A note on the discrete approximation of discontinuous curves and surfaces

This is a note on the paper [A. Kouibia, A.J. López-Linares, M. Pasadas, Approximation of discontinuous curves and surfaces with tangent conditions, J. Comput. Appl. Math. 193 (2006) 51–64]. We consider the constructing problem of a discontinuous parametric curve or surface from a finite set of points and tangent conditions. We develop a method based on the theory of discrete smoothing variational splines conveniently adapted to introduce the tangent conditions and the discontinuity set. We give a convergence result and we analyze some numerical and graphical examples in order to illustrate the effectiveness of the presented method.