Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics

  • Laurent Dupont
  • Michael Hemmer
  • Sylvain Petitjean
  • Elmar Schömer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4698)


We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always computes the mathematically correct result. It is efficient measured in running times, i.e. it compares favorably to the only previous implementation.


Intersection Point Interval Arithmetic Intersection Curve Quadric Surface Implicit Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Laurent Dupont
    • 1
  • Michael Hemmer
    • 2
  • Sylvain Petitjean
    • 1
  • Elmar Schömer
    • 2
  1. 1.LORIA, NancyFrance
  2. 2.Johannes Gutenberg-Universität, Institut für Informatik, MainzGermany

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