You can find geodesic paths in triangle meshes by just flipping edges
This paper introduces a new approach to computing geodesics on polyhedral surfaces---the
basic idea is to iteratively perform edge flips, in the same spirit as the classic Delaunay flip …
basic idea is to iteratively perform edge flips, in the same spirit as the classic Delaunay flip …
Poly-dodecahedrane: A new allotrope of carbon
S Hasanvandi, E Neisi, JM De Sousa - Chemical Physics Letters, 2024 - Elsevier
In this study, regular dodecahedron (dodecahedrane) oligomers by extending the dodeca-
hedrane units in 3-dimensions were designed. Computational studies reveal that with an …
hedrane units in 3-dimensions were designed. Computational studies reveal that with an …
Survey lecture on billiards
RE Schwartz - Proceedings of the 2002 International Congress of …, 2021 - content.ems.press
Survey lecture on billiards Page 1 Survey lecture on billiards Richard Evan Schwartz Abstract
In this survey of billiards, I will discuss a variety of topics: rational polygonal billiards, irrational …
In this survey of billiards, I will discuss a variety of topics: rational polygonal billiards, irrational …
Kontsevich–Zorich monodromy groups of translation covers of some platonic solids
R Gutiérrez-Romo, D Lee, A Sanchez - Groups, Geometry, and …, 2024 - ems.press
We compute the Zariski closure of the Kontsevich–Zorich monodromy groups arising from
certain square-tiled surfaces that are geometrically motivated. Specifically we consider three …
certain square-tiled surfaces that are geometrically motivated. Specifically we consider three …
Closed simple geodesics on a polyhedron
VY Protasov - arXiv preprint arXiv:2312.10554, 2023 - arxiv.org
It is well-known that every isosceles tetrahedron (disphenoid) admits infinitely many simple
closed geodesics on its surface. They can be naturally enumerated by pairs of co-prime …
closed geodesics on its surface. They can be naturally enumerated by pairs of co-prime …
Vertex to vertex geodesics on Platonic solids
S Troubetzkoy - The American Mathematical Monthly, 2023 - Taylor & Francis
Full article: Vertex to Vertex Geodesics on Platonic Solids Skip to Main Content Taylor and
Francis Online homepage Browse Search Publish Login | Register Log in or Register Login …
Francis Online homepage Browse Search Publish Login | Register Log in or Register Login …
PIGTIKAL (puzzles in geometry that I know and love)
A Petrunin - arXiv preprint arXiv:0906.0290, 2009 - arxiv.org
PIGTIKAL: puzzles in geometry that I know and love Page 1 PIGTIKAL (puzzles in geometry
that I know and love) Anton Petrunin Association for Mathematical Research Monographs …
that I know and love) Anton Petrunin Association for Mathematical Research Monographs …
The Necker cube surface
WP Hooper, P Javornik - arXiv preprint arXiv:2310.03115, 2023 - arxiv.org
We study geodesics on the Necker cube surface, $\mathbf N $, an infinite periodic Euclidean
cone surface that is homeomorphic to the plane and is tiled by squares meeting three or six …
cone surface that is homeomorphic to the plane and is tiled by squares meeting three or six …
The extremal length systole of the cube punctured at its vertices
S Dobchies, MF Bourque - arXiv preprint arXiv:2404.00336, 2024 - arxiv.org
We prove that the extremal length systole of the cube punctured at its vertices is realized by
the 12 curves surrounding its edges and give a characterization of the corresponding …
the 12 curves surrounding its edges and give a characterization of the corresponding …
Simple Closed Geodesics on a Polyhedron
VY Protasov - The Mathematical Intelligencer, 2024 - Springer
Geodesics on a surface are locally shortest curves. They play a role analogous to that of
straight lines in the plane. However, they may possess properties different from those …
straight lines in the plane. However, they may possess properties different from those …