Locality and bounding-box quality of two-dimensional space-filling curves
The central objects of study of the paper are the the so-called space filling curves. These are continuous surjective mappings from \(\mathbb{R}\) to \(\mathbb{R}^d\). Beside the paper by \textit{G. Peano} [On a curve which entirely fills a plane domain. (Sur une courbe, qui remplit toute une aire plane.) Math. Ann. XXXVI. 157--160 (1890; JFM 22.0405.01)], one can check the reference [\textit{H. Sagan}, Space-filling curves. Universitext. New York: Springer-Verlag. xv, 193 p. (1994; Zbl 0806.01019)] for an extensive treatise of these type of geometric objects. In the introduction of the paper, some applications of space filling curves are commented. In this paper, the authors investigate which space filling curves are better in the sense of sorting points into bounding boxes with small total area and small total perimeter. For this purpose, the authors propose new quality measures to analyze how efficient the mapping are. In addition, they provide an algorithm to approximate these measures for a given curve.
scientific article; zbMATH DE number 5633796