A subdivision arrangement algorithm for semi-algebraic curves: an overview

Julien Wintz 1 Bernard Mourrain 1
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We overview a new method for computing the arrangement of semi-algebraic curves. A subdivision approach is used to compute the topology of the algebraic objects and to segment the boundary of regions defined by these objects. An efficient insertion technique is described, which detects regions in conflict and updates the underlying arrangement structure. We describe the general framework of this method, the main region insertion operation and the specializations of the key ingredients for the different types of objects: implicit, parametric or piecewise linear curves.
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Julien Wintz, Bernard Mourrain. A subdivision arrangement algorithm for semi-algebraic curves: an overview. 15th Pacific Conference on Computer Graphics and Applications, Ron Goldman, Oct 2007, Lahaina, Maui, Hawaii, United States. pp.449-452, ⟨10.1109/ISBN0-7695-3009-5⟩. ⟨inria-00189560⟩

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