I was interested in this and did a very quick google search. Measuring concavity/convexity of a generic 2D surface object doesn't seem to be a very common oper

I was interested in this and did a very quick google search. Measuring concavity/convexity of a generic 2D surface object doesn't seem to be a very common operation. The one reference I found seems to do what you describe: http://www.ncbi.nlm.nih.gov/pubmed/7945702 http://www.ncbi.nlm.nih.gov/pubmed/7945702 Although I don't have PubMed access so I can't be sure. This is an interesting problem. I chose the "random points" method because it seemed easier to me to get an approximate answer for a generic shape rather than try to figure out areas. Lengths didn't occur to me though and seems interesting, although the shape you describe doesn't "feel" concave to me.