Computing the shape of a planar points set

摘要

In this article, we introduce a mathematical formalism defining the shape of a finite point set which we call A-shape. The parameter A is a finite set of points which positions variation allows A-shape to generate a family of graphs extracted from Delaunay triangulation. Each graph corresponds to an element of a shapes set presenting more and more details and going from the convex hull of the points set to the points set itself. It is obvious that the shape having the suitable level of details is obtained by a judicious choice of A. We also propose a method to determine A for which A-shape gives the adequate shape for points sets containing dense and sparse regions.