Geometry Boost List: [ggl] boost geometry rtree

Subject: [ggl] boost geometry rtree
From: Adam Wulkiewicz (adam.wulkiewicz)
Date: 2011-07-14 11:03:59

Barend Gehrels wrote:
>>>> (http://mathworld.wolfram.com/Content.html) because in dimensions
>>>> greater than 4 3d volume may have different meaning. Hypersurface of
>>>> a 4d object is 3-dimensional and someone may call it the volume,
>>>> like 2d surface of a 3d object is called the surface.
>>>>
>>>> I use also a function calculating the margin of a box (this term is
>>>> taken from: R*tree: An Efficient and Robust Access Method for Points
>>>> and Rectangles by Beckmann at al.). I assumed that this is nD
>>>> hypersurface so for 2d it's the perimeter of a box, for 3d it's
>>>> surface, for 4d it's 3d hypersurface etc.
>>>> (http://mathworld.wolfram.com/Hypersurface.html).
>>>
>>>
>>> OK, good idea. If "margin" is the right term for that, we should use
>>> that. Thanks.
>>
>> In the original paper 'margin' refers to 'perimeter' but they only
>> describe 2d. I've searched for the meaning of this in 3d but didn't
>> find anything. I think the best is to check which one gives best
>> results in dimensions greater than 2 - perimeter or hypersurface.
>
> OK, I will look/ask for this in more detail. If anyone on this list know
> the very right term, it is welcome. So the question is:
>
> "content" means: length-in-1-D, area-in-2-D, volume-in-3-D
> "XXX" means: perimeter-in-2-D, area-in-3-D
>
> where "XXX" might be margin. The term "content" is quite difficult to
> Google, by the way.

Other possibility is to use straightforward hypervolume and 
hypersurface. They're both at MathWorld's pages I've mentioned and to be 
honest I've found pages googling these terms. Other ideas?

Regards,
Adam