[Gstat-info] non-Euclidean distance functions?

[Ashton Shortridge]

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.

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.

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
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>
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-- 
Ashton Shortridge
Associate Professor			ashton at msu.edu
Dept of Geography			http://www.msu.edu/~ashton
235 Geography Building			ph (517) 432-3561
Michigan State University		fx (517) 432-1671