Sciweavers

CIE
2005
Springer

Computability in Computational Geometry

13 years 9 months ago
Computability in Computational Geometry
We promote the concept of object directed computability in computational geometry in order to faithfully generalise the wellestablished theory of computability for real numbers and real functions. In object directed computability, a geometric object is computable if it is the effective limit of a sequence of finitary objects of the same type as the original object, thus allowing a quantitative measure for the approximation. The domain-theoretic model of computational geometry provides such an object directed theory, which supports two such quantitative measures, one based on the Hausdorff metric and one on the Lebesgue measure. With respect to a new data type for the Euclidean space, given by its non-empty compact and convex subsets, we show that the convex hull, Voronoi diagram and Delaunay triangulation are Hausdorff and Lebesgue computable.
Abbas Edalat, Ali Asghar Khanban, André Lie
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where CIE
Authors Abbas Edalat, Ali Asghar Khanban, André Lieutier
Comments (0)