13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004
Sandia National Laboratories
Livermore, CA, U.S.A.
This paper presents a technique for the adaptive refinement of tetrahedral meshes. What makes it unique is that no
neighbor information is required for the refined mesh to be compatible everywhere. Refinement consists of inserting
new vertices at edge midpoints until some tolerance (geometric or otherwise) is met. For a tetrahedron, the six edges
present 26 = 64 possible subdivision combinations. The challenge is to triangulate the new vertices (i.e., the original
vertices plus some subset of the edge midpoints) in a way that neighboring tetrahedra always generate the same
triangles on their shared boundary. A geometric solution based on geometric properties (edge lengths) was developed
previously, but did not account for geometric degeneracies (edges of equal length). This paper provides a solution
that works in all cases.
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