[Gstat-info] non-Euclidean distance functions?

[Edzer Pebesma]

Ashton Shortridge wrote:
> I'm getting off-topic, but Quaternary Triangular Meshes offer a decomposition 
> of the globe. I wrote a paper using QTM that no one really wanted to publish, 
> There's stuff by Geoffrey Dutton as well as others on QTM.
>   
Is this the hexagonal decomposition? I read some papers about it, after 
discussions on r-sig-geo.
> A quadtree structure could be used on catesian lat-lon, but it wouldn't be 
> very efficient, since the distances aren't true, and results would be very 
> messy around the poles.
>   
That was my thought. You'd have to set the "distances" very large 
anyway, so the advantage vanishes.
--
Edzer
> Ashton
>
> On Tuesday 18 March 2008, Edzer Pebesma wrote:
>   
>> Carlos, here's a comment:
>>
>> if you ignore the quadtree search structure, you can get away without
>> working point-block distance function; see the examples of pb_norm_gc in
>> data.c, where great-circle distances are used without quadtrees (could
>> never figure out how/whether a quadtree on a globe works).
>> --
>> Edzer
>>
>> Carlos Rueda wrote:
>>     
>>> Many thanks Edzer for your suggestions.
>>>
>>> The function pointers in the DATA structure easily allow one to
>>> register customized functions! I already have plugged in my
>>> point-to-point distance function and made a preliminary test of
>>> computing the semivariogram. However, I still need to think about the
>>> vector norm and the point-bbox functions so everything is of course
>>> consistent. What happens is that I'm using a 'network distance' (ie,
>>> computed as the shortest path between the two points over a network,
>>> eg, a stream network, but ignoring flow direction for now). All
>>> pair-wise distances are pre-computed and saved in a look-up table,
>>> which is then used by the point-to-point distance function. I will
>>> continue examining the code and looking into the related math, but any
>>> further comments are most welcome!
>>>
>>> Carlos
>>>
>>> On Fri, Mar 14, 2008 at 12:27 AM, Edzer Pebesma
>>>
>>> <edzer.pebesma at uni-muenster.de> wrote:
>>>       
>>>> It can be done at the C code level only. In data.h you'll find three
>>>>  functions,
>>>>
>>>>    double (*point_norm)(const DPOINT *); /* eucl. vector length */
>>>>    double (*pp_norm2)(const DPOINT *, const DPOINT *); /* point-point
>>>>  squared distance */
>>>>    double (*pb_norm2)(const DPOINT *, BBOX); /* point-BBOX distance:
>>>>  nsearch.c */
>>>>
>>>>  that a DATA structure needs; they are set in data.c. They are used to
>>>>  compute distances. See how they're set currently; you would have to
>>>>  override them with your own versions. The question of course is whether
>>>>  the input arguments provide sufficient information to compute your
>>>>  distance.
>>>>
>>>>  Another option I can see is non-linearly transformating your space to a
>>>>  space where you can use the Euclidian distance measure, then
>>>>  back-transforming.
>>>>  --
>>>>  Edzer
>>>>
>>>>  Carlos Rueda wrote:
>>>>  > Hello list,
>>>>  >
>>>>  > I'm just starting to look into gstat to see the feasibility of
>>>>  > incorporating user-defined distance functions to compute models and
>>>>  > do interpolation. I already searched the gstat-info archives but it
>>>>  > seems this aspect hasn't been discussed here. I'm not an expert in
>>>>  > geostatistical analysis but, according to some references(*), it
>>>>  > would be sufficient that the distance function be a valid metric. Is
>>>>  > this correct? If so, can anyone provide some hints regarding the
>>>>  > parts in the source code that would have to be modified? (I already
>>>>  > have glanced over the code and have a preliminary approach that I can
>>>>  > discuss off-list.)
>>>>  >
>>>>  >    (*) - http://www.mail-archive.com/ai-geostats@jrc.it/msg03008.html
>>>>  >         - A geostatistical approach for describing spatial pattern in
>>>>  > stream networks.
>>>>  >           Ganio, Torgersen, Gresswell. Frontiers in Ecology and the
>>>>  > Environment. 2005
>>>>  >
>>>>  > Thanks!
>>>>  >
>>>>  > Carlos Rueda
>>>>  > Postdoctoral Researcher
>>>>  > Center for Spatial Technologies and Remote Sensing
>>>>  > University of California, Davis
>>>>  > _______________________________________________
>>>>  > Gstat-info mailing list
>>>>  > Gstat-info at geo.uu.nl
>>>>  > http://mailman.geo.uu.nl/mailman/listinfo/gstat-info
>>>>         
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