[GRASS-user] Computing major and minor axes for polygons

[Sören Gebbert]

Hi Ben,

2014-11-24 22:50 GMT+01:00 Benjamin Ducke <benducke at fastmail.fm>:
> Right, a PCA of the polygon vertices, I assume?

Exactly, create a covariance matrix from the vertices coordinates of
each polygon
and compute the eigenvectors and eigenvalues of these matrices.

Best regards
Soeren

> Maybe "v.to.db" could be enhanced to allow it to upload
> the lengths of the first two/three components to the
> attribute table?
>
> For a quick fix, I solved the problem in a shell script using
> a crude approximation. FWIW:
> 0. Set major axis length=-1
> 1. Rotate polygon by 10° (v.transform)
> 2. Fit region to polygon (g.region vect=).
> 3. Get width of region. If it is greater than major axis length,
>    set "major axis length = width"
> 4. Repeat from 1, until polygon has been rotated 350°
> 5. Minor axis length = height of current region.
>
> Like I said, it's just a crude approximation (precision can
> be increased by using smaller rotation steps) and slow, too.
> But it's good enough for my purposes, which is basically to
> calculate "elongation=len(major)/len(min)".
>
> Best,
>
> Ben
>
> On 24/11/14 19:27, Sören Gebbert wrote:
>> IIRC is the code to compute the major and minor axes already in GRASS.
>> You need to perform a Karhunen-Loewe-Transformation for each Polygon.
>> This is also known as principal components analysis.
>>
>> Best regards
>> Soeren
>>
>> Am 21.11.2014 23:33 schrieb "Benjamin Ducke" <benducke at fastmail.fm
>> <mailto:benducke at fastmail.fm>>:
>>
>>     Hi All --
>>
>>     Does anybody here know of an existing GRASS modules that
>>     will compute the major and minor axes for the polygons of
>>     a vector map?
>>
>>     Thanks and best,
>>
>>     Ben
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>
>
>
> --
> Dr. Benjamin Ducke
> {*} Geospatial Consultant
> {*} GIS Developer
>
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