Smooth closed surfaces with discrete triangular interpolants (Q1070747)

When using discrete interpolants which involve cross boundary derivatives in an attempt to form \(C^ 1\) surfaces, an impossibility is found if the surface contains more connections that can be achieved in the domain. The usual solution is to relax the \(C^ 1\) continuity of an interpolant to ''visually \(C^ 1\)'' (see \textit{G. Farin}, Comput. Graphics Image Process. 20, 272-282 (1982; Zbl 0541.65006)). The author develops a method of forming smooth closed surfaces from a discrete triangular interpolant; the only constraint on the scheme is that the data define a unique tangent plane at each vertex where several triangles meet. Some examples with the list of needed calculations and pictures are given.