threejs/examples/js/utils/GeometryUtils.js

( function () {

	/**
 * 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.
 */
	function 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 ) {

			return [ ...hilbert2D( vec[ 0 ], half, iterations, v0, v3, v2, v1 ), ...hilbert2D( vec[ 1 ], half, iterations, v0, v1, v2, v3 ), ...hilbert2D( vec[ 2 ], half, iterations, v0, v1, v2, v3 ), ...hilbert2D( vec[ 3 ], half, iterations, v2, v1, v0, v3 ) ];

		}

		// Return complete Hilbert Curve.
		return vec;

	}

	/**
 * Generates 3D-Coordinates in a very fast way.
 *
 * Based on work by:
 * @link https://openprocessing.org/user/5654
 *
 * @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.
 */
	function 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 ) {

			return [ ...hilbert3D( vec[ 0 ], half, iterations, v0, v3, v4, v7, v6, v5, v2, v1 ), ...hilbert3D( vec[ 1 ], half, iterations, v0, v7, v6, v1, v2, v5, v4, v3 ), ...hilbert3D( vec[ 2 ], half, iterations, v0, v7, v6, v1, v2, v5, v4, v3 ), ...hilbert3D( vec[ 3 ], half, iterations, v2, v3, v0, v1, v6, v7, v4, v5 ), ...hilbert3D( vec[ 4 ], half, iterations, v2, v3, v0, v1, v6, v7, v4, v5 ), ...hilbert3D( vec[ 5 ], half, iterations, v4, v3, v2, v5, v6, v1, v0, v7 ), ...hilbert3D( vec[ 6 ], half, iterations, v4, v3, v2, v5, v6, v1, v0, v7 ), ...hilbert3D( vec[ 7 ], half, iterations, v6, v5, v2, v1, v0, v3, v4, v7 ) ];

		}

		// 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.
 */
	function 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 = {};
	THREE.GeometryUtils.gosper = gosper;
	THREE.GeometryUtils.hilbert2D = hilbert2D;
	THREE.GeometryUtils.hilbert3D = hilbert3D;

} )();