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

( function () {

	var 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.
	 */
		hilbert2D: function ( center, size, iterations, v0, v1, v2, v3 ) {

			// Default Vars
			var center = center !== undefined ? center : new THREE.Vector3( 0, 0, 0 ),
				size = size !== undefined ? size : 10,
				half = size / 2,
				iterations = iterations !== undefined ? iterations : 1,
				v0 = v0 !== undefined ? v0 : 0,
				v1 = v1 !== undefined ? v1 : 1,
				v2 = v2 !== undefined ? v2 : 2,
				v3 = v3 !== undefined ? v3 : 3;
			var 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 ) ];
			var vec = [ vec_s[ v0 ], vec_s[ v1 ], vec_s[ v2 ], vec_s[ v3 ] ]; // Recurse iterations

			if ( 0 <= -- iterations ) {

				var 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.
	 */
		hilbert3D: function ( center, size, iterations, v0, v1, v2, v3, v4, v5, v6, v7 ) {

			// Default Vars
			var center = center !== undefined ? center : new THREE.Vector3( 0, 0, 0 ),
				size = size !== undefined ? size : 10,
				half = size / 2,
				iterations = iterations !== undefined ? iterations : 1,
				v0 = v0 !== undefined ? v0 : 0,
				v1 = v1 !== undefined ? v1 : 1,
				v2 = v2 !== undefined ? v2 : 2,
				v3 = v3 !== undefined ? v3 : 3,
				v4 = v4 !== undefined ? v4 : 4,
				v5 = v5 !== undefined ? v5 : 5,
				v6 = v6 !== undefined ? v6 : 6,
				v7 = v7 !== undefined ? v7 : 7;
			var 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 ) ];
			var 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 ) {

				var 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.
	 */
		gosper: function ( size ) {

			size = size !== undefined ? size : 1;

			function fractalize( config ) {

				var output;
				var input = config.axiom;

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

					output = '';

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

						var char = input[ j ];

						if ( char in config.rules ) {

							output += config.rules[ char ];

						} else {

							output += char;

						}

					}

					input = output;

				}

				return output;

			}

			function toPoints( config ) {

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

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

					var 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;

			} //


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

			} );
			return points;

		}
	};

	THREE.GeometryUtils = GeometryUtils;

} )();