Computer Science – Computational Geometry
Scientific paper
2009-12-16
Computer Science
Computational Geometry
Approximately 30 pages. Contains 25 figures. Some figures include multiple graphics
Scientific paper
An n-simplex is said to be n-well-centered if its circumcenter lies in its interior. We introduce several other geometric conditions and an algebraic condition that can be used to determine whether a simplex is n-well-centered. These conditions, together with some other observations, are used to describe restrictions on the local combinatorial structure of simplicial meshes in which every simplex is well-centered. In particular, it is shown that in a 3-well-centered (2-well-centered) tetrahedral mesh there are at least 7 (9) edges incident to each interior vertex, and these bounds are sharp. Moreover, it is shown that, in stark contrast to the 2-dimensional analog, where there are exactly two vertex links that prevent a well-centered triangle mesh in R^2, there are infinitely many vertex links that prohibit a well-centered tetrahedral mesh in R^3.
Guoy Damrong
Hirani Anil N.
Ramos Edgar
VanderZee Evan
Zharnitsky Vadim
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