Dense Curves

Simple and efficient implementations of space-filling / Peano / FASS curves.

Installation

The package is available on pypi:

pip install -U densecurves

Hilbert Curve

Nomenclature

The Hilbert curve is a finite approximation of a space filling curve.

The curve of order $p$ and rank $n$ is characteristized by:

• $n$ distinct axes, the number of coordinates of its points
• $2 ^ {p}$, the dimension along each axis
• $2 ^ {p n}$ vertexes, the "corners" of its graph

The order of the curve $p$ is often referred to as the "iteration".

The intermediate points between the vertexes are ignored. Here, the vertexes are represented by integer coordinates.

Load

import densecurves.hilbert

Compute

Convert a position / distance along the 1D curve to a ND point:

densecurves.hilbert.point(position=42, order=4, rank=2)
# [7, 7]

And the reverse operation:

densecurves.hilbert.position(coords=[1, 2, 3], order=4, rank=3)
# 36

Credits

"Programming the Hilbert curve" by John Skilling.

License

Licensed under the aGPLv3.