three.js/examples/js/geometries/ParametricGeometry.js

( function () {

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

	class ParametricGeometry extends THREE.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 THREE.Vector3();
			const p0 = new THREE.Vector3(),
				p1 = new THREE.Vector3();
			const pu = new THREE.Vector3(),
				pv = new THREE.Vector3(); // 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 THREE.Float32BufferAttribute( vertices, 3 ) );
			this.setAttribute( 'normal', new THREE.Float32BufferAttribute( normals, 3 ) );
			this.setAttribute( 'uv', new THREE.Float32BufferAttribute( uvs, 2 ) );

		}

	}

	THREE.ParametricGeometry = ParametricGeometry;

} )();