Efficient approximation algorithms. Part I: approximation of unknown fault lines from scattered data

A method for the detection of fault lines of a surface only known at scattered data is presented. In particular, we use a technique for the 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 accurate approximation of fault lines, considering procedures based on polygonal line, least squares, and best l∞ approximations. Moreover, an adaptive method enables us to locally increase (step by step) the number of nodes to be dealt with in the detection process, reducing considerably the entire number of data points to be considered. Numerical results point out the efficiency of our approaches.