Seron, F.J.Torrens, J.JMagallon, J.A.2014-10-212014-10-2119931467-8659https://doi.org/10.1111/1467-8659.1230461In this paper we study a finite element interpolation method for fitting discontinuous parametric surfaces when the data points are the nodes of a curvilinear grid. Quality control of the interpolating surfaces is also considered, focussing on the display of isophotes and reflection lines using ray tracing techniques. Finally, graphical and numerical examples are given.10.1111/1467-8659.1230461461-471