Applicable Algebra in Engineering, Communication and Computing

, Volume 6, Issue 6, pp 345–352

Reconsidering algorithms for real parametric curves

Authors

  • Cesar Alonso
    • Departamento de Matemáticas, Estadistica y ComputaciónUniversidad de Cantabria
  • Jaime Gutierrez
    • Departamento de Matemáticas, Estadistica y ComputaciónUniversidad de Cantabria
  • Tomas Recio
    • Departamento de Matemáticas, Estadistica y ComputaciónUniversidad de Cantabria
Article

DOI: 10.1007/BF01198014

Cite this article as:
Alonso, C., Gutierrez, J. & Recio, T. AAECC (1995) 6: 345. doi:10.1007/BF01198014

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 curvesParametrizationsAlgorithmsCAD

Copyright information

© Springer-Verlag 1995