Advanced surface fitting techniques

Abstract

In spite of extensive research on fitting parametric surfaces, the published ‘standard’ solutions often fail, when data points are irregularly distributed over topologically irregular domains, high accuracy is required and the free quantities of least squares fitting—such as the number and placement of knots, the weights of the smoothing functionals and the best parametrisation of the data points—must be set without user assistance. Further difficulties arise when the fitted surface needs to be extended in a natural way and hole loops without underlying point data need to be covered smoothly. This paper attempts to analyse the above difficulties and provide practical solutions to overcome these. Main results include algorithms to compute a good initial parametrisation, a fitting strategy to maintain tight tolerances and smoothness simultaneously, to handle weakly defined control points and a shape dependent knot refinement procedure. A few examples and suggestions for future work conclude the paper.