Given a polyhedral surface, is it self-intersection-free?

Given a polyhedral surface, is it self-intersection-free? Full article

Source

Wolfram Community
Compilation, 2025.

Output data

Year: 2025, Article number : 3382354, Pages count : 7

Tags

Euclidean 3-space, polyhedral surface, exible polyhedron, self-intersection-free exible polyhedra, geometric intersection, segment-triangle intersection algorithm

Authors

Alexandrov V. ^1,2 , Volokitin E. ^1,2

Affiliations

1	Sobolev Institute of Mathematics
2	NGU

Being motivated by the theory of flexible polyhedra we present an algorithm implemented in Mathematica that answers the question of whether a polyhedral surface in three-dimensional Euclidean space has self-intersections, and give an example of its application. The main feature of our algorithm is that its implementation uses only symbolic calculations, i.e., no floating point calculations are used. The point is that we consider the conclusions about the presence or absence of self-intersections of a polyhedral surface based on floating point calculations to be insufficiently rigorous for use in the theory of flexible polyhedra. The algorithm presented in this publication is the main tool for studying the presence or absence of self-intersections used in our original article. CITATION (original article): Alexandrov, V.A., Volokitin, E.P. An Embedded Flexible Polyhedron with Nonconstant Dihedral Angles. Sib Math J 65, 1259–1280 (2024). https://doi.org/10.1134/S003744662406003X

Alexandrov V. , Volokitin E.
Given a polyhedral surface, is it self-intersection-free?
In compilation Wolfram Community. 2025.

Published online:

Feb 6, 2025

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