12th International Meshing Roundtable
September 14-17, 2003
Santa Fe, New Mexico, U.S.A.
University of Las Palmas de Gran Canaria, Spain
DCC, University of Chile, Santiago de Chile, Chile
The 8-tetrahedra longest-edge (8T-LE) partition of any tetrahedron is defined in terms of three consecutive edge
bisections, the first one performed by the longest-edge. The associated local refnement algorithm can be described
in terms of the polyhedron skeleton concept using either a set of precomputed partition patterns or by a simple edgemidpoint
tetrahedron bisection procedure. An efective 3D derefinement algorithm can be also simply stated. In this
paper we discuss the 8-tetrahedra partition, the refnement algorithm and its properties, including a non-degeneracy
fractal property. Empirical experiments show that the 3D partition has analogous behavior to the 2D case in the
sense that after the first refinement level, a clear monotonic improvement behavior holds. For some tetrahedra a
limited decreasing of the tetrahedron quality can be observed in the first partition due to the introduction of a new
face which refects a local feature size related with the tetrahedron thickness.
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