Type
Text
Type
Thesis
Advisor
Gao, Jie | Gu, Xianfeng D | Jiao, Xiangmin.
Date
2012-05-01
Keywords
Computer science | Tetrahedralization, Triangulation, Variational Delaunay
Department
Department of Computer Science
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71155
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
In this thesis I present an algorithm and its implementation for 2D and 3D simplicial mesh optimization. An energy function for each simplex of a mesh in Rn , where 2 &le n &ge 3, is defined as the volume of the ideal hyperbolic simplex in Rn+1 constructed from the said simplex. It has been proven otherwise and mentioned here as well that a regular simplex has maximum energy. Thus maximizing this energy by reshaping each individual simplex of the mesh will improve the overall quality of the mesh. The algorithm maximizes this energy to achieve an optimal mesh by displacing vertices and updating connectivity of the mesh conforming to the delaunay property by following a gradient descent method. The details of the energy function, proof of correctness and implementation details are presented herewith. | 39 pages
Recommended Citation
Bhagavatula, Phanindra, "Variational Delaunay Triangulation" (2012). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 362.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/362