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Robust adaptive floating-point geometric predicates
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Efficient exact evaluation of signs of determinants
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SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
IEEE Transactions on Computers
Interval arithmetic yields efficient dynamic filters for computational geometry
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ESOLID---A System for Exact Boundary Evaluation
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Robust Geometric Computation Based on Topological Consistency
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
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ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
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Automatic Generation of Staged Geometric Predicates
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Structural filtering: a paradigm for efficient and exact geometric programs
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Residual iteration and accurate polynomial evaluation for shape-interrogation applications
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Reliable and efficient geometric computing
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Computing the Implicit Voronoi Diagram in Triple Precision
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Structural filtering: a paradigm for efficient and exact geometric programs
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A general approach to the analysis of controlled perturbation algorithms
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ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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Computer-Aided Design
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We experiment with exact integer arithmetic to implement primitives for geometric algorithms. Naive use of exact arithmetic—either modular or multiprecision integer—increases execution time dramatically over the use of floating-point arithmetic. By combining tuned multiprecision integer arithmetic and a floating-point filter based on interval analysis, we can obtain the effect of exact integer arithmetic at a cost close to that of floating-point arithmetic. We describe an experimental expression compiler that conveniently packages our techniques.