Properties and Applications of Connecting Functions for GC¹-Connected B-Spline Surfaces

In order to improve the convenience of surface modeling with B-spline surfaces,the properties of G¹ continuity conditions are studied between two B-spline surfaces with arbitrary degrees,such as constraint conditions defined by the connecting functions,the intrinsic equations and the common boundary.By investigating the continuity property of connecting functions at interior knots,a new method is proposed for G¹ connection of two B-spline surfaces by adopting B-spline functions as connecting functions.To demonstrate the results,the implement of the G¹ continuity of two bicubic B-spline surfaces is achieved by selecting a special kind of piecewise quadratic polynomial functions.Due to the release of added degree of freedom along the common boundary upon double knots near to two ends of interval,the presented method is rather flexible in smooth connection of B-spline surfaces.