.create( Curve.prototype );
TrefoilPolynomialKnot.prototype.constructor = TrefoilPolynomialKnot;
TrefoilPolynomialKnot.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 1 : scale;
}
FigureEightPolynomialKnot.prototype = Object.create( Curve.prototype );
FigureEightPolynomialKnot.prototype.constructor = FigureEightPolynomialKnot;
FigureEightPolynomialKnot.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 40 : scale;
}
DecoratedTorusKnot4a.prototype = Object.create( Curve.prototype );
DecoratedTorusKnot4a.prototype.constructor = DecoratedTorusKnot4a;
DecoratedTorusKnot4a.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 40 : scale;
}
DecoratedTorusKnot4b.prototype = Object.create( Curve.prototype );
DecoratedTorusKnot4b.prototype.constructor = DecoratedTorusKnot4b;
DecoratedTorusKnot4b.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 40 : scale;
}
DecoratedTorusKnot5a.prototype = Object.create( Curve.prototype );
DecoratedTorusKnot5a.prototype.constructor = DecoratedTorusKnot5a;
DecoratedTorusKnot5a.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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 ) {
Curve.call( this );
this.scale = ( scale === undefined ) ? 40 : scale;
}
DecoratedTorusKnot5c.prototype = Object.create( Curve.prototype );
DecoratedTorusKnot5c.prototype.constructor = DecoratedTorusKnot5c;
DecoratedTorusKnot5c.prototype.getPoint = function ( t, optionalTarget ) {
var point = optionalTarget || new 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
};
} )();
export { Curves };
