Handbook of logic in computer science (vol. 4)
A domain-theoretic approach to computability on the real line
Theoretical Computer Science - Special issue on real numbers and computers
Foundation of a computable solid modeling
Proceedings of the fifth ACM symposium on Solid modeling and applications
Computability on subsets of Euclidean space I: closed and compact subsets
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Theoretical Computer Science
Foundation of a computable solid modelling
Theoretical Computer Science
On Extreme Points of Convex Compact Turing Located Set
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Theoretical Computer Science - Mathematical foundations of programming semantics
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We promote the concept of object directed computability in computational geometry in order to faithfully generalise the well-established 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.