6. Numerical experiments
The following numerical examples illustrate RAGS surfaces obtained by methods described in previous sections. The surfaces displayed in Figs. 7 and 8 are examples of local and global interpolation by C1 Powell–Sabin macro-elements for the mesh in Fig. 6 (left). In the former case, the required directional derivatives are estimated by the local approach presented in Section 4.1, which guarantees that the RAGS spline has the quadratic reproduction property. For the surface in Fig. 8, the derivatives are computed by requiring that the surface minimize the energy functional (13). As a consequence,the latter approach is global in nature and, as can be reasonably expected, it results in better aesthetic quality. Finally, the example in Fig. 9 is generated by the global interpolation method described in Section 4.2, employing degree-6 patches and C2-continuity conditions. It turns out that each surface is tangent to its respective control net at the vertices of , in the same way as in the case of standard splines. The illustrations in Figs. 7, 8, and 9 depict, from left to right, collections of individual surface patches, the final surface plots, the Gaussian curvature, and the zebra-line plots.
