Surface smoothing is a well-studied topic. Given a triangle mesh, vertices have to be perturbed such that noise is eliminated, maintaining the overall shape, or that a surface is obtained that is optimal, given constraints. A simple approach is to iteratively replace vertices by an average of their neighboring points. More advanced methods lean heavily on approaches from differential geometry and finite element methods. When a boundary is given and fixed, very good results can be obtained. How to deal with interior constraints is open still. Suppose for instance that on a closed surface (without boundaries) a set of vertices is fixed, whereas others can be modified, and that the overall aim is to obtain a surface that is smooth everywhere. This problem has occured for instance in mathematical visualization (see seifertview). Suppose that a fixed sequence of edges is given (a knot), and that this knot splits a surface in two parts. How to smooth the surface?

This topic is not easy, and requires interest in mathematics and simulation.

• seifertview