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

Subject: Re: [boost] [geometry] area, length, centroid, behavior
From: Sebastian Redl (sebastian.redl_at_[hidden])
Date: 2009-02-24 13:47:54

Brandon Kohn wrote:
> --------------------------------------------------
> 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
>> 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