2015/10/26 by Géza Csima, Csima, Géza, Jenő Szirmai +1
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG
paper · pdf · doi:10.48550/arxiv.1510.07718
arxiv created 2015/10/26 · openalex publication_date 2015/10/26 · arxiv updated 2015/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The theory of the isoptic curves is widely studied in the Euclidean plane \bE2 (see \citeCMM91 and \citeWi and the references given there). The analogous question was investigated by the authors in the hyperbolic \bH2 and elliptic \cE2 planes (see \citeCsSz1, \citeCsSz2, \citeCsSz5), but in the higher dimensional spaces there are only a few result in this topic. In \citeCsSz4 we gave a natural extension of the notion of the isoptic curves to the n-dimensional Euclidean space \bEn (n≥ 3) which are called isoptic hypersurfaces. Now we develope an algorithm to determine the isoptic surface H\cP of a 3-dimensional polytop P. We will determine the isoptic surfaces for Platonic solids and for some semi-regular Archimedean polytopes and visualize them with Wolfram Mathematica.