CS-RBF interpolation of surfaces with vertical faults from scattered data

In this paper, the problem of the interpolation of explicit surfaces with vertical faults from scattered data is studied. A new interpolation scheme for compactly supported radial basis functions is proposed which is well adapted to our purpose. This method is based on the construction of an interpolant of the same type in dimension 3 by moving the centers to a convenient auxiliary bivariate explicit surface. Several numerical and graphical examples are shown which illustrate the efficiency of the method.