Visualization of Escher‐like Kaleidoscopic Spherical Patterns of Regular Polyhedron Symmetry

Abstract

In this paper, we present a method for creating Escher‐like spherical patterns with regular polyhedron symmetries. Using the generators of the symmetry groups associated with regular polyhedra, we first provide fast algorithms to construct spherical tilings. Then, to obtain Escher‐like patterns, we specify texturing techniques to decorate the resulting tilings. Moreover, we present a strategy to create a novel dynamic effect of Escher‐like kaleidoscopes in which the motifs have a complete body. The method has the advantages of simple implementation, fast calculation, good graphics, and artistic effects, which can be used to create rich elegant spherical patterns.