Bicubic B-spline surfaces constrained by the Biharmonic PDE

摘要

Bicubic B-spline surface constrained by the Biharmonic PDE is presented in this paper. By representing the Biharmonic PDE in the form of the bilinear B-spline bases, we find the regular vector-valued coefficients and discover that bicubic B-spline surface can satisfy the Biharmonic PDE. When the control points of the boundaries for open or closed surfaces are given, the inner control points can be fully determined. For each case of the surfaces open in both directions, closed in one direction and closed in both directions, a linear system for solving inner control points is established. Some examples show the effectiveness of the given method.