Subdivision over the hyperbolic plane

Abstract

This paper presents a new method of subdividing the {p,q}-gon tessellated hyperbolic plane. This is done by pulling the plane toward the center. Generally, subdivisions of the curves and surfaces are useful in many applications and multiresolution requiring a repeated subdivision is one of the hot issues, recently. But most subdivisions are being used on the set of patches forming an object. This research is motivated from a single patched genus-n object, rather than a set of various patches for a genus-n object. Since the single domain provides many advantages, for an instance, a simpler data structure, the study on the single domain will be continued. The goal of this research is to find a way of subdividing the tessellation over the they are transformed into other objects. The subdivision in this paper provides various scale of the polygon over the hyperbolic plane. That is, the fundamental polygon can be divided into 2-level, 3-level, and so on.