TY - JOUR
T1 - Characterisation of Rational and NURBS Developable Surfaces in Computer Aided Design
AU - Fernández-Jambrina , Leonardo
JO - Journal of Computational Mathematics
VL - 4
SP - 556
EP - 573
PY - 2021
DA - 2021/05
SN - 39
DO - http://doi.org/10.4208/jcm.2003-m2019-0226
UR - https://global-sci.org/intro/article_detail/jcm/19150.html
KW - NURBS, Bézier, Rational, Spline, NURBS, Developable surfaces.
AB - <p style="text-align: justify;">In this paper we provide a characterisation of rational developable surfaces in terms of
the blossoms of the bounding curves and three rational functions $Λ, M, ν.$ Properties of
developable surfaces are revised in this framework. In particular, a closed algebraic formula
for the edge of regression of the surface is obtained in terms of the functions $Λ, M, ν,$ which
are closely related to the ones that appear in the standard decomposition of the derivative
of the parametrisation of one of the bounding curves in terms of the director vector of the
rulings and its derivative. It is also shown that all rational developable surfaces can be
described as the set of developable surfaces which can be constructed with a constant $Λ,
M, ν .$ The results are readily extended to rational spline developable surfaces.</p>