101 lines
2.9 KiB
JavaScript
101 lines
2.9 KiB
JavaScript
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/**
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* @module ParametricFunctions
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* @three_import import * as ParametricFunctions from 'three/addons/geometries/ParametricFunctions.js';
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*/
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/**
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* A parametric function representing the Klein bottle.
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*
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* @param {number} v - The `v` coordinate on the surface in the range `[0,1]`.
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* @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
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* @param {Vector3} target - The target vector that is used to store the method's result.
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*/
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function klein( v, u, target ) {
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u *= Math.PI;
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v *= 2 * Math.PI;
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u = u * 2;
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let x, z;
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if ( u < Math.PI ) {
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x = 3 * Math.cos( u ) * ( 1 + Math.sin( u ) ) + ( 2 * ( 1 - Math.cos( u ) / 2 ) ) * Math.cos( u ) * Math.cos( v );
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z = - 8 * Math.sin( u ) - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( u ) * Math.cos( v );
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} else {
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x = 3 * Math.cos( u ) * ( 1 + Math.sin( u ) ) + ( 2 * ( 1 - Math.cos( u ) / 2 ) ) * Math.cos( v + Math.PI );
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z = - 8 * Math.sin( u );
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}
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const y = - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( v );
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target.set( x, y, z );
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}
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/**
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* A parametric function representing a flat plane.
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*
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* @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
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* @param {number} v - The `v` coordinate on the surface in the range `[0,1]`.
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* @param {Vector3} target - The target vector that is used to store the method's result.
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*/
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function plane( u, v, target ) {
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target.set( u, 0, v );
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}
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/**
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* A parametric function representing a flat mobius strip.
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*
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* @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
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* @param {number} t - The `v` coordinate on the surface in the range `[0,1]`.
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* @param {Vector3} target - The target vector that is used to store the method's result.
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*/
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function mobius( u, t, target ) {
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// http://www.wolframalpha.com/input/?i=M%C3%B6bius+strip+parametric+equations&lk=1&a=ClashPrefs_*Surface.MoebiusStrip.SurfaceProperty.ParametricEquations-
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u = u - 0.5;
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const v = 2 * Math.PI * t;
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const a = 2;
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const x = Math.cos( v ) * ( a + u * Math.cos( v / 2 ) );
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const y = Math.sin( v ) * ( a + u * Math.cos( v / 2 ) );
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const z = u * Math.sin( v / 2 );
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target.set( x, y, z );
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}
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/**
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* A parametric function representing a volumetric mobius strip.
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*
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* @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
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* @param {number} t - The `v` coordinate on the surface in the range `[0,1]`.
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* @param {Vector3} target - The target vector that is used to store the method's result.
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*/
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function mobius3d( u, t, target ) {
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u *= Math.PI;
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t *= 2 * Math.PI;
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u = u * 2;
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const phi = u / 2;
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const major = 2.25, a = 0.125, b = 0.65;
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let x = a * Math.cos( t ) * Math.cos( phi ) - b * Math.sin( t ) * Math.sin( phi );
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const z = a * Math.cos( t ) * Math.sin( phi ) + b * Math.sin( t ) * Math.cos( phi );
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const y = ( major + x ) * Math.sin( u );
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x = ( major + x ) * Math.cos( u );
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target.set( x, y, z );
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}
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export { klein, plane, mobius, mobius3d };
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