All examples below are based on the results in paper Chui, C. K. and Lai, M. J., Filling Polygonal Holes using $C^1$ Cubic Triangular Spline Patches, Computer Aided Geometric Design, vol. 17 (2000) pp. 297--307
Example 2. Given a surface with hole as shown below. I used C^1 quintic splines to find a surface which interpolates the values and derivatives on the boundary of the hole. The mending surface is shown in the following
Example 3. Given a surface with hole as shown below. I used C^1 quintic splines to find a surface which interpolates the values and derivatives on the boundary of the hole. The mending surface is shown below.
Example 4. Given a surface with hole as shown below. I used C^1 quintic triangulated spherical splines to find a surface which interpolates the values and derivatives on the boundary of the hole. The mending surface is shown in the following. Another filling with articifial horns added is shown in the end.