Geometry :

Subject: [ggl] boost geometry rtree
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.

>>>
>>>
>>> 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