hilbert
A module that computes Hilbert space-filling-curve coordinates in 2- or 3-dimensions.
npm install hilbert
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Version | 2.0.0 last updated a month ago |
Keywords | hilbert, curve, space-filling, fractal |
Repository | http://github.com/ryan-williams/hilbert-js.git (git) |
Homepage | https://github.com/ryan-williams/hilbert-js |
Bugs | https://github.com/ryan-williams/hilbert-js/issues |
Dependencies | None |
Hilbert-js
Node library for working with 2-d and 3-d hilbert curves.
Install
npm install hilbert
Run Tests
npm test
Examples
> var H = require('./hilbert')
// Basic 2x2 square
> H.d2xy(0)
{ x: 0, y: 0 }
> H.d2xy(1)
{ x: 1, y: 0 }
> H.d2xy(2)
{ x: 1, y: 1 }
> H.d2xy(3)
{ x: 0, y: 1 }
// Inverse of previous call
> H.xy2d(0, 1)
3
> H.d2xy(1024)
{ x: 0, y: 32 }
> H.xy2d(0, 32)
1024
// 3-d mode
> H.d2xyz(10).arr
[ 0, 1, 3 ]
> H.xyz2d(0, 1, 3)
10
// Create a 2-d Hilbert curve that will follow the axis path 'xy'
// on its "4" level, i.e. its 4x4 square, which will be made up of
// 4 2x2 squares, the first of which will consequently follow a
// 'yx' axis path.
> var H2 = H.Hilbert2d;
> var h2 = new H2(4)
> h2.xy(0)
{ x: 0, y: 0 }
> h2.xy(1)
{ x: 0, y: 1 } // order is reversed at this (2x2) level.
> h2.xy(2)
{ x: 1, y: 1 }
> h2.xy(3)
{ x: 1, y: 0 }
> h2.xy(4)
{ x: 2, y: 0 } // order is 'x'-axis, then 'y'-, at the 4x4 level.
API
The module, require('hilbert')
, exposes the following functions:
xy2d(x,y)
(aliases d2(x,y)
, d(x,y)
)
Convert an (x,y)
tuple to a distance along a 2-dimensional Hilbert walk.
d2xy(d)
(alias xy(d)
)
The inverse of xy2d
.
xyz2d(x,y,z)
(aliases d3(x,y,z)
, d(x,y,z)
)
Convert an (x,y,z)
tuple to a distance along a 3-dimensional Hilbert walk.
d2xyz(d)
(alias xyz(d)
)
The inverse of xyz2d
.
Hilbert2d, Hilbert3d
These classes can be used for more advanced 2d- and 3d- Hilbert-curve calculations.
Their constructors take 2 optional arguments:
axis order
(string): the order in which the curve should progress through available axes.Defaults to
'xy'
or'xyz'
in 2- and 3-dimensional modes, respectively; this can be interpreted as indicating that, starting from an origin, the curve should move along the x-axis, then the y-axis, (then the z-axis), etc.size
: which size square or cube should be fixed to the axis ordering dictated byaxis order
above?Defaults to
2
, meaning the smallest level of the curve (that fills out the 2x2 square in 2d or the 2x2x2 cube in 3d) will progress through available axes; the next level up will progress through them in a rotated order, as the definition of a Hilbert curve dictates.
Bash Helpers
Three helper scripts, ./d
, ./xy
, and ./xyz
are available for quick command-line sanity-checking of values.
# Call `d2xyz` on a Hilbert curve with axis order `xzy` for
# the integers [0,8]:
$ ./xyz "-'xzy'" 0 1 2 3 4 5 6 7 8
0: [ 0, 0, 0 ]
1: [ 1, 0, 0 ]
2: [ 1, 0, 1 ]
3: [ 0, 0, 1 ]
4: [ 0, 1, 1 ]
5: [ 1, 1, 1 ]
6: [ 1, 1, 0 ]
7: [ 0, 1, 0 ]
8: [ 0, 2, 0 ]
# Inverse of the above.
$ ./d "'xzy'" 0,0,0 1,0,0 1,0,1 0,0,1 0,1,1 1,1,1 1,1,0 0,1,0 0,2,0
0
1
2
3
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