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

  • Mădălina Hodorog
  • Bernard Mourrain
  • Josef Schicho
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6784)


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.


adapted Bentley-Ottmann algorithm sweep technique graph data structure implicitly defined space algebraic curve topological invariants plane curves singularities 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mădălina Hodorog
    • 1
  • Bernard Mourrain
    • 2
  • Josef Schicho
    • 1
  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  2. 2.INRIA Sophia-AntipolisSophia-AntipolisFrance

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