CSAR Seminar
SPEAKER: Tathagata Ray, Ohio State University
TITLE:
Quality Delaunay Meshing of Volumes and Surfaces
DATE: Wednesday, April 19, 2006
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
ABSTRACT
Many applications, such as finite element methods, computer graphics,
and numerical simulations, require meshing a surface or the volume
enclosed by it in three dimensions. We consider polyhedral surfaces
and volumes and mesh them with Delaunay refinement. We present two
algorithms, QUALMESH and SURFREMESH. The first one, QUALMESH, computes
a Delaunay mesh conforming to a polyhedron, possibly with small input
angles. The radius to shortest edge ratios of most of the tetrahedra
in the output mesh are bounded above by a constant. Some of the output
tetrahedra remain bad, but only in the vicinity of small input angles.
The second algorithm, SURFREMESH, remeshes a polygonal surface
approximating a smooth one. The output surface is guaranteed to be
homeomorphic to the input, and the output triangles have bounded aspect
ratio. This algorithm starts with very few points chosen from the
input surface and gradually builds the entire surface to satisy a
user-defined threshold for paramaters capturing the geometric closeness
to the input surface. These parameters allow the user to extract the
surface at different level of details. Implementation results of both
algorithms will be presented.