three.js/examples/js/utils/GeometryUtils.js

( function () {

	class GeometryUtils {

		/**
   * Generates 2D-Coordinates in a very fast way.
   *
   * Based on work by:
   * @link http://www.openprocessing.org/sketch/15493
   *
   * @param center     Center of Hilbert curve.
   * @param size       Total width of Hilbert curve.
   * @param iterations Number of subdivisions.
   * @param v0         Corner index -X, -Z.
   * @param v1         Corner index -X, +Z.
   * @param v2         Corner index +X, +Z.
   * @param v3         Corner index +X, -Z.
   */
		static hilbert2D( center = new THREE.Vector3( 0, 0, 0 ), size = 10, iterations = 1, v0 = 0, v1 = 1, v2 = 2, v3 = 3 ) {

			const half = size / 2;
			const vec_s = [ new THREE.Vector3( center.x - half, center.y, center.z - half ), new THREE.Vector3( center.x - half, center.y, center.z + half ), new THREE.Vector3( center.x + half, center.y, center.z + half ), new THREE.Vector3( center.x + half, center.y, center.z - half ) ];
			const vec = [ vec_s[ v0 ], vec_s[ v1 ], vec_s[ v2 ], vec_s[ v3 ] ]; // Recurse iterations

			if ( 0 <= -- iterations ) {

				const tmp = [];
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 0 ], half, iterations, v0, v3, v2, v1 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 1 ], half, iterations, v0, v1, v2, v3 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 2 ], half, iterations, v0, v1, v2, v3 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 3 ], half, iterations, v2, v1, v0, v3 ) ); // Return recursive call

				return tmp;

			} // Return complete Hilbert Curve.


			return vec;

		}
		/**
   * Generates 3D-Coordinates in a very fast way.
   *
   * Based on work by:
   * @link http://www.openprocessing.org/visuals/?visualID=15599
   *
   * @param center     Center of Hilbert curve.
   * @param size       Total width of Hilbert curve.
   * @param iterations Number of subdivisions.
   * @param v0         Corner index -X, +Y, -Z.
   * @param v1         Corner index -X, +Y, +Z.
   * @param v2         Corner index -X, -Y, +Z.
   * @param v3         Corner index -X, -Y, -Z.
   * @param v4         Corner index +X, -Y, -Z.
   * @param v5         Corner index +X, -Y, +Z.
   * @param v6         Corner index +X, +Y, +Z.
   * @param v7         Corner index +X, +Y, -Z.
   */


		static hilbert3D( center = new THREE.Vector3( 0, 0, 0 ), size = 10, iterations = 1, v0 = 0, v1 = 1, v2 = 2, v3 = 3, v4 = 4, v5 = 5, v6 = 6, v7 = 7 ) {

			// Default Vars
			const half = size / 2;
			const vec_s = [ new THREE.Vector3( center.x - half, center.y + half, center.z - half ), new THREE.Vector3( center.x - half, center.y + half, center.z + half ), new THREE.Vector3( center.x - half, center.y - half, center.z + half ), new THREE.Vector3( center.x - half, center.y - half, center.z - half ), new THREE.Vector3( center.x + half, center.y - half, center.z - half ), new THREE.Vector3( center.x + half, center.y - half, center.z + half ), new THREE.Vector3( center.x + half, center.y + half, center.z + half ), new THREE.Vector3( center.x + half, center.y + half, center.z - half ) ];
			const vec = [ vec_s[ v0 ], vec_s[ v1 ], vec_s[ v2 ], vec_s[ v3 ], vec_s[ v4 ], vec_s[ v5 ], vec_s[ v6 ], vec_s[ v7 ] ]; // Recurse iterations

			if ( -- iterations >= 0 ) {

				const tmp = [];
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 0 ], half, iterations, v0, v3, v4, v7, v6, v5, v2, v1 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 1 ], half, iterations, v0, v7, v6, v1, v2, v5, v4, v3 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 2 ], half, iterations, v0, v7, v6, v1, v2, v5, v4, v3 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 3 ], half, iterations, v2, v3, v0, v1, v6, v7, v4, v5 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 4 ], half, iterations, v2, v3, v0, v1, v6, v7, v4, v5 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 5 ], half, iterations, v4, v3, v2, v5, v6, v1, v0, v7 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 6 ], half, iterations, v4, v3, v2, v5, v6, v1, v0, v7 ) );
				Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 7 ], half, iterations, v6, v5, v2, v1, v0, v3, v4, v7 ) ); // Return recursive call

				return tmp;

			} // Return complete Hilbert Curve.


			return vec;

		}
		/**
   * Generates a Gosper curve (lying in the XY plane)
   *
   * https://gist.github.com/nitaku/6521802
   *
   * @param size The size of a single gosper island.
   */


		static gosper( size = 1 ) {

			function fractalize( config ) {

				let output;
				let input = config.axiom;

				for ( let i = 0, il = config.steps; 0 <= il ? i < il : i > il; 0 <= il ? i ++ : i -- ) {

					output = '';

					for ( let j = 0, jl = input.length; j < jl; j ++ ) {

						const char = input[ j ];

						if ( char in config.rules ) {

							output += config.rules[ char ];

						} else {

							output += char;

						}

					}

					input = output;

				}

				return output;

			}

			function toPoints( config ) {

				let currX = 0,
					currY = 0;
				let angle = 0;
				const path = [ 0, 0, 0 ];
				const fractal = config.fractal;

				for ( let i = 0, l = fractal.length; i < l; i ++ ) {

					const char = fractal[ i ];

					if ( char === '+' ) {

						angle += config.angle;

					} else if ( char === '-' ) {

						angle -= config.angle;

					} else if ( char === 'F' ) {

						currX += config.size * Math.cos( angle );
						currY += - config.size * Math.sin( angle );
						path.push( currX, currY, 0 );

					}

				}

				return path;

			} //


			const gosper = fractalize( {
				axiom: 'A',
				steps: 4,
				rules: {
					A: 'A+BF++BF-FA--FAFA-BF+',
					B: '-FA+BFBF++BF+FA--FA-B'
				}
			} );
			const points = toPoints( {
				fractal: gosper,
				size: size,
				angle: Math.PI / 3 // 60 degrees

			} );
			return points;

		}

	}

	THREE.GeometryUtils = GeometryUtils;

} )();