The Nine Morse Generic Tetrahedra
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概要
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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.
- 2008-04-18
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