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An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities

Madalina Hodorog 1 Bernard Mourrain 2 Joseph Schicho 1
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We report on an adapted version of the Bentley-Ottmann algorithm for computing all the intersection points among the edges of the projection of a three-dimensional graph. This graph is given as a set of vertices together with their space Euclidean coordinates, and a set of edges connecting them. More precisely, the three-dimensional graph represents the approximation of a closed and smooth implicitly defined space algebraic curve, that allows us a simplified treatment of the events encountered in the Bentley-Ottmann algorithm. As applications, we use the adapted algorithm to compute invariants for each singularity of a plane complex algebraic curve, i.e. the Alexander polynomial, the Milnor number, the delta-invariant, etc.
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https://hal.inria.fr/hal-00646566
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Submitted on : Wednesday, November 30, 2011 - 11:48:27 AM
Last modification on : Monday, October 12, 2020 - 10:27:38 AM
Long-term archiving on: : Friday, November 16, 2012 - 12:25:35 PM

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Madalina Hodorog, Bernard Mourrain, Joseph Schicho. An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities. 11th International Conference on Computational Science and Its Applications (ICCSA), Jun 2011, Santander, Spain. pp.121-131, ⟨10.1007/978-3-642-21931-3_10⟩. ⟨hal-00646566⟩

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