Hi,
I asked about this a couple of weeks ago and had a handful of useful
replies. The position seems to be that there are methods and S+ tools
available for data on a flat plane, but nothing for an arbitary surface.
Unfortunately my data is on a a closed surface defined by the points
themselves which cannot be transformed onto a plane.
So it seems that the only approach is simulation. This is relatively
easy to say, but tricky in practice - basically I need tools to:
1) Construct a representation of a closed surface form a series of (xyz)
co-ordinates - Dirichlet tesselation/Delunnay triangles or similar
2) Measure distances along the surface to nearest neighbours (easy) and
between arbitary pairs of points (hard)
3) Place simulated points on the surface using a Poisson hard-core
process - here I can probably justify a spherical core rather than a
disk to make the computations tractable (might also be biologically more
realistic). (easy I think if I have a ploygonal representation of the
surface, but still need functions to give area of polygon and whether a
point is inside the polygon)
4) Maybe should be using a smoothed surface - any algorithms here?
5) Then I can compute things analogous to Ripley's K, neighbour
distances etc and compare the observed distributioins with a set of
simulated ones.
So the questions are
1) are the necessary tools available in S? (or anything else!) The MASS
spatial librarry and the spatial module seem to be inherently 2D
2) any comments on the proposed methodology before I start hacking code?
Thanks,
Steve.
Dr Steve Roberts
Paterson Institute for Cancer Research
Christie Hospital
Manchester M20 4BX UK
Tel: 0161 446 3074
Email: sroberts@picr.man.ac.uk
-----Original Message-----
From: Steve Roberts
Sent: 14 January 2000 15:55
To: 's-news@wubios.wustl.edu'
Subject: [S] Spatial statistics on an irregular surface
Greetings,
Maybe off-topic, maybe not but... We have some data which are the
distribution of points on an irregular 3-d surface (so we have (x,y,z)
values which define the points and (at least approximately) the
surface). We are interested in quantifying and testing hypotheses about
the clustering on that surface (a cell membrane) - and comparing the
distributions after various treatments. The surface is very irregular
and maybe even a bit folded in places, which doesn't help, on the other
hand it may be possible to get more accurate surface co-ordinates in the
future.
Can anyone point me to any methods and/or software for handling such
data? Clearly one can get a reasonable nearest-neighbour distribution,
but it is not clear how to compute a Poisson-based(actually poisson with
a minimum distance as these things are really discs) distribution with
which to compare it. How do you put random points on a complex-shaped
surface? (one thought would be to use some form of lattice which if fine
enough would approximate the surface...)
Anybody done anything like this? Any suggestions?
Cheers,
Steve.
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