Detecting regions with undesirable curvature

The use of Brzier curves or Brzier surfaces as "faired" interpolation (approximation) curves or surfaces occasionally yields inflection points or changes of sign of the Gaussian curvature which are undesirable in some applications, notably the fairing of ship lines (surfaces) or the fairing of car body surfaces. In the following investigation we use a polarity to detect such undesirable points, then these points can be removed by the use of the well known Brzier techniques.