This picture shows several G1 surfaces fit to a sampling of the torus. The top row shows shaded images; the bottom row shows Gaussian curvature curvature plots.
The different columns are using different techniques for constructing boundary curves. The surface at the far right was built by using boundary curves that interpolate second derivatives of the torus. Although we see that improving the shape of the boundary curves improves the surface quality, even the use of good boundaries gives poor quality surface.