173 lines
3.7 KiB
JavaScript
173 lines
3.7 KiB
JavaScript
import {
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BufferGeometry,
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Float32BufferAttribute,
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Vector3
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} from 'three';
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/**
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* This class can be used to generate a geometry based on a parametric surface.
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*
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* Reference: [Mesh Generation with Python]{@link https://prideout.net/blog/old/blog/index.html@p=44.html}
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*
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* ```js
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* const geometry = new THREE.ParametricGeometry( klein, 25, 25 );
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* const material = new THREE.MeshBasicMaterial( { color: 0x00ff00 } );
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* const klein = new THREE.Mesh( geometry, material );
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* scene.add( klein );
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* ```
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*
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* @augments BufferGeometry
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* @three_import import { ParametricGeometry } from 'three/addons/geometries/ParametricGeometry.js';
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*/
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class ParametricGeometry extends BufferGeometry {
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/**
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* Constructs a new parametric geometry.
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*
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* @param {ParametricGeometry~Func} func - The parametric function. Default is a function that generates a curved plane surface.
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* @param {number} [slices=8] - The number of slices to use for the parametric function.
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* @param {number} [stacks=8] - The stacks of slices to use for the parametric function.
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*/
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constructor( func = ( u, v, target ) => target.set( u, v, Math.cos( u ) * Math.sin( v ) ), slices = 8, stacks = 8 ) {
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super();
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this.type = 'ParametricGeometry';
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/**
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* Holds the constructor parameters that have been
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* used to generate the geometry. Any modification
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* after instantiation does not change the geometry.
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*
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* @type {Object}
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*/
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this.parameters = {
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func: func,
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slices: slices,
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stacks: stacks
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};
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// buffers
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const indices = [];
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const vertices = [];
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const normals = [];
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const uvs = [];
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const EPS = 0.00001;
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const normal = new Vector3();
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const p0 = new Vector3(), p1 = new Vector3();
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const pu = new Vector3(), pv = new Vector3();
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// generate vertices, normals and uvs
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const sliceCount = slices + 1;
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for ( let i = 0; i <= stacks; i ++ ) {
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const v = i / stacks;
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for ( let j = 0; j <= slices; j ++ ) {
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const u = j / slices;
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// vertex
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func( u, v, p0 );
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vertices.push( p0.x, p0.y, p0.z );
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// normal
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// approximate tangent vectors via finite differences
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if ( u - EPS >= 0 ) {
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func( u - EPS, v, p1 );
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pu.subVectors( p0, p1 );
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} else {
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func( u + EPS, v, p1 );
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pu.subVectors( p1, p0 );
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}
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if ( v - EPS >= 0 ) {
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func( u, v - EPS, p1 );
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pv.subVectors( p0, p1 );
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} else {
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func( u, v + EPS, p1 );
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pv.subVectors( p1, p0 );
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}
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// cross product of tangent vectors returns surface normal
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normal.crossVectors( pu, pv ).normalize();
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normals.push( normal.x, normal.y, normal.z );
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// uv
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uvs.push( u, v );
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}
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}
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// generate indices
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for ( let i = 0; i < stacks; i ++ ) {
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for ( let j = 0; j < slices; j ++ ) {
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const a = i * sliceCount + j;
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const b = i * sliceCount + j + 1;
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const c = ( i + 1 ) * sliceCount + j + 1;
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const d = ( i + 1 ) * sliceCount + j;
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// faces one and two
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indices.push( a, b, d );
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indices.push( b, c, d );
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}
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}
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// build geometry
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this.setIndex( indices );
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this.setAttribute( 'position', new Float32BufferAttribute( vertices, 3 ) );
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this.setAttribute( 'normal', new Float32BufferAttribute( normals, 3 ) );
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this.setAttribute( 'uv', new Float32BufferAttribute( uvs, 2 ) );
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}
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copy( source ) {
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super.copy( source );
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this.parameters = Object.assign( {}, source.parameters );
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return this;
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}
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}
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/**
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* Parametric function definition of `ParametricGeometry`.
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*
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* @callback ParametricGeometry~Func
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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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export { ParametricGeometry };
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