Volume of a doubly truncated hyperbolic tetrahedron
Alexander Kolpakov, Jun Murakami
TL;DR
This paper develops a unified approach to compute the volume of doubly truncated hyperbolic tetrahedra using dilogarithm functions, extending previous results and addressing various geometric cases with numeric examples.
Contribution
It introduces a comprehensive method to express the volume across different geometric configurations of doubly truncated hyperbolic tetrahedra using dilogarithm functions.
Findings
Unified volume formula for various geometric cases
Proper treatment of analytic strata of dilogarithm functions
Numerical examples demonstrating the method's effectiveness
Abstract
The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the previous results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases via dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.
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Taxonomy
TopicsMathematics and Applications · Computational Geometry and Mesh Generation · Advanced Numerical Analysis Techniques