Generating Regular Hyperbolic Honeycombs
Dorota Celi\'nska-Kopczy\'nska, Eryk Kopczy\'nski
TL;DR
This paper introduces a method for generating regular hyperbolic honeycombs in 3D hyperbolic space, aiding large-scale geometric computations and algorithms involving hyperbolic tessellations.
Contribution
It presents a novel approach to constructing geodesic regular tree structures for 3D hyperbolic tessellations, addressing numerical precision issues.
Findings
Effective generation of hyperbolic honeycombs demonstrated
Improved accuracy in hyperbolic geometric computations
Potential applications in hyperbolic algorithms and modeling
Abstract
Geodesic regular tree structures are essential to combat numerical precision issues that arise while working with large-scale computational hyperbolic geometry and have applications in algorithms based on distances in such tessellations. We present a method of generating and applying such structures to the tessellations of 3-dimensional hyperbolic space.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Numerical Analysis Techniques · Computer Graphics and Visualization Techniques