California Soil Resource Lab

Simple Comparision of Two Least-Cost Path Approaches

Submitted by dylan on Tue, 2008-02-19 08:19.

Least Cost Path Comparision Map r.walk in blue, r.cost in orange

Premise:
Simple comparison between the least-cost path as computed by r.walk vs. r.cost. Default parameters, unity travel friction, and λ = 1 were used with r.walk. Slope percent was used as the accumulated cost for r.cost. Test region similar to that used in a previous navigation example.

Results:

r.walk
- Shorter total path (6.03 km)
- Tendency to stay mid-slope, and cross large drainage at the gentlest possible position
r.cost
- Longer total path (7.12 km)
- Tendency to follow drainages upstream-- not always possible in steep terrain

Code:

Prep work see attached files at bottom of page to re-create

# generate cost "friction" maps

# unity friction for r.walk

r.mapcalc "friction = 1.0"

# use slope percent as the friction for r.cost

r.slope.aspect elev=elev slope=slope format=percent

Compute the least-cost path via two methods

# compute cumulative cost surfaces

r.walk -k elev=elev friction=friction out=walk.cost start_points=start stop_points=end lambda=1

# Peak cost value: 14030.894105

r.cost -k in=slope out=cost start_points=start stop_points=end

# Peak cost value: 11557.934493

# compute shortest path from start to end points

r.drain in=walk.cost out=walk.drain vector_points=end

r.drain in=cost out=cost.drain vector_points=end

Vectorize least-cost paths for further analysis

r.to.vect -s in=walk.drain out=path_1

r.to.vect -s in=cost.drain out=path_2

# add DB column for length calculation

v.db.addcol path_1 columns="len double"

v.db.addcol path_2 columns="len double"

# how long are the two paths?

v.to.db path_1 option=length column=len units=me

# 6.03 km

v.to.db path_2 option=length column=len units=me

# 7.12 km

Simple map

d.rast shade

d.vect start icon=basic/circle fcol=green size=15

d.vect end icon=basic/circle fcol=red size=15

d.vect path_1 width=2 col=blue

d.vect path_2 width=2 col=orange

Sample the elevation raster at a regular interval

# add a vertex every 100m along each line

# this will create two tables for each 

# path_1_pts_1   <-- original atts

# path_1_pts_2   <-- original cat + distance along the original line

v.to.points in=path_1 out=path_1_pts -i dmax=100

v.to.points in=path_2 out=path_2_pts -i dmax=100

# add column for elevation values

v.db.addcol map=path_1_pts layer=2 columns="elev double"

v.db.addcol map=path_2_pts layer=2 columns="elev double"

# upload elev values for profile graph

v.what.rast vector=path_1_pts raster=elev layer=2 column=elev

v.what.rast vector=path_2_pts raster=elev layer=2 column=elev

# dump profiles to CSV files

db.select path_1_pts_2 fs="," > p1.csv

db.select path_2_pts_2 fs="," > p2.csv

Least Cost Path Comparision Profile

Plot an elevation profile for each path

## startup R

R

## load data from previous steps

p1 <- read.csv('p1.csv')

p2 <- read.csv('p2.csv')

## can't guarantee that the two lines will be in the same direction (a r.to.vect thing?)

## p1 is correct, p2 is reversed

## make a nicer plot

## library(Cairo)

## Cairo(type='png', bg='white', width=800, height=400)

plot(elev ~ rev(along), data=p2, type='l', col='orange', lwd=2, xlab='Travel Distance (meters)', ylab='Elevation Change (meters)')

lines(elev ~ along, data=p1, col='RoyalBlue', lwd=2)

legend(0, 3000, legend=c('r.walk', 'r.cost'), col=c('RoyalBlue', 'orange'), lwd=2)

Attachment	Size
elev.ascii_.gz	543.35 KB
start.txt	35 bytes
end.txt	34 bytes

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Simple Comparision of Two Least-Cost Path Approaches

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