Vertex-labeling algorithms for the Hilbert spacefilling curve

We describe a method, based on vertex-labeling, to generate algorithms for manipulating the Hilbert spacefilling curve. The method leads to algorithms for: computing the image of a point in R-1; computing a pre-image of a point in R-2; drawing a finite approximation of the curve; finding neighbor cells in a decomposition ordered according to the curve. The method is straightforward and flexible, resulting in short, intuitive procedures that are as efficient as specialized procedures found in the literature, Moreover, the same method can be applied to many other spacefilling curves. We demonstrate vertex-labeling algorithms for the Sierpinski and Peano spacefilling curves, and variations. Copyright (C) 2001 John Wiley & Sons, Ltd.