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Pointerless Implementation of Hierarchical Simplicial Meshes and Efficient Neighbor Finding In Arbitrary Dimensions

Atalay, F. Betul and David M. Mount

Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.15-26, September 19-22 2004

IMR
PROCEEDINGS

13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004

Department of Computer Science, University of Maryland, College Park, MD 20742.
{fbetul, mountg}@cs.umd.edu

Abstract
We describe a pointerless representation of hierarchical regular simplicial meshes, based on a bisection approach proposed by Maubach. We introduce a new labeling scheme, called an LPT code, which uniquely encodes each simplex of the hierarchy. We present rules to compute the neighbors of a given simplex efficiently through the use of these codes. In addition, we show how to traverse the associated tree and how to answer point location and interpolation queries. Our system works in arbitrary dimensions.

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