ACS Algorithms for Complex Shapes with Certified Numerics and Topology A General Approach to the Analysis of Controlled Perturbation Algorithms
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چکیده
Controlled Perturbation (CP, for short) is an approach to implement efficient and robust geometric algorithms using the computational speed of builtin finite precision arithmetic, while bypassing precision problems during the computation. Furthermore it avoids the time-consuming and error-prone discussion of degenerate cases. CP replaces the input objects by a set of randomly perturbed (moved, scaled, stretched, etc.) objects such that the algorithm is guaranteed to compute the exact combinatorial structure that these objects imply. This paper is meant as a guide how to decide if CP can be applied to a given algorithm, and if, how to correlate all CP parameters: the perturbation amount δ , the arithmetic precision L, the maximum range of input values [−m,m], the number of input objects n, the error bound B f of the (chosen) predicate evaluations, and the probability P of a successful computation. For this purpose we present a general methodology to analyze predicate functions that leads to an inequality correlating these parameters and hence to bounds on the precision or perturbation amount. In particular we treat the case of the wide used class of polynomial predicates in detail. Advantages, drawbacks and implementation issues are discussed.
منابع مشابه
ACS Algorithms for Complex Shapes with Certified Numerics and Topology Application of algebraic tools to CSG operations on curves and surfaces
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تاریخ انتشار 2008