Symbolic treatment of geometric degeneracies
Journal of Symbolic Computation
Robust Geometric Computation Based on Topological Consistency
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
K-Order Neighbor: The Efficient Implementation Strategy for Restricting Cascaded Update in Realm
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Proceedings of the twenty-fourth annual symposium on Computational geometry
Inner and outer rounding of Boolean operations on lattice polygonal regions
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Configurations induced by discrete rotations: periodicity and quasi-periodicity properties
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Consistent digital line segments
Proceedings of the twenty-sixth annual symposium on Computational geometry
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Proceedings of the twenty-seventh annual symposium on Computational geometry
A content-based publish/subscribe matching algorithm for 2d spatial objects
Middleware'11 Proceedings of the 12th ACM/IFIP/USENIX international conference on Middleware
A content-based publish/subscribe matching algorithm for 2D spatial objects
Proceedings of the 12th International Middleware Conference
Computational Geometry: Theory and Applications
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Geometric algorithms are usually designed with continuous parameters in mind. When the underlying geometric space is intrinsically discrete, as is the case for computer graphics problems, such algorithms are apt to give invalid solutions if properties of a finite-resolution space are not taken into account. In this paper we discuss an approach for transforming geometric concepts and algorithms from the continuous domain to the discrete domain. As an example we consider the discrete version of the problem of finding all intersections of a collection of line segments. We formulate criteria for a satisfactory solution to this problem, and design an interface between the continuous domain and the discrete domain which supports certain invariants. This interface enables us to obtain a satisfactory solution by using plane-sweep and a variant of the continued fraction algorithm.