Implicit Equations of Non-degenerate Rational Bezier Quadric Triangles

  • Alicia Cantón
  • L. Fernández-JambrinaEmail author
  • E. Rosado María
  • M. J. Vázquez-Gallo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9213)


In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bézier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is grounded on the pencil of quadrics circumscribed to a tetrahedron formed by vertices of the control net and an additional point which is required for the Steiner surface to be a non-degenerate quadric.


Quadric Steiner surfaces Rational Bézier triangles 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alicia Cantón
    • 1
  • L. Fernández-Jambrina
    • 1
    Email author
  • E. Rosado María
    • 1
  • M. J. Vázquez-Gallo
    • 1
  1. 1.Universidad Politécnica de MadridMadridSpain

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