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import { Vector3 } from 'three'; /** * Generates 2D-Coordinates in a very fast way. * * 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<Array<number>>} 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 in a very fast way. * * Based on work by: * @link https://openprocessing.org/user/5654 * * @param {Vector3} [center=new Vector3( 0, 0, 0 )] - 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<Array<number>>} - 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) * * https://gist.github.com/nitaku/6521802 * * @param {number} [size=1] - The size of a single gosper island. * @return {Array<[number, number, 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, };
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