Brandon Kohn wrote:
-------------------------------------------------- From: "Mathias Gaunard" <mathias.gaunard@ens-lyon.org> Sent: Tuesday, February 24, 2009 12:37 PM To: <boost@lists.boost.org> Subject: Re: [boost] [geometry] area, length, centroid, behavior
Points (a point is just a set of points which one element) and lines have zero area, this is common knowledge. This is even stated in the definition on "area" on wikipedia, for example.
I don't agree that this is common knowledge. It may seem like 'common-sense', but I don't think such notions have much merit in the face of something as mathematically rigorous as a computational geometry library. It's a matter of interpretation. If you consider a point a 0-dimensional object placed in the n-dimensional space you're working with, it doesn't have an extent over any number of dimensions. If, however, you consider it an n-dimensional object with an extent of 0 along every dimension, it does have length, area, volume, and whatever you want to call hyper-volumes in more than 3 dimensions, all of them being 0.
Sebastian