Characterisation of Rational and NURBS Developable Surfaces in Computer Aided Design (Journal of Computational Mathematics, 2021)
In this paper we provide a characterisation of rational developable surfaces in terms ofthe blossoms of the bounding curves and three rational functions $Λ, M, ν.$ Properties ofdevelopable surfaces are revised in this framework. In particular, a closed algebraic formulafor the edge of regression of the surface is obtained in terms of the functions $Λ, M, ν,$ whichare closely related to the ones that appear in the standard decomposition of the derivativeof the parametrisation of one of the bounding curves in terms of the director vector of therulings and its derivative. It is also shown that all rational developable surfaces can bedescribed 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.