You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
422 lines
7.2 KiB
422 lines
7.2 KiB
import {
|
|
Curve,
|
|
Vector3
|
|
} from 'three';
|
|
|
|
/**
|
|
* 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 Curve {
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 5 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve
|
|
|
|
class VivianiCurve extends Curve {
|
|
|
|
constructor( scale = 70 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 10 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 10 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 10 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 10 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 1 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 40 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 40 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 40 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 Curve {
|
|
|
|
constructor( scale = 40 ) {
|
|
|
|
super();
|
|
|
|
this.scale = scale;
|
|
|
|
}
|
|
|
|
getPoint( t, optionalTarget = new 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 );
|
|
|
|
}
|
|
|
|
}
|
|
|
|
export {
|
|
GrannyKnot,
|
|
HeartCurve,
|
|
VivianiCurve,
|
|
KnotCurve,
|
|
HelixCurve,
|
|
TrefoilKnot,
|
|
TorusKnot,
|
|
CinquefoilKnot,
|
|
TrefoilPolynomialKnot,
|
|
FigureEightPolynomialKnot,
|
|
DecoratedTorusKnot4a,
|
|
DecoratedTorusKnot4b,
|
|
DecoratedTorusKnot5a,
|
|
DecoratedTorusKnot5c
|
|
};
|
|
|