Towards an Open Curved Kernel

Ioannis Emiris 1, 2 Athanasios Kakargias 1 Sylvain Pion 3 Monique Teillaud 2 Elias P. Tsigaridas 1
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
3 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Our work goes towards answering the growing need for the robust and efficient manipulation of curved objects in numerous applications. The kernel of the CGAL library provides several functionalities which are, however, mostly restricted to linear objects. We focus here on the arrangement of conic arcs in the plane. Our first contribution is the design, implementation and testing of a kernel for computing arrangements of circular arcs. A preliminary C++ implementation exists also for arbitrary conic curves. We discuss the representation and predicates of the geometric objects. Our implementation is targeted for inclusion in the CGAL library. Our second contribution concerns exact and efficient algebraic algorithms for the case of conics. They treat all inputs, including degeneracies, and they are implemented as part of the library SYNAPS 2.1. Our tools include Sturm sequences, resultants, Descartes' rule, and isolating points. Thirdly, our experiments on circular arcs show that our methods compare favorably to existing alternatives using CORE 1.6x and LEDA 4.5.
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Ioannis Emiris, Athanasios Kakargias, Sylvain Pion, Monique Teillaud, Elias P. Tsigaridas. Towards an Open Curved Kernel. ACM Symposium on Computational Geometry, Jun 2004, New York, United States. pp.438-446. ⟨inria-00344433⟩

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