An automated curve fairing algorithm for cubic B-spline curves

The fairing of contours is an important part of the computerised production of curved objects. A number of different fairing strategies have been proposed. In a recent paper we have introduced an extension of Kjellanderʹs algorithm for fairing parametric B-splines, which can be applied to a wide range of two- and three-dimensional curves. In this paper we describe developments towards a fully automated fairing procedure based on our new algorithm. Like that of Kjellander, our algorithm fairs by an iterative process. The key problems are to decide which points need to be faired and how many times to iterate. Sapidis (1992) has proposed a curve fairness indicator to locate points to be faired and a criterion for termination of fairing. However, we have found that for interpolating curves with great variation in curvature Sapidisʹ criterion tends to concentrate fairing on regions with large curvature. Therefore we have developed a new scale-independent curve fairness indicator which does not suffer from this drawback. A number of examples of faired curves are presented.