Accueil / npm / three@0.186.1 / examples / jsm / geometries / ParametricFunctions.js
ParametricFunctions.js
/**
* @module ParametricFunctions
* @three_import import * as ParametricFunctions from 'three/addons/geometries/ParametricFunctions.js';
*/
/**
* 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.
*/
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 );
}
/**
* 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.
*/
function plane( u, v, target ) {
target.set( u, 0, v );
}
/**
* 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.
*/
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 );
}
/**
* 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.
*/
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 );
}
export { klein, plane, mobius, mobius3d };