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Subject: Re: [boost] [geometry] area, length, centroid, behavior
From: Brandon Kohn (blkohn_at_[hidden])
Date: 20090224 13:39:51

From: "Mathias Gaunard" <mathias.gaunard_at_[hidden]>
Sent: Tuesday, February 24, 2009 12:37 PM
To: <boost_at_[hidden]>
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 2simplex ... 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 (nonzero.) Can anyone think of a usecase?
>
> 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
'commonsense', 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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