⬅️ Back to Table of Contents

📄 ParametricFunctions.js

📊 Analysis Summary

Metric	Count
🔧 Functions	4
📊 Variables & Constants	15

📚 Table of Contents

• Variables & Constants
• Functions

🛠️ File Location:

📂 examples/jsm/geometries/ParametricFunctions.js

Variables & Constants

Name	Type	Kind	Value	Exported
x	any	let/var	*not shown*	✗
z	any	let/var	*not shown*	✗
y	number	let/var	- 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( v )	✗
v	number	let/var	2 * Math.PI * t	✗
a	2	let/var	2	✗
x	number	let/var	Math.cos( v ) * ( a + u * Math.cos( v / 2 ) )	✗
y	number	let/var	Math.sin( v ) * ( a + u * Math.cos( v / 2 ) )	✗
z	number	let/var	u * Math.sin( v / 2 )	✗
phi	number	let/var	u / 2	✗
major	2.25	let/var	2.25	✗
a	0.125	let/var	0.125	✗
b	0.65	let/var	0.65	✗
x	number	let/var	a * Math.cos( t ) * Math.cos( phi ) - b * Math.sin( t ) * Math.sin( phi )	✗
z	number	let/var	a * Math.cos( t ) * Math.sin( phi ) + b * Math.sin( t ) * Math.cos( phi )	✗
y	number	let/var	( major + x ) * Math.sin( u )	✗

---

Functions

klein(v: number, u: number, target: Vector3): void

JSDoc:

/**
 * A parametric function representing the Klein bottle.
 *
 * @param {number} v - The `v` coordinate on the surface in the range `[0,1]`.
 * @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
 * @param {Vector3} target - The target vector that is used to store the method's result.
 */

Parameters:

• v number
• u number
• target Vector3

Returns: void

Calls:

• Math.cos
• Math.sin
• target.set

Code

function klein( v, u, target ) {

    u *= Math.PI;
    v *= 2 * Math.PI;

    u = u * 2;
    let x, z;
    if ( u < Math.PI ) {

        x = 3 * Math.cos( u ) * ( 1 + Math.sin( u ) ) + ( 2 * ( 1 - Math.cos( u ) / 2 ) ) * Math.cos( u ) * Math.cos( v );
        z = - 8 * Math.sin( u ) - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( u ) * Math.cos( v );

    } else {

        x = 3 * Math.cos( u ) * ( 1 + Math.sin( u ) ) + ( 2 * ( 1 - Math.cos( u ) / 2 ) ) * Math.cos( v + Math.PI );
        z = - 8 * Math.sin( u );

    }

    const y = - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( v );

    target.set( x, y, z );

}

plane(u: number, v: number, target: Vector3): void

JSDoc:

/**
 * A parametric function representing a flat plane.
 *
 * @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
 * @param {number} v - The `v` coordinate on the surface in the range `[0,1]`.
 * @param {Vector3} target - The target vector that is used to store the method's result.
 */

Parameters:

• u number
• v number
• target Vector3

Returns: void

Calls:

• target.set

Code

function plane( u, v, target ) {

    target.set( u, 0, v );

}

mobius(u: number, t: number, target: Vector3): void

JSDoc:

/**
 * A parametric function representing a flat mobius strip.
 *
 * @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
 * @param {number} t - The `v` coordinate on the surface in the range `[0,1]`.
 * @param {Vector3} target - The target vector that is used to store the method's result.
 */

Parameters:

• u number
• t number
• target Vector3

Returns: void

Calls:

• Math.cos
• Math.sin
• target.set

Internal Comments:

// http://www.wolframalpha.com/input/?i=M%C3%B6bius+strip+parametric+equations&lk=1&a=ClashPrefs_*Surface.MoebiusStrip.SurfaceProperty.ParametricEquations- (x3)

Code

function mobius( u, t, target ) {

    // http://www.wolframalpha.com/input/?i=M%C3%B6bius+strip+parametric+equations&lk=1&a=ClashPrefs_*Surface.MoebiusStrip.SurfaceProperty.ParametricEquations-
    u = u - 0.5;
    const v = 2 * Math.PI * t;

    const a = 2;

    const x = Math.cos( v ) * ( a + u * Math.cos( v / 2 ) );
    const y = Math.sin( v ) * ( a + u * Math.cos( v / 2 ) );
    const z = u * Math.sin( v / 2 );

    target.set( x, y, z );

}

mobius3d(u: number, t: number, target: Vector3): void

JSDoc:

/**
 * A parametric function representing a volumetric mobius strip.
 *
 * @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
 * @param {number} t - The `v` coordinate on the surface in the range `[0,1]`.
 * @param {Vector3} target - The target vector that is used to store the method's result.
 */

Parameters:

• u number
• t number
• target Vector3

Returns: void

Calls:

• Math.cos
• Math.sin
• target.set

Code

function mobius3d( u, t, target ) {

    u *= Math.PI;
    t *= 2 * Math.PI;

    u = u * 2;
    const phi = u / 2;
    const major = 2.25, a = 0.125, b = 0.65;

    let x = a * Math.cos( t ) * Math.cos( phi ) - b * Math.sin( t ) * Math.sin( phi );
    const z = a * Math.cos( t ) * Math.sin( phi ) + b * Math.sin( t ) * Math.cos( phi );
    const y = ( major + x ) * Math.sin( u );
    x = ( major + x ) * Math.cos( u );

    target.set( x, y, z );

}

---