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Determination and (re)parametrization of rational developable surfaces

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Abstract

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors first determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affirmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Liyong Shen

  2. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Liyong Shen

  3. Key Laboratory of Big Data Mining and Knowledge management, Chinese Academy of Sciences, Beijing, 100190, China

    Liyong Shen

  4. Dpto de Física y Matemáticas, Universidad de Alcalá, Madrid, E-28871, Spain

    Sonia Pérez-Díaz

Authors
  1. Liyong Shen
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  2. Sonia Pérez-Díaz
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Corresponding author

Correspondence to Liyong Shen.

Additional information

This research was supported by Beijing Nova Program under Grant No. Z121104002512065. The author Pérez-Díaz S is a member of the Research Group ASYNACS (Ref. CCEE2011/R34).

This paper was recommended for publication by Editor LI Ziming.

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Shen, L., Pérez-Díaz, S. Determination and (re)parametrization of rational developable surfaces. J Syst Sci Complex 28, 1426–1439 (2015). https://doi.org/10.1007/s11424-015-3119-z

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  • DOI: https://doi.org/10.1007/s11424-015-3119-z

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