Refinement, Derefinement, and Optimization of Tetrahedral Geometric Triangulations in Three Dimensions

Draft, 1995

MESHING
RESEARCH
CORNER

Scientific Computation Research Center Rensselaer Polytechnic Institute Troy, NY 12180-3590

Abstract
A procedure to locally derefine (coarsen), refine, and/or optimize three dimensional tetrahedral triangulations is presented. Derefinement is based on an edge collapsing technique which does not require any storage of refinement history information. Refinement is edge-based and considers subdivision stencils (templates) at the tetrahedron level for each possible refinement configuration. The optimization procedure improves the quality of any given three-dimensional tetrahedral triangulation. It relies on two local retriangulation techniques: i) edge removal [8] and ii) its reverse operation multi-face removal. This paper also reviews existing algorithms relate-' a refinement, derefinement, and local retriangulation (swapping).