I became pretty interested in this topic not too long ago. Convex hulls are pretty well understood. I wanted to figure out a decent notion of "concave hull" (which is not a uniquely defined construct, unlike the convex hull). It turns out alpha shapes are pretty well suited to this:<p><a href="http://bl.ocks.org/zpconn/11387143" rel="nofollow">http://bl.ocks.org/zpconn/11387143</a>
I have a hard time understanding why the author go out of his/her way to rename standard definitions.<p>1. The definition of convex hull of a set S in the article, is the boundary of a convex set that contains all the points in S. The standard definition is the "intersection of all convex sets that contains S".
Edit: Yes, this is not a good definition for the article, but there is a equivalent for finite set of points in 2D which is much better suited: "The smallest convex polygon contain all the points in S"<p>2. The definition of minimal convex hull in the article, in the standard terminology, is the boundary of the convex hull.<p>The article links to wikipedia which clearly explains what is a convex hull, but still decides to come up with new terminology. As a warning, the "convex hull" in this article is not equivalent to the "convex hull" in wikipedia(or any other textbook definitions I have seen).
Another good source for convex hull code (I was using this recently):
<a href="http://marknelson.us/2007/08/22/convex/" rel="nofollow">http://marknelson.us/2007/08/22/convex/</a>