Modeling and Rendering Non-Euclidean Spaces Approximated With Concatenated Polytopes

Abstract

A non-Euclidean space is characterized as a manifold with a specific structure that violates Euclid's postulates. This paper proposes to approximate a manifold with polytopes. Based on the scene designer's specification, the polytopes are automatically concatenated and embedded in a higher-dimensional Euclidean space. Then, the scene is navigated and rendered via novel methods tailored to concatenated polytopes. The proof-of-concept implementation and experiments with it show that the proposed methods bring the virtual-world users unusual and fascinating experiences, which cannot be provided in Euclidean-space applications.