THIN-PLATE SPLINE SURFACE APPROXIMATION USING COONS PATCHES

In the process of thin plate spline surface approximation, a discrete formulation is often used to minimize the energy of the surface. Discrete formulation leads naturally to discrete representation of the surface. As a result, a large number of nodal variables is required to represent the surface when a high resolution of the surface is demanded. Since such a large number of variables is involved in the discrete formulation, the speed of energy minimization is slow. The usage of patches for thin plate spline surface approximation has been proposed to improve the speed of energy minimization. If C1 third-order non-parametric patches are used, only sixteen variables are needed to represent each patch which can cover a large area of the surface. Techniques for minimizing the energy of the surface by using patches are presented and the problem of allocating the patches in the surface is discussed in this paper.