Hilbert-Curve-Generator

A WIP Hilbert Space-Filling Curve Coordinate Generator. Can produce cartesian coordinates for the vertices of a Hilbert Space-Filling Curve in 2 or 3 dimensions using the Skilling Transform Method.

Project Structure:

Hilbert-Curve

This module contains functionality for generating the Cartesian coordinates of the vertices in a Hilbert Space-Filling Curve in both 2D and 3D.

It also contains utility functions for converting the output vertices into different formats:

• (x,y,z) in binary
• (x,y,z) in decimal

BRGC

Brgc is the Binary Reflected Gray Code Iterator

This module generates the cartesian coordinates of each vertex in the HSFC using a technique that begins with a list of the first n binary numbers counted using the Binary Reflected Gray Code counting system.

The iterator exposed by this module can be used to generate points in a BRGC of any magnitude, although for the typical purposes of generating square hilbert curves and cubic hilbert cubes, the number of generated points will typically be p^n, where n is the number of dimensions for the resulting cartesian coordinates (2D and 3D currently supported), and p is the number of data bits for each coordinate (each side of your square/cube will have 2^p vertices)

Skilling_Transform

This module contains functions for applying the Skilling Transform to an existing Vec of BRGC.

The Skilling Transform is an algorithm for generating the cartesian coordinates of vertices in a Hilbert curve without using the traditional recursive method.

I've optimized for readability and ease of understanding in the code, since the algorithm is not immediately clear. There was a good deal of trial and error in implementing this algorithm. If I spend more time on this project, I'll try replacing all the string manipulation with bit manipulation and benchmark the speed difference.