Summary: Many applications require to extract the surface of an object from a discrete set of valued points, applications in which the topological soundness of the obtained surface is, in many case, of the utmost importance. In this paper, we introduce the notion of frontier order which provides a discrete framework for defining frontiers of arbitrary objects. A major result we obtained is a theorem which guarantees the topological soundness of such frontiers in any dimension. Furthermore, we show how frontier orders can be used to design topologically coherent “marching cubes-like” algorithms.
For the entire collection see [Zbl 1029.00061].