Reconstruction of convergent smooth B-spline surfaces

Recently, there have been improvements on reconstruction of smooth B-spline surfaces of arbitrary topological type, but the most important problem of smoothly stitching B-spline surface patches (the continuity problem of B-spline surface patches) in surface reconstruction has not been solved in an effective way. Therefore, the motivation of this paper is to study how to better improve and control the continuity between adjacent B-spline surfaces.

In this paper, we present a local scheme of constructing convergent G¹ smooth bicubic B-spline surface patches with single interior knots over a given arbitrary quad partition of a polygonal model. Unlike previous work which only produces (non-controllable) toleranced G¹ smooth B-spline surfaces, our algorithm generates convergent G¹ smooth B-spline surfaces, which means the continuity of the B-spline surfaces tends to G¹ smoothness as the number of control points increases. The most important feature of our algorithm is, in the meaning of convergent approximation order, the ability to control the continuity of B-spline surfaces within the given tolerance and capture the geometric details presented by the given data points.