Topology of Families of Implicit Algebraic Surfaces Depending on a Parameter

  • Juan Gerardo Alcázar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)


Given a family of algebraic surfaces, implicitly defined, depending on a parameter t, here we provide an algorithm for computing the different shapes arising in the family. The algorithm decomposes the real line into finitely many pieces (points and intervals) so that over each interval the shape is invariant, in the sense that the topology of the family can be described by means of the same simplicial complex. As a consequence, by applying known algorithms ([1], [6], [7], [11]) the different shapes in the family can be computed. The algorithm is due to a generalization of the ideas in [2] to the surface case.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Juan Gerardo Alcázar
    • 1
  1. 1.Departamento de MatemáticasUniversidad de AlcaláMadridSpain

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