2004-Fez conference on Differential Equations and Mechanics. Electronic Journal of Differential Equations, Conference 11, 2004, pp. 157-166. Title: Approximation of discontinuous curves and surfaces by discrete splines with tangent conditions Authors: Abdelouahed Kouibia (Centre d'Etudes Univ. de Taza, Maroc) Miguel Pasadas (Univ. de Granada, Spain) Abstract: This paper concerns the construction of a discontinuous parametric curve or surface from a finite set of points and tangent conditions. The method is adapted from the theory of the discrete smoothing variational splines to introduce a discontinuity set and some tangent conditions. Such method is justified by a convergence result. Published October 15, 2004. Math Subject Classifications: 65D07, 65D10, 65D17. Key Words: Discrete smoothing; curve; surface; discontinuity; spline; tangent condition.