|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
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)
|
Submitter: Martijn van Manen
|
