CSE Seminar
SPEAKER: Evan VanderZee,
UIUC/Mathematics
TITLE:
Well-Centered Planar Triangulation – An Iterative Approach
DATE: Wednesday, October 3, 2007
TIME: 12:00-12:30 P.M.
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
ABSTRACT
A well-centered planar triangulation is one in which all angles are
acute. Well-centered meshes have the advantage of having nice
orthogonal dual meshes (the dual Voronoi diagram), which is useful for
certain numerical algorithms. 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 mesh connectivity
fixed. Our approach is based on minimizing a certain energy that we
propose. For some mesh connectivities there is no well-centered
configuration. We present a preprocessing algorithm that modifies the
mesh connectivity of such meshes and increases the possibility of
finding a well-centered configuration. We show the results of applying
our energy minimization approach to a variety of meshes.
This is a joint work with Anil Hirani (CS), Damrong Guoy (CSE), and
Edgar Ramos (CS).