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, 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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Murgante, B. and Gervasi, O. and Iglesias, A. and Taniar, D. and Apduhan, B. O. 11th International Conference on Computational Science and Its Applications (ICCSA), Jun 2011, Santander, Spain. Springer, Heidelberg, 6784, pp.121-131, 2011, Lecture Notes in Computer Science. 〈10.1007/978-3-642-21931-3_10〉
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Madalina Hodorog, Bernard Mourrain, Joseph Schicho. An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities. Murgante, B. and Gervasi, O. and Iglesias, A. and Taniar, D. and Apduhan, B. O. 11th International Conference on Computational Science and Its Applications (ICCSA), Jun 2011, Santander, Spain. Springer, Heidelberg, 6784, pp.121-131, 2011, Lecture Notes in Computer Science. 〈10.1007/978-3-642-21931-3_10〉. 〈hal-00646566〉

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