An adapted version of the Bentley-Ottmann algorithm for invariants of plane curves singularities

Authors:
Mădălina Hodorog;Bernard Mourrain;Josef Schicho
Affiliations:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria;INRIA Sophia-Antipolis, Sophia-Antipolis, France;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria
Venue:
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Year:
2011

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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.