Adaptive detection and approximation of unknown surface discontinuities from scattered data

We consider a method for the detection and approximation of fault lines of a surface, which is known only on a finite number of scattered data. In particular, we present an adaptive approach to detect surface discontinuities, which allows us to give an (accurate) approximation of the detected faults. First, to locate all the fault points, i.e. the nodes on or close to fault lines, we consider a procedure based on a local interpolation scheme involving a cardinal radial basis formula. Second, we find further sets of points generally closer to the faults than the fault points. Finally, after applying a nearest-neighbour searching procedure and a powerful refinement technique, we outline some different approximation methods. Numerical results highlight the efficiency of our approach.