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📄 CurveExtras.js

📊 Analysis Summary

Metric Count
🔧 Functions 15
🧱 Classes 14
📦 Imports 2
📊 Variables & Constants 67

📚 Table of Contents

🛠️ File Location:

📂 examples/jsm/curves/CurveExtras.js

📦 Imports

Name Source
Curve three
Vector3 three

Variables & Constants

Name Type Kind Value Exported
point Vector3 let/var optionalTarget ✗
x number let/var - 0.22 * Math.cos( t ) - 1.28 * Math.sin( t ) - 0.44 * Math.cos( 3 * t ) - 0.... ✗
y number let/var - 0.1 * Math.cos( 2 * t ) - 0.27 * Math.sin( 2 * t ) + 0.38 * Math.cos( 4 * t... ✗
z number let/var 0.7 * Math.cos( 3 * t ) - 0.4 * Math.sin( 3 * t ) ✗
point Vector3 let/var optionalTarget ✗
x number let/var 16 * Math.pow( Math.sin( t ), 3 ) ✗
y number let/var 13 * Math.cos( t ) - 5 * Math.cos( 2 * t ) - 2 * Math.cos( 3 * t ) - Math.cos... ✗
z 0 let/var 0 ✗
point Vector3 let/var optionalTarget ✗
a number let/var this.scale / 2 ✗
x number let/var a * ( 1 + Math.cos( t ) ) ✗
y number let/var a * Math.sin( t ) ✗
z number let/var 2 * a * Math.sin( t / 2 ) ✗
point Vector3 let/var optionalTarget ✗
R 10 let/var 10 ✗
s 50 let/var 50 ✗
x number let/var s * Math.sin( t ) ✗
y number let/var Math.cos( t ) * ( R + s * Math.cos( t ) ) ✗
z number let/var Math.sin( t ) * ( R + s * Math.cos( t ) ) ✗
point Vector3 let/var optionalTarget ✗
a 30 let/var 30 ✗
b 150 let/var 150 ✗
t2 number let/var 2 * Math.PI * t * b / 30 ✗
x number let/var Math.cos( t2 ) * a ✗
y number let/var Math.sin( t2 ) * a ✗
z number let/var b * t ✗
point Vector3 let/var optionalTarget ✗
x number let/var ( 2 + Math.cos( 3 * t ) ) * Math.cos( 2 * t ) ✗
y number let/var ( 2 + Math.cos( 3 * t ) ) * Math.sin( 2 * t ) ✗
point Vector3 let/var optionalTarget ✗
p 3 let/var 3 ✗
q 4 let/var 4 ✗
x number let/var ( 2 + Math.cos( q * t ) ) * Math.cos( p * t ) ✗
y number let/var ( 2 + Math.cos( q * t ) ) * Math.sin( p * t ) ✗
point Vector3 let/var optionalTarget ✗
p 2 let/var 2 ✗
q 5 let/var 5 ✗
x number let/var ( 2 + Math.cos( q * t ) ) * Math.cos( p * t ) ✗
y number let/var ( 2 + Math.cos( q * t ) ) * Math.sin( p * t ) ✗
point Vector3 let/var optionalTarget ✗
x number let/var Math.pow( t, 3 ) - 3 * t ✗
y number let/var Math.pow( t, 4 ) - 4 * t * t ✗
z number let/var 1 / 5 * Math.pow( t, 5 ) - 2 * t ✗
r number let/var y - x ✗
point Vector3 let/var optionalTarget ✗
x number let/var 2 / 5 * t * ( t * t - 7 ) * ( t * t - 10 ) ✗
y number let/var Math.pow( t, 4 ) - 13 * t * t ✗
z number let/var 1 / 10 * t * ( t * t - 4 ) * ( t * t - 9 ) * ( t * t - 12 ) ✗
point Vector3 let/var optionalTarget ✗
x number let/var Math.cos( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t... ✗
y number let/var Math.sin( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t... ✗
z number let/var 0.35 * Math.sin( 5 * t ) ✗
point Vector3 let/var optionalTarget ✗
fi number let/var t * Math.PI * 2 ✗
x number let/var Math.cos( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi... ✗
y number let/var Math.sin( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi... ✗
z number let/var 0.2 * Math.sin( 9 * fi ) ✗
point Vector3 let/var optionalTarget ✗
fi number let/var t * Math.PI * 2 ✗
x number let/var Math.cos( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi... ✗
y number let/var Math.sin( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi... ✗
z number let/var 0.2 * Math.sin( 20 * fi ) ✗
point Vector3 let/var optionalTarget ✗
fi number let/var t * Math.PI * 2 ✗
x number let/var Math.cos( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * ... ✗
y number let/var Math.sin( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * ... ✗
z number let/var 0.35 * Math.sin( 15 * fi ) ✗

Functions

GrannyKnot.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set( x, y, z ).multiplyScalar
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.pow
  • Math.sin
  • Math.cos
  • point.set( x, y, z ).multiplyScalar
Code 
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 );

    }

VivianiCurve.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.sin
  • Math.cos
  • point.set
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set( x, y, z ).multiplyScalar
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set( x, y, z ).multiplyScalar
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set( x, y, z ).multiplyScalar
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.pow
  • point.set( x, y, z ).multiplyScalar
Code 
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 );

    }

scaleTo(x: any, y: any, t: any): any

Parameters:

  • x any
  • y any
  • t any

Returns: any

Code 
function scaleTo( x, y, t ) {

    const r = y - x;
    return t * r + x;

}

FigureEightPolynomialKnot.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • scaleTo
  • Math.pow
  • point.set( x, y, z ).multiplyScalar
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set( x, y, z ).multiplyScalar
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set( x, y, z ).multiplyScalar
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set( x, y, z ).multiplyScalar
Code 
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.getPoint(t: number, optionalTarget: Vector3): Vector3

JSDoc: 

/**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */

Parameters:

  • t number
  • optionalTarget Vector3

Returns: Vector3

Calls:

  • Math.cos
  • Math.sin
  • point.set( x, y, z ).multiplyScalar
Code 
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 );

    }

Classes

GrannyKnot

Class Code 
class GrannyKnot extends Curve {

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the 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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class HeartCurve extends Curve {

    /**
     * Constructs a new heart curve.
     *
     * @param {number} [scale=5] - The curve's scale.
     */
    constructor( scale = 5 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 5
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 );

    }

VivianiCurve

Class Code 
class VivianiCurve extends Curve {

    /**
     * Constructs a new Viviani curve.
     *
     * @param {number} [scale=70] - The curve's scale.
     */
    constructor( scale = 70 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 70
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class KnotCurve extends Curve {

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the 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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class HelixCurve extends Curve {

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the 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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class TrefoilKnot extends Curve {

    /**
     * Constructs a new Trefoil Knot.
     *
     * @param {number} [scale=10] - The curve's scale.
     */
    constructor( scale = 10 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 10
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class TorusKnot extends Curve {

    /**
     * Constructs a new torus knot.
     *
     * @param {number} [scale=10] - The curve's scale.
     */
    constructor( scale = 10 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 10
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class CinquefoilKnot extends Curve {

    /**
     * Constructs a new Cinquefoil Knot.
     *
     * @param {number} [scale=10] - The curve's scale.
     */
    constructor( scale = 10 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 10
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class TrefoilPolynomialKnot extends Curve {

    /**
     * Constructs a new Trefoil Polynomial Knot.
     *
     * @param {number} [scale=10] - The curve's scale.
     */
    constructor( scale = 10 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 10
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 );

    }

FigureEightPolynomialKnot

Class Code 
class FigureEightPolynomialKnot extends Curve {

    /**
     * Constructs a new Figure Eight Polynomial Knot.
     *
     * @param {number} [scale=1] - The curve's scale.
     */
    constructor( scale = 1 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 1
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class DecoratedTorusKnot4a extends Curve {

    /**
     * Constructs a new Decorated Torus Knot 4a.
     *
     * @param {number} [scale=1] - The curve's scale.
     */
    constructor( scale = 40 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 40
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class DecoratedTorusKnot4b extends Curve {

    /**
     * Constructs a new Decorated Torus Knot 4b.
     *
     * @param {number} [scale=1] - The curve's scale.
     */
    constructor( scale = 40 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 40
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class DecoratedTorusKnot5a extends Curve {

    /**
     * Constructs a new Decorated Torus Knot 5a.
     *
     * @param {number} [scale=1] - The curve's scale.
     */
    constructor( scale = 40 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 40
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 Code 
class DecoratedTorusKnot5c extends Curve {

    /**
     * Constructs a new Decorated Torus Knot 5c.
     *
     * @param {number} [scale=1] - The curve's scale.
     */
    constructor( scale = 40 ) {

        super();

        /**
         * The curve's scale.
         *
         * @type {number}
         * @default 40
         */
        this.scale = scale;

    }

    /**
     * This method returns a vector in 3D space for the given interpolation factor.
     *
     * @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
     * @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
     * @return {Vector3} The position on the curve.
     */
    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 );

    }

}

Methods

getPoint(t: number, optionalTarget: Vector3): Vector3
Code 
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 );

    }