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b797337 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 | import { Vector3 } from 'three';
/**
* 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 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 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 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 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;
}
export {
hilbert2D,
hilbert3D,
gosper,
};
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