On a Special Class of Polynomial Surfaces with Pythagorean Normal Vector Fields

  • Miroslav Lávička
  • Jan Vršek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6920)


Rational shapes with rational offsets, especially Pythagorean hodograph (PH) curves and Pythagorean normal vector (PN) surfaces, have been thoroughly studied for many years. However compared to PH curves, Pythagorean normal vector surfaces were introduced using dual approach only in their rational version and a complete characterization of polynomial surfaces with rational offsets, i.e., a polynomial solution of the well-known surface Pythagorean condition, still remains an open and challenging problem. In this contribution, we study a remarkable family of cubic polynomial PN surfaces with birational Gauss mapping, which represent a surface counterpart to the planar Tschirnhausen cubic. A full description of these surfaces is presented and their properties are discussed.


Geometric Design Rational Surface Polynomial Solution Parameter Line Isothermal Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Miroslav Lávička
    • 1
  • Jan Vršek
    • 1
  1. 1.Faculty of Applied Sciences, Department of MathematicsUniversity of West BohemiaPlzeňCzech Republic

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