-------------------------------------------------- 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
Shapes, volumes, etc. are sets of points. Various sets have a null area. This is perfectly valid and is not a logic error.
I don't agree. There are perhaps conventions that say a point or line has zero area, but it doesn't follow that these should be viable arguments to calculate an area. My thoughts are that you really need at minimum a representation which supports 3 points (the 2-simplex ... 2 vectors ... etc) to define an area. If you have three equal points then fine 0 area. If you have 3 points where the third lies on the line defined by the other two, fine 0 area. If you have a circle with 0 radius, fine 0 area. For anything else you are making assumptions or accepting the assumptions made implicit via a convention. I do not think that these should dictate the interface. In my opinion the only shapes which would make sense are those that may actually have an area (non-zero.) Can anyone think of a use-case?
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.
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