Semi-implicit representations of surfaces in P3, resultants and applications

  • Authors:
  • Laurent Busé;André Galligo

  • Affiliations:
  • INRIA Sophia-Antipolis, GALAAD, 2004 route des Lucioles, B.P. 93, 06902 Sophia-Antipolis, Cedex, France;Université de Nice Sophia-Antipolis, Parc Valrose, BP 71, 06108 Nice Cedex 02, France

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2005

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Abstract

In this paper we introduce an intermediate representation of surfaces that we call semi-implicit. We give a general definition in the language of projective complex algebraic geometry, and we begin its systematic study with an effective view-point. Our last section will apply this representation to investigate the intersection of two bi-cubic surfaces; these surfaces are widely used in Computer Aided Geometric Design.