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

import { Vector3 } from 'three';

/** @module GeometryUtils */

/**
 * Generates 2D-Coordinates along a Hilbert curve.
 *
 * Based on work by: {@link http://www.openprocessing.org/sketch/15493}
 *
 * @param {Vector3} [center] - Center of Hilbert curve.
 * @param {number} [size=10] - Total width of Hilbert curve.
 * @param {number} [iterations=10] - Number of subdivisions.
 * @param {number} [v0=0] - Corner index -X, -Z.
 * @param {number} [v1=1] - Corner index -X, +Z.
 * @param {number} [v2=2] - Corner index +X, +Z.
 * @param {number} [v3=3] - Corner index +X, -Z.
 * @returns {Array<Vector3>} The Hilbert curve points.
 */
function hilbert2D( center = new Vector3( 0, 0, 0 ), size = 10, iterations = 1, v0 = 0, v1 = 1, v2 = 2, v3 = 3 ) {

	const half = size / 2;

	const vec_s = [
		new Vector3( center.x - half, center.y, center.z - half ),
		new Vector3( center.x - half, center.y, center.z + half ),
		new Vector3( center.x + half, center.y, center.z + half ),
		new 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 along a Hilbert curve.
 *
 * Based on work by: {@link https://openprocessing.org/user/5654}
 *
 * @param {Vector3} [center] - Center of Hilbert curve.
 * @param {number} [size=10] - Total width of Hilbert curve.
 * @param {number} [iterations=1] - Number of subdivisions.
 * @param {number} [v0=0] - Corner index -X, +Y, -Z.
 * @param {number} [v1=1] - Corner index -X, +Y, +Z.
 * @param {number} [v2=2] - Corner index -X, -Y, +Z.
 * @param {number} [v3=3] - Corner index -X, -Y, -Z.
 * @param {number} [v4=4] - Corner index +X, -Y, -Z.
 * @param {number} [v5=5] - Corner index +X, -Y, +Z.
 * @param {number} [v6=6] - Corner index +X, +Y, +Z.
 * @param {number} [v7=7] - Corner index +X, +Y, -Z.
 * @returns {Array<Vector3>}  - The Hilbert curve points.
 */
function hilbert3D( center = new 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 Vector3( center.x - half, center.y + half, center.z - half ),
		new Vector3( center.x - half, center.y + half, center.z + half ),
		new Vector3( center.x - half, center.y - half, center.z + half ),
		new Vector3( center.x - half, center.y - half, center.z - half ),
		new Vector3( center.x + half, center.y - half, center.z - half ),
		new Vector3( center.x + half, center.y - half, center.z + half ),
		new Vector3( center.x + half, center.y + half, center.z + half ),
		new 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).
 *
 * Reference: {@link https://gist.github.com/nitaku/6521802}
 *
 * @param {number} [size=1] - The size of a single gosper island.
 * @return {Array<number>} The gosper island points.
 */
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;

}



export {
	hilbert2D,
	hilbert3D,
	gosper,
};