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- Evan VanderZee, Anil N. Hirani, Damrong Guoy, Edgar A. Ramos
- SIAM J. Scientific Computing
- 2010

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have optimality properties and relationships to Delaunay and minmax angle triangulations. We present an iterative algorithm… (More)

We present an iterative algorithm to transform a given planar triangle mesh into a well-centered one by moving the interior vertices while keeping the connectivity fixed. A well-centered planar triangulation is one in which all angles are acute. Our approach is based on minimizing a certain energy that we propose. Well-centered meshes have the advantage of… (More)

- Evan VanderZee, Anil N. Hirani, Vadim Zharnitsky, Damrong Guoy
- Comput. Geom.
- 2010

It is shown that there exists a dihedral acute triangulation of the three-dimensional cube. The method of constructing the acute triangulation is described, and symmetries of the triangulation are discussed.

- Evan VanderZee, Anil N. Hirani, Damrong Guoy
- IMR
- 2008

A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple domains using completely well-centered tetrahedra. The domains we… (More)

- Evan VanderZee, Anil N. Hirani, Damrong Guoy, Vadim Zharnitsky, Edgar A. Ramos
- Comput. Geom.
- 2013

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… (More)

- Anil N. Hirani, Kaushik Kalyanaraman, Evan VanderZee
- Computer-Aided Design
- 2013

We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such… (More)

We present an iterative algorithm to transform a given planar triangle mesh into a well-centered one by moving the interior vertices while keeping the connectivity fixed. A well-centered planar triangulation is one in which all angles are acute. Our approach is based on minimizing a certain energy that we propose. Well-centered meshes have the advantage of… (More)

- Talib S. Hussain, Lisa Tiberio, Evan VanderZee
- 2015 Winter Simulation Conference (WSC)
- 2015

Due to the large size of the airlift and sealift analyses performed by the United States Transportation Command (USTRANSCOM) using the Analysis of Mobility Platform (AMP), AMP has historically used a greedy heuristic algorithm focused on specific criteria in order to be able to compute solutions efficiently. We introduce a multi-year effort to enhance the… (More)

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