An approximate lofting approach for B-spline surface fitting to functional surfaces

Owing to their specific functionality, surfaces are often given as bivariate functions including non-polynomial or higher-order polynomial terms. It is necessary to represent them in standard formats such as non-uniform rational B-splines (NURBS) for approximation. As most such surfaces require fine quality of surfacing and high precision of manufacturing, accuracy should be guaranteed in their representations. As high accuracy is likely to result in bulky, and redundant representations, it is also important to make them more compact. For NURBS surfaces, control points must be reduced without sacrificing accuracy. This paper presents an approximate lofting method for B-spline surface fitting to a functional surface within a specified accuracy. It adopts adaptive sampling and multiple B-spline curve fitting. The method is very effective when the surface shape is longish or the cross-sectional curves vary regularly in shape along a specific direction. Some experimental results demonstrate its usefulness and quality.