Construction of surfaces with parallelism conditions (Q1410482)

A common problem in computer aided geometric design is the generation of offset surfaces. In this article, an alternative is presented in the form of pseudo-parallel surfaces which are only parallel in a weak formulation. These surfaces are then generated by generalisation of thin-plate spline interpolants (also called \(D^m\)-splines) over a bounded domain. They fit scattered data given in the domain. In order that the interpolation problem be well-posed, the domain must contain \(P_{m-1}\) unisolvent subsets and also the boundary has to be Lipschitz. Convergence results and numerical examples are also provided.