Coping with degeneracies in Delaunay triangulation
- NIST, Gaithersburg, MD (United States)
- SRC, Bowie, MD (United States)
Degeneracy is a serious issue in geometry. In their original form, many geometric algorithms simply assume that there is no degeneracy. As a result, when these methods are used on data that is degenerate or nearly degenerate, they either fail to complete or else give nonsensical results. We will describe a new method that removes only those 3-d degeneracies that cause ambiguity in determining Delaunay tetrahedra and only those 3-d degeneracies that cause ambiguity in determining Delaunay triangles. The mathematical justification is based on classical results of real analysis. The proof identifies degeneracies with the polynomial derived from the determinants that express geometrical primitives. Our result is a probabilistic statement about the real numbers; with probability one, degeneracies are removed in real arithmetic. In floating-point arithmetic, detection of degeneracies is based on relative error criteria that we describe here.
- OSTI ID:
- 198190
- Report Number(s):
- CONF-9307220--Vol.75
- Country of Publication:
- United States
- Language:
- English
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