MorseSmale complexes on convex polyhedra
Abstract
Motivated by applications in geomorphology, the aim of this paper is to extend MorseSmale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3dimensional Euclidean space. The resulting polyhedral MorseSmale complex may be regarded, on one hand, as a generalization of the MorseSmale complex of the smooth radial distance function defining a smooth, convex body, on the other hand, it could be also regarded as a generalization of the MorseSmale complex of the piecewise linear parallel distance function (measured from a plane), defining a polyhedral surface. Beyond similarities, our paper also highlights the marked differences between these three problems and it also includes the design, implementation and testing of an explicit algorithm computing the MorseSmale complex on a convex polyhedron.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.11626
 Bibcode:
 2021arXiv210611626L
 Keywords:

 Computer Science  Computational Geometry;
 Mathematics  Combinatorics;
 Mathematics  Metric Geometry;
 57Q70;
 52B70;
 52B10
 EPrint:
 19 pages, 8 figures