Construction of B-spline Surface via Interpolating to Boundary Informationand Approximating Inner Points

摘要

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 simultaneouslyapproximates given inner points. Then, the approach is extended to interpolate the cross-boundary derivatives aswell. The main idea of this method is that an initial surface interpolating four given boundary curves and the crossboundaryderivatives is constructed at first. Then, the inner control vertices of the surface are repositioned through energyoptimization while the boundary control vertices of the initial surface remain unchanged. Examples are given which provethat the algorithm is practicable and effective.