Stellt euch vor, ihr möchtet einen R^d gefüllt mit Eiscreme auslöffeln ohne an Schokoladenstücke zu stossen ... As mentioned in Edelsbrunner’s and Mücke’s paper [3], one can intuitively think of an α-shape as the following. Imagine a huge mass of ice-cream making up the space R^d and containing the points S as “hard” chocolate pieces. Using one of these sphere-formed ice-cream spoons we carve out all parts of the ice-cream block we can reach without bumping into chocolate pieces, thereby even carving out holes in the inside (eg. parts not reachable by simply moving the spoon from the outside). We will eventually end up with a (not necessarily convex) object bounded by caps, arcs and points. If we now straighten all “round” faces to triangles and line segments, we have an intuitive description of what is called the α-shape of S. Here’s an example for this process in 2D (where our ice-cream spoon is simply a circle) http://www.cs.uu.nl/docs/vakken/ddm/texts/Delaunay/alphashapes.pdf