From scattered samples to smooth surfaces

The problem of reconstructing smooth surfaces from discrete scattered sample points arises in many fields of science and engineering and the data sources in-clude measured values (laser range scanning, meteo-rology, geology) as well as experimental results (engi-neering, physics, chemistry) and computational values (evaluation of functions, finite element solutions, nu-merical simulations). We describe a processing pipeline that can be understood as gradually adding order to a given unstructured point cloud until it is completely organized in terms of a smooth surface. The individ-ual steps of this pipeline are triangulation, remeshing, and surface fitting and have in common that they are much simpler to perform in two dimensions than in three. We therefore propose to use a parameterization in each of these steps so as to decrease the dimension-ality of the problem and to reduce the computational complexity