Accurate approximation of unknown fault lines from scattered data

In a previous paper we proposed a method for the detection of fault lines of a surface only known at scattered data. Now, we present some techniques suitable to give accurate approximation of the detected faults. First, we improve the technique of detection of fault points, picking out and collecting in a set all the data points close to fault lines. To select these points we use a cardinal radial basis interpolation formula. Then, applying a powerful refinement technique, we discuss different methods for the accurate approximation of fault lines, considering procedures based on polygonal line, least squares, and best lapproximations. Numerical results point out the efficiency of our approach.