Reconsidering algorithms for real parametric curves

  • Cesar Alonso
  • Jaime Gutierrez
  • Tomas Recio
Article

Abstract

Complex parametric curves have been subject of a symbolic algorithm approach in recent years. In this paper we analyze the theoretical applicability of some of these algorithms to the real parametric curve case. In particular, we show how several results are valid both over the real and the complex numbers, as they hold equivalently over a real curve and its complexification. Therefore, the standard algorithms for the complex case can be applied to obtain real answers in the real case. A second issue in our paper is the study of the very different behaviour of the real parametric mapping and we characterize here the properties of being (almost) injective or surjective.

Keywords

Real parametric curves Parametrizations Algorithms CAD 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Cesar Alonso
    • 1
  • Jaime Gutierrez
    • 1
  • Tomas Recio
    • 1
  1. 1.Departamento de Matemáticas, Estadistica y ComputaciónUniversidad de CantabriaE-SantanderSpain

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