Computational Aspects of Discrete Minimal Surfaces
Konrad Polthier · 2002
ids. ii Printer: Opaque this Introduction to Polyhedral Meshes Polyhedral meshes belong to the most basic structures for the representation of geometric shapes not only in numerics and computer graphics. Especially the niteness of the set of vertices and of their combinatorial relation makes them an ideal tool to reduce innite dimensional problems to nite problems. In this section we will review the basic combinatorial and topological denitions and state some of their di#erential geometric properties. In practice, a variety of di#erent triangle and other polyhedral meshes are used. In this introduction we restrict ourselves to simplicial complexes, or conforming meshes, where two polygons must either be disjoint or have a common vertex or a common edge. Or for short, a polygon is not allowed to contain a vertex of another polygon in the interior of one of its edges. This restriction avoids discontinuity problems in the shape, so-called hanging nodes. Further, we restrict our discu