Construction of three-dimensional Delaunay triangulations using local transformations.(English)Zbl 0729.65120

For a set of points in $$R^ 3$$ the problem of Delaunay triangulation is to find a set of nonoverlapping tetrahedra that fill the convex hull of the set so that no point is in the circumscribed sphere of any tetrahedron of which it is not a vertex. The author gives the pseudocode description of two programs that solve the problem by local decisions involving five points at a time and proves that the worst case time complexity is $$O(n^ 2)$$ and the expected complexity for random points is O(n(log n)$${}^ 2)$$.

MSC:

 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 14Q15 Computational aspects of higher-dimensional varieties 32B25 Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions
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