Construction of B-spline Surface via Interpolating to Boundary Informa- tion and Approximating Inner Points

This paper discusses how to construct a B-spline surface from its boundary information and inner points. First, an algorithm is presented which can construct a B-spline surface that interpolates four given boundary curves and simultaneously approximates given inner points. Then, the approach is extended to interpolate the cross-boundary derivatives as well. The main idea of this method is that an initial surface interpolating four given boundary curves and the crossboundary derivatives is constructed at first. Then, the inner control vertices of the surface are repositioned through energy optimization while the boundary control vertices of the initial surface remain unchanged. Examples are given which prove that the algorithm is practicable and effective.