Tech Report CS-97-11

Checking the Convexity of Polytopes and the Planarity of Subdivisions

Olivier Devillers, Giuseppe Liotta, Franco P. Preparata, and Roberto Tamassia

Revised December 1997


This paper studies the problem of verifying the correctness of geometric structures. In particular, we design optimal checkers for convex polytopes in two and higher dimensions, and for various types of planar subdivisions, such as triangulations, Delaunay triangulations, and convex subdivisions. Our checkers are simpler and more general than the ones previously described in the literature. Their performance is studied also in terms of the degree, which characterizes the arithmetic precision required.

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