[GRASS-user] shortest distance using cost between centroid/lines

GRASS GRASS user
1

A problem with which I am currently working relates to the r.walk feature, for calculating anisotropic movement cost between two points, and v.distance, for calculating the shortest distance between my archaeological sites (areas) and river drainages (represented as lines). I could convert everything to raster data, if that improves the ability to calculate what I am interested in, but that’s a different story, and not worth noting right now…what I need to do has not been described by any of the available examples and questions, or maybe I am still not comprehending how to do it properly, but here is the issue:

I want to find the shortest distance between an archaeological site and a drainage. I do NOT want to specify to which drainage one should look from each site, because I want it to be the least cost to get to a source of water. I suppose that technically I would not NEED anisotropic modeling, because the trips would be round trip, but I still would prefer to do this with anisotropic distances because down the road I may want distances calculated from one site, to a drainage, to a different site, and back to the original site (for example, total shortest distance from a pueblo to a river to a grid garden back to the pueblo).

Therefore, the requirement of r.walk and r.cost to specify start/stop points is not good for me.

Obviously, first I need a cost surface. For ease of argument, I’m going to stick with slope and only slope right now. So, I have these data:

All_sites - vector, polygons of sites (I also have a point version of this map, where the centroids of the areas were converted to a point topology)
Drainages - vector, lines of drainages
DEM_16 - elevation at 16 foot resolution
Slope_16 - slope at 16 foot resolution (calculated from DEM)
Aspect_16 - aspect at 16 foot resolution (also calc. from DEM)

Once I have identified the closest drainage based on least-cost-distance, I want to upload two columns to the All_sites db, one for the distance, one for the drainage identified as closest - just like v.distance allows.

r.drain does some of what I want, but not completely. I have been staring at the manual pages and searching the archives for a while now, and it really seems that everyone has specified start/stop points in mind (all of the talk about Tobler’s hiking function a few months back, for example).

Chances are that I am making this more complicated than necessary, but I hoped there could be some sort of solution. If specifying a destination is really the way I have to go, I can convert my drainage lines into points, and just find the shortest distance to one of those points via a cost surface. But again, I still don’t know how to let GRASS decide which of 2 lines, points, etc. are closer (via a cost surface) and then have it give me that least-cost distance.

Any ideas?

Thanks much in advance,
Brandon

Brandon M. Gabler
Doctoral Candidate
Department of Anthropology
University of Arizona
Tucson, AZ 85721
Phone: (520) 621-8455
Fax: (520) 621-2088
bgabler@email.arizona.edu

“Who? When? Whither? are the questions with which the archaeologist challenges the refuse heaps, scattered potsherds, and broken shafts, to tell of the builders who came and lived and went their way into the templed past.” – Edgar Lee Hewett, in Pajarito Plateau and its Ancient People, 1938

2

Hi Brandon,

On 4/8/07, Brandon M. Gabler <bgabler@email.arizona.edu> wrote:

A problem with which I am currently working relates to the r.walk feature,
for calculating anisotropic movement cost between two points, and
v.distance, for calculating the shortest distance between my archaeological
sites (areas) and river drainages (represented as lines). I could convert
everything to raster data, if that improves the ability to calculate what I
am interested in, but that's a different story, and not worth noting right
now...what I need to do has not been described by any of the available
examples and questions, or maybe I am still not comprehending how to do it
properly, but here is the issue:

Interesting problem.

I want to find the shortest distance between an archaeological site and a
drainage. I do NOT want to specify to which drainage one should look from
each site, because I want it to be the least cost to get to a source of
water. I suppose that technically I would not NEED anisotropic modeling,
because the trips would be round trip, but I still would prefer to do this
with anisotropic distances because down the road I may want distances
calculated from one site, to a drainage, to a different site, and back to
the original site (for example, total shortest distance from a pueblo to a
river to a grid garden back to the pueblo).

I have worked a bit with r.cost / r.drain analizing the cost moving
between a trail and a set of points off-traill. If you look at the
manual page for r.cost, it is possible to use an input raster as a set
of starting points
(http://169.237.35.250/~dylan/temp/r.cost_example.png). If you do your
analysis backwards from drainages to your sites, I think that you can
use r.cost to get a resonable answer.

Here is how I would approach it;

1. identify a vector drainage layer, and convert to raster at a
suitible resolution
g.region
r.to.vect

2. identify your archealogical sites

3. use r.cost to compute the cumulative cost surface- use the
appropriate cost surface: distance, slope, or perhaps a surrogate for
3D distance combining planar distance with the local slope * .

* use the slope and cell size to compute the 3d length across a single cell:
r.mapcalc "z = 1 / cos(slope_angle)"
accumulate z-cost, and then convert to meters :
dist_3d_meters = z-cost * (ewres()+nsres())/2.0

4. pickup the cumulative cost at each point with v.what.rast

5. ???

6. profit

Here is an example with spearfish60:

g.region vect=roads res=100 -a
v.to.rast in=roads out=roads.rast use=val val=1
r.cost -k in=slope out=cost start_rast=roads.rast
v.db.addcol archsites columns='cost double'
v.what.rast archsites column=cost raster=cost
echo 'select * from archsites order by cost asc' | db.select

# cleanup
g.remove rast=cost
v.db.dropcol archsites col=cost

will that work?

note that the 3D distance seems correct, but you might want some
verification from a specialist.

Cheers,

dylan

Therefore, the requirement of r.walk and r.cost to specify start/stop points
is not good for me.

Obviously, first I need a cost surface. For ease of argument, I'm going to
stick with slope and only slope right now. So, I have these data:

All_sites - vector, polygons of sites (I also have a point version of this
map, where the centroids of the areas were converted to a point topology)
Drainages - vector, lines of drainages
DEM_16 - elevation at 16 foot resolution
Slope_16 - slope at 16 foot resolution (calculated from DEM)
Aspect_16 - aspect at 16 foot resolution (also calc. from DEM)

Once I have identified the closest drainage based on least-cost-distance, I
want to upload two columns to the All_sites db, one for the distance, one
for the drainage identified as closest - just like v.distance allows.

r.drain does some of what I want, but not completely. I have been staring at
the manual pages and searching the archives for a while now, and it really
seems that everyone has specified start/stop points in mind (all of the talk
about Tobler's hiking function a few months back, for example).

Chances are that I am making this more complicated than necessary, but I
hoped there could be some sort of solution. If specifying a destination is
really the way I have to go, I can convert my drainage lines into points,
and just find the shortest distance to one of those points via a cost
surface. But again, I still don't know how to let GRASS decide which of 2
lines, points, etc. are closer (via a cost surface) and then have it give me
that least-cost distance.

Any ideas?

Thanks much in advance,
Brandon

_______________________
Brandon M. Gabler
Doctoral Candidate
Department of Anthropology
University of Arizona
Tucson, AZ 85721
Phone: (520) 621-8455
Fax: (520) 621-2088
bgabler@email.arizona.edu

"Who? When? Whither? are the questions with which the archaeologist
challenges the refuse heaps, scattered potsherds, and broken shafts, to tell
of the builders who came and lived and went their way into the templed
past." -- Edgar Lee Hewett, in Pajarito Plateau and its Ancient People, 1938

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