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A Generic Lazy Evaluation Scheme for Exact Geometric Computations

Sylvain Pion 1 Andreas Fabri 2
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We present a generic C++ design to perform exact geometric computations efficiently using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also important for many applications, hence the need for delaying the costly exact computations at run time until they are actually needed, if at all. Our approach is generic and extensible in the sense that it is possible to make it a library that users can apply to their own geometric objects and primitives. It involves techniques such as generic functor-adaptors, static and dynamic polymorphism, reference counting for the management of directed acyclic graphs, and exception handling for triggering exact computations when needed. It also relies on multi-precision arithmetic as well as interval arithmetic. We apply our approach to the whole geometry kernel of CGAL.
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Submitted on : Thursday, February 3, 2011 - 6:16:58 AM
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Sylvain Pion, Andreas Fabri. A Generic Lazy Evaluation Scheme for Exact Geometric Computations. Science of Computer Programming, Elsevier, 2011, Special issue on library-centric software design (LCSD 2006), 76 (4), pp.307-323. ⟨10.1016/j.scico.2010.09.003⟩. ⟨inria-00562300⟩

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