Computability of Partial Delaunay Triangulation and Voronoi Diagram [ Extended
نویسندگان
چکیده
Using the domain-theoretic model for geometric computation, we define the partial Delaunay triangulation and the partial Voronoi diagram of N partial points in R2 and show that these operations are domain-theoretically computable and effectively computable with respect to Hausdorff distance and Lebesgue measure. These results are obtained by showing that the map which sends three partial points to the partial disc passing through them is computable. This framework supports the design of robust algorithms for computing the Delaunay triangulation and the Voronoi diagram with imprecise input.
منابع مشابه
Basic algorithms in computational geometry with imprecise input
The domain-theoretic model of computational geometry provides us with continuous and computable predicates and binary operations. It can also be used to generalise the theory of computability for real numbers and real functions into geometric objects and geometric operations. A geometric object is computable if it is the effective limit of a sequence of finitary partial objects of the same type...
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