( 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;
} )();
