Elias' Article

Algebraic issues in Computational Geometry.
Bernard Mourrain, Sylvain Pion, Susan Schmitt, Jean-Pierre Técourt, Elias P. Tsigaridas, and Nicola Wolpert.
In J.-D. Boissonnat and M. Teillaud, editors, Effective Computational Geometry for Curves and Surfaces, Mathematics and Visualization, pp. 117–155, Springer, 2006.

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Abstract:

We describe methods for the treatment of algebraic models. We focus on the problem of computing the topology of implicit curves or surfaces. Our objective is to devise certified and output-sensitive methods, in order to combine control and efficiency. We distinguish two types of subproblems: (i) the construction of new geometric objects such as points of intersection, and (ii) predicates such as the comparison of coordinates of intersection points.

@InCollection{mpsttw-ecg-2006,
  author =       {Bernard Mourrain and Sylvain Pion and Susan Schmitt
                  and Jean-Pierre T{\'e}court and Elias P. Tsigaridas
                  and Nicola Wolpert},
  booktitle =    {{Effective Computational Geometry for Curves and
                  Surfaces}},
  editor =       {Boissonnat, J.-D. and Teillaud, M.},
  title =        {{Algebraic issues in Computational Geometry}},
  chapter =      3,
  pages =        "117--155",
  series =       {Mathematics and Visualization},
  publisher =    {Springer},
  year =         2006,
  abstract =     "We describe methods for the treatment of algebraic
                  models. We focus on the problem of computing the
                  topology of implicit curves or surfaces. Our
                  objective is to devise certified and
                  output-sensitive methods, in order to combine
                  control and efficiency. We distinguish two types of
                  subproblems: (i) the construction of new geometric
                  objects such as points of intersection, and (ii)
                  predicates such as the comparison of coordinates of
                  intersection points. ",
}

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