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SCG '87 Proceedings of the third annual symposium on Computational geometry
Partitioning Polyhedral Objects into Nonintersecting Parts
IEEE Computer Graphics and Applications
Verifiable implementation of geometric algorithms using finite precision arithmetic
Artificial Intelligence - Special issue on geometric reasoning
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SCG '88 Proceedings of the fourth annual symposium on Computational geometry
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SCG '89 Proceedings of the fifth annual symposium on Computational geometry
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ACM Transactions on Graphics (TOG)
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Efficient exact evaluation of signs of determinants
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
IEEE Transactions on Computers
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Proceedings of the fourteenth annual symposium on Computational geometry
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ESOLID---A System for Exact Boundary Evaluation
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ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
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ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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Proceedings of the nineteenth annual symposium on Computational geometry
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PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
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SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete 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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Computational Geometry: Theory and Applications
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Many fundamental tests performed by geometric algorithms can be formulated in terms of finding the sign of a determinant. When these tests are implemented using fixed precision arithmetic such as floating point, they can produce incorrect answers; when they are implemented using arbitrary-precision arithmetic, they are expensive to compute. We present adaptive-precision algorithms for finding the signs of determinants of matrices with integer and rational elements. These algorithms were developed and tested by integrating them into the Guibas-Stolfi Delaunay triangulation algorithm. Through a combination of algorithm design and careful engineering of the implementation, the resulting program can triangulate a set of random rational points in the unit circle only four to five times slower than can a floating-point implementation of the algorithm. The algorithms, engineering process, and software tools developed are described.