A Symbolic-Numeric Approach for Parametrizing Ruled Surfaces

Abstract

This paper presents symbolic algorithms to determine whether a given surface (implicitly or parametrically defined) is a rational ruled surface and find a proper parametrization of the ruled surface. However, in practical applications, one has to deal with numerical objects that are given approximately, probably because they proceed from an exact data that has been perturbed under some previous measuring process or manipulation. For these numerical objects, the authors adapt the symbolic algorithms presented by means of the use of numerical techniques. The authors develop numeric algorithms that allow to determine ruled surfaces “close” to an input (not necessarily ruled) surface, and the distance between the input and the output surface is computed.

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Correspondence to Li-Yong Shen.

Additional information

This work has been partially supported by FEDER/Ministerio de Ciencia, Innovación y Universidades — Agencia Estatal de Investigacin/MTM2017-88796-P (Symbolic Computation: New challenges in Algebra and Geometry together with its applications), and the National Natural Science Foundation of China under Grant No. 61872332 and the University of Chinese Academy of Sciences. The first author belongs to the Research Group ASYNACS (Ref. CCEE2011/R34).

This paper was recommended for publication by Editor LI Hongbo.

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Pérez-Díaz, S., Shen, L. A Symbolic-Numeric Approach for Parametrizing Ruled Surfaces. J Syst Sci Complex 33, 799–820 (2020). https://doi.org/10.1007/s11424-019-8188-y

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Keywords

  • Implicit representation
  • numeric algorithm
  • ruled surface
  • standard parametrization