Adaptive fairing of digitized point data with discrete curvature

Abstract

An algorithm for fairing two-dimensional (2D) shape formed by digitised data points is described. The application aims to derive a fair curve from a set of dense and error-filled data points digitised from a complex surface, such that the basic shape information recorded in the original point data is relatively unaffected. The algorithm is an adaptive process in which each cycle consists of several steps. Given a 2D point set, the bad points are identified by analysing the property of their discrete curvatures ( D-curvatures) and first-order difference of D-curvatures, in two consecutive fairing stages. The point set is then segmented into single bad point (SBP) segments and multiple bad point (MBP) segments. For each MBP segment, a specially designed energy function is used to identify the bad point to be modified in the current cycle. Each segment is then faired by directly adjusting the geometric position of the worst point. The amount of adjustment in each cycle is kept less than a given shape tolerance. This algorithm is particularly effective in terms of shape preservation when dealing with MBP segments. Case studies are presented that illustrate the efficacy of the developed technique.