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Volume 38, Issue 5
Developable Surface Patches Bounded by NURBS Curves

Leonardo Fernández-Jambrina & Francisco Pérez-Arribas

DOI: 10.4208/jcm.1904-m2018-0209

J. Comp. Math., 38 (2020), pp. 715-731.

Published online: 2020-04

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  • Abstract

In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary curves. The reparameterization function is the solution of an algebraic equation. For the relevant case of cubic or cubic spline curves, this equation is quartic at most, quadratic if the curves are Bézier or splines and lie on parallel planes, and hence it may be solved either by standard analytical or numerical methods.

  • Keywords

NURBS, Bézier, Rational, spline, Developable surfaces.

  • AMS Subject Headings

65D17, 68U07

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

leonardo.fernandez@upm.es (Leonardo Fernández-Jambrina)

francisco.perez.arribas@upm.es (Francisco Pérez-Arribas)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-715, author = {Fernández-Jambrina , Leonardo and Pérez-Arribas , Francisco}, title = {Developable Surface Patches Bounded by NURBS Curves}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {5}, pages = {715--731}, abstract = {

In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary curves. The reparameterization function is the solution of an algebraic equation. For the relevant case of cubic or cubic spline curves, this equation is quartic at most, quadratic if the curves are Bézier or splines and lie on parallel planes, and hence it may be solved either by standard analytical or numerical methods.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1904-m2018-0209}, url = {http://global-sci.org/intro/article_detail/jcm/16666.html} }
TY - JOUR T1 - Developable Surface Patches Bounded by NURBS Curves AU - Fernández-Jambrina , Leonardo AU - Pérez-Arribas , Francisco JO - Journal of Computational Mathematics VL - 5 SP - 715 EP - 731 PY - 2020 DA - 2020/04 SN - 38 DO - http://doi.org/10.4208/jcm.1904-m2018-0209 UR - https://global-sci.org/intro/article_detail/jcm/16666.html KW - NURBS, Bézier, Rational, spline, Developable surfaces. AB -

In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary curves. The reparameterization function is the solution of an algebraic equation. For the relevant case of cubic or cubic spline curves, this equation is quartic at most, quadratic if the curves are Bézier or splines and lie on parallel planes, and hence it may be solved either by standard analytical or numerical methods.

Fernández-Jambrina , Leonardo and Pérez-Arribas , Francisco. (2020). Developable Surface Patches Bounded by NURBS Curves. Journal of Computational Mathematics. 38 (5). 715-731. doi:10.4208/jcm.1904-m2018-0209
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