Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Classical computational geometry in GeomNet
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A strong and easily computable separation bound for arithmetic expressions involving square roots
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
Linfinity Voronoi Diagrams and Applications to VLSI Layout and Manufacturing
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
A Probabilistic Zero-Test for Expressions Involving Root of Rational Numbers
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
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In the context of methodologies intended to confer robustness to geometric algorithms, we elaborate on the exact computation paradigm and formalize the notion of degree of a geometric algorithm, as a worst-case quantification of the precision (number of bits) to which arithmetic calculation have to be executed in order to guarantee topological correctness. We also propose a formalism for the expeditious evaluation of algorithmic degree. As an application of this paradigm and an illustration of our general approach, we consider the important classical problem of proximity queries in 2 and 3 dimensions, and develop a new technique for the efficient and robust execution of such queries based on an implicit representation of Voronoi diagrams. Our new technique gives both low degree and fast query time, and for 2D queries is optimal with respect to both cost measures of the paradigm, asymptotic number of operations and arithmetic degree.