Tiling Three-Dimensional Space with Simplices

Dr Shankar Krishnan (AT&T Labs - Research)

DATE: 2006-03-17
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU

ABSTRACT:
A simplex in d dimensions is the convex hull of d+1 points in general (non-degenerate) position. A triangle is a simplex in two dimensions, and a tetrahedron is the corresponding simplex in three dimensions. Tiling entire space or a particular region of space with simplices is also called a triangulation. Triangulations of two- and three-dimensional domains find numerous applications in scientific computing, computer graphics, simulations and solid modeling. Most of these applications impose a quality constraint on the elements of the triangulation. The most popular measures in three dimensions are aspect ratio (circumradius over inradius), maximum dihedral angle and radius-to-edge ratio (circumradius over shortest edge). While each of these measures are equivalent in two dimensions, it is not so in three dimensions. There are some inherent mathematical limitations to the best possible meshes in three dimensions. It is well-known that three-dimensional Euclidean space cannot be tiled with regular tetrahedra. In this talk, I will try to answer the following question: What is the best possible set of tetrahedra, in terms of their regularity, that can tile three-dimensional Euclidean space?

BIO:
Shankar Krishnan is a senior member of technical staff at AT&T Shannon Laboratory in the Visualization department. He received his Bachelor's degree in Computer Science from the Indian Institute of Technology, Madras in 1991. He received his M.S. and Ph.D. degrees in Computer Science from the University of North Carolina, Chapel Hill in 1993 and 1997, respectively. Shankar's main research interests include 3D computer graphics and visualization, computational geometry, streaming algorithms, and general purpose computing on commodity graphics hardware. He has authored over 80 papers and has given a number of technical presentations and tutorials on these topics in leading conferences in computer graphics, computational geometry and visualization.

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