Abstract
The problem of accurate and robust implementation of geometric algorithms has received considerable attention for more than a decade. Despite much progress in computational geometry and geometric modeling, practical implementations of geometric algorithms are prone to error. Much of the difficulty arises from the fact that reasoning about geometry most naturally occurs in the domain of the real numbers, which can only be represented approximately on a digital computer. Many times, the correctness of geometric algorithms depends on correctly evaluating the signs of arithmetic expressions, and errors due to rounding or imprecise inputs can lead to grossly incorrect results or failure to run to completion.
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Foskey, M., Manocha, D., Culver, T., Keyser, J., Krishnan, S. (2002). Reliable Geometric Computations with Algebraic Primitives and Predicates. In: Winkler, J., Niranjan, M. (eds) Uncertainty in Geometric Computations. The Springer International Series in Engineering and Computer Science, vol 704. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0813-7_8
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