ParametricGeometry.js

/**
 * Parametric Surfaces Geometry
 * based on the brilliant article by @prideout https://prideout.net/blog/old/blog/index.html@p=44.html
 */

import {
	BufferGeometry,
	Float32BufferAttribute,
	Vector3
} from '../../../build/three.module.js';

class ParametricGeometry extends BufferGeometry {

	constructor( func = ( u, v, target ) => target.set( u, v, Math.cos( u ) * Math.sin( v ) ), slices = 8, stacks = 8 ) {

		super();

		this.type = 'ParametricGeometry';

		this.parameters = {
			func: func,
			slices: slices,
			stacks: stacks
		};

		// buffers

		const indices = [];
		const vertices = [];
		const normals = [];
		const uvs = [];

		const EPS = 0.00001;

		const normal = new Vector3();

		const p0 = new Vector3(), p1 = new Vector3();
		const pu = new Vector3(), pv = new Vector3();

		if ( func.length < 3 ) {

			console.error( 'THREE.ParametricGeometry: Function must now modify a Vector3 as third parameter.' );

		}

		// generate vertices, normals and uvs

		const sliceCount = slices + 1;

		for ( let i = 0; i <= stacks; i ++ ) {

			const v = i / stacks;

			for ( let j = 0; j <= slices; j ++ ) {

				const u = j / slices;

				// vertex

				func( u, v, p0 );
				vertices.push( p0.x, p0.y, p0.z );

				// normal

				// approximate tangent vectors via finite differences

				if ( u - EPS >= 0 ) {

					func( u - EPS, v, p1 );
					pu.subVectors( p0, p1 );

				} else {

					func( u + EPS, v, p1 );
					pu.subVectors( p1, p0 );

				}

				if ( v - EPS >= 0 ) {

					func( u, v - EPS, p1 );
					pv.subVectors( p0, p1 );

				} else {

					func( u, v + EPS, p1 );
					pv.subVectors( p1, p0 );

				}

				// cross product of tangent vectors returns surface normal

				normal.crossVectors( pu, pv ).normalize();
				normals.push( normal.x, normal.y, normal.z );

				// uv

				uvs.push( u, v );

			}

		}

		// generate indices

		for ( let i = 0; i < stacks; i ++ ) {

			for ( let j = 0; j < slices; j ++ ) {

				const a = i * sliceCount + j;
				const b = i * sliceCount + j + 1;
				const c = ( i + 1 ) * sliceCount + j + 1;
				const d = ( i + 1 ) * sliceCount + j;

				// faces one and two

				indices.push( a, b, d );
				indices.push( b, c, d );

			}

		}

		// build geometry

		this.setIndex( indices );
		this.setAttribute( 'position', new Float32BufferAttribute( vertices, 3 ) );
		this.setAttribute( 'normal', new Float32BufferAttribute( normals, 3 ) );
		this.setAttribute( 'uv', new Float32BufferAttribute( uvs, 2 ) );

	}

}

export { ParametricGeometry };