Abstract: With Bspline surfaces with single interior knots as an example, an algorithm and some examples of constructing local scheme on bi quartic Bspline surfaces with single interior knots are presented by taking the advantages of the continuity restriction between surfaces and blending functions. The novel G¹ and G² continuousconditions of Bspline surfaces are obtained. By means of releasing the restriction on the blending functions, the degree of the freedom of the common boundary is increased. The local scheme of G¹ continuity can be carried to biquartic Bspline surfaces with single interior knots while the local scheme of G² continuity can be carried to bieightpowerBspline surfaces.

Key words: B spline surface, G¹ continuity, local scheme 