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The Nine Morse Generic Tetrahedra
Title: | The Nine Morse Generic Tetrahedra |
Authors: | Siersma, Dirk Browse this author | van Manen, Martijn Browse this author |
Keywords: | Morse theory | polyhedra | Voronoi diagram | tetrahedral shape |
Issue Date: | 18-Apr-2008 |
Publisher: | Society for Industrial and Applied Mathematics |
Journal Title: | SIAM Journal on Discrete Mathematics |
Volume: | 22 |
Issue: | 2 |
Start Page: | 737 |
End Page: | 746 |
Publisher DOI: | 10.1137/060656395 |
Abstract: | There are two types of shapes for a generic triangle-acute and obtuse. These shapes are also distinguished by the (topological) Morse theory of the minimal distance function to the vertices. We can use the same method for a tetrahedron, and we show in this paper that there exist nine generic shapes. These can be described by a Morse poset or by a Gabriel graph. We also report on some computer experiments and compare our classification to another criterion used in computational geometry. |
Rights: | Copyright © 2008 Society for Industrial and Applied Mathematics |
Type: | article |
URI: | http://hdl.handle.net/2115/34122 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: Martijn van Manen
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