Fair interpolation and approximation of B splines by energy minimization and points insertion

An efficient method for interpolation and approximation of both curve and surface points using B-splines is described. Automatic fairing is presented based on minimizing an energy functional. Additional data points, used as degrees of freedom for the fairing, are inserted only where the curve (the surface) needs them. This reduces the number of the unknowns to a minimum which makes the algorithm very fast and efficient especially when a huge amount of data is concerned. Results of applying the algorithm for about 15,000 face data points, subject to measurement errors due to the digitization, are presented at the end of the paper. Copyright (C) 1996 Elsevier Science Ltd