Transforming Euclidean Object files to Hyperbolic Data files

Abstract

The creation of repeating hyperbolic patterns has been of interest for more than 100 years. However, manual creation of these patterns was very tedious and time-consuming. Escher created such patterns manually in 1950's. At that time, he had no access to computers. Later on, several researchers, tried to create these patterns automatically. For this purpose, they had written code in C. Programs for automatic creation of these patterns now exist in C++ and JAVA. These programs take parameters p and q to generate a regular tesselation p,q of hyperbolic plane. Here p represents a regular p-sided polygon and q specifies the number of them that meet at each vertex. These program generates repeating hyperbolic patterns from hyperbolic data files. However, there is no means to generate hyperbolic data files from Euclidean object files.