Re: [boost] [geometry] area, length, centroid, behavior

Subject: Re: [boost] [geometry] area, length, centroid, behavior
From: Brandon Kohn (blkohn_at_[hidden])
Date: 2009-02-24 13:39:51

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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 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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