Space-Filling Curves based on Residue Number System

Abstract

Space-filling curves are a useful tool for fast multi-dimensional space indexing, dimension reduction, and fast optimization of complex problems. Several curves such as Hilbert, Peano, Gray, Morton or Z-order were discovered, and their properties and features were intensely studied. In this paper, a new space-filling curve is described, and its features are analyzed and compared with the other space-filling curves. The novel algorithm for a space-filling curve is based on the Residue Number System that is extensively studied during the last thirty years. The proposed curve has specific behavior and may be controlled by several parameters.