NAME¶

r.walk - Outputs a raster map layer showing the anisotropic cumulative cost of moving between different geographic locations on an input elevation raster map layer whose cell category values represent elevation combined with an input raster map layer whose cell values represent friction cost.

KEYWORDS¶

raster, cost surface, cumulative costs

SYNOPSIS¶

r.walk r.walk help r.walk [-knr] elevation=string friction=string output=string [outdir=string] [ start_points=string] [stop_points= string] [coordinate=x,y[,x,y,...]] [ stop_coordinate=x,y[, x,y,...]] [max_cost=integer] [ null_cost=float] [percent_memory= integer] [nseg=integer] [walk_coeff= a,b,c,d] [lambda=float] [slope_factor= float] [--overwrite] [--verbose] [-- quiet]

Flags:¶

-k

 

Use the 'Knight's move'; slower, but more accurate

-n

 

Keep null values in output map

-r

 

Start with values in raster map

--overwrite

 

Allow output files to overwrite existing files

--verbose

 

Verbose module output

--quiet

 

Quiet module output

Parameters:¶

elevation=string

 

Name of elevation input raster map

friction=string

 

Name of input raster map containing friction costs

output=string

 

Name of raster map to contain results

outdir=string

 

Name of output raster map to contain movement directions

start_points=string

 

Starting points vector map

stop_points=string

 

Stop points vector map

coordinate=x,y[,x,y,...]

 

The map E and N grid coordinates of a starting point (E,N)

stop_coordinate=x,y[,x,y,...]

 

The map E and N grid coordinates of a stopping point (E,N)

max_cost=integer

 

An optional maximum cumulative cost

 

Default: 0

null_cost=float

 

Cost assigned to null cells. By default, null cells are excluded

percent_memory=integer

 

Percent of map to keep in memory

 

Default: 100

nseg=integer

 

Number of the segment to create (segment library)

 

Default: 4

walk_coeff=a,b,c,d

 

Coefficients for walking energy formula parameters a,b,c,d

 

Default: 0.72,6.0,1.9998,-1.9998

lambda=float

 

Lambda coefficients for combining walking energy and friction cost

 

Default: 1.0

slope_factor=float

 

Slope factor determines travel energy cost per height step

 

Default: -0.2125

DESCRIPTION¶

r.walk outputs 1) a raster map layer showing the lowest cumulative cost of moving between each cell and the user-specified starting points and 2) a second raster map layer showing the movement direction to the next cell on the path back to the start point (see Movement Direction). It uses an input elevation raster map layer whose cell category values represent elevation, combined with a second input raster map layer whose cell values represent friction costs. This function is similar to r.cost, but in addiction to a friction map, it considers an anisotropic travel time due to the different walking speed associated with downhill and uphill movements. The formula from Aitken 1977/Langmuir 1984 (based on Naismith's rule for walking times) has been used to estimate the cost parameters of specific slope intervals: T= [(a)*(Delta S)] + [(b)*(Delta H uphill)] + [(c)*(Delta H moderate downhill)] + [(d)*(Delta H steep downhill)] where: T is time of movement in seconds, Delta S is the distance covered in meters, Delta H is the altitude difference in meter. The a, b, c, d parameters take in account movement speed in the different conditions and are linked to: a: underfoot condition (a=1/walking_speed) b: underfoot condition and cost associated to movement uphill c: underfoot condition and cost associated to movement moderate downhill d: underfoot condition and cost associated to movement steep downhill It has been proved that moving downhill is favourable up to a specific slope value threshold, after that it becomes unfavourable. The default slope value threshold (slope factor) is -0.2125, corresponding to tan(-12), calibrated on human behaviour (>5 and <12 degrees: moderate downhill; >12 degrees: steep downhill). The default values for a, b, c, d are those proposed by Langmuir (0.72, 6.0, 1.9998, -1.9998), based on man walking effort in standard conditions. The lambda parameter of the linear equation combining movement and friction costs: total cost = movement time cost + (lambda) * friction costs must be set in the option section of r.walk. For a more accurate result, the "knight's move" option can be used (although it is more time consuming). In the diagram below, the center location (O) represents a grid cell from which cumulative distances are calculated. Those neighbours marked with an x are always considered for cumulative cost updates. With the "knight's move" option, the neighbours marked with a K are also considered.
K K K x x x K
x O x K x x x K
K K The minimum cumulative costs are computed using Dijkstra's algorithm, that find an optimum solution (for more details see r.cost, that uses the same algorithm).

Movement Direction¶

The movement direction surface is created to record the sequence of movements that created the cost accumulation surface. Without it r.drain would not correctly create a path from an end point back to the start point. The direction shown in each cell points away from the cell that came before it. The directions are recorded as
112.5 90 67.5 i.e. a cell with the value 135 157.5 135 0 45 22.5 means the cell before it is
180 x 0 to the south-east. 202.5 225 270 315 337.5
247.5 292.5 Once r.walk computes the cumulative cost map as a linear combination of friction cost (from friction map) and the altitude and distance covered (from the digital elevation model), r.drain can be used to find the minimum cost path. Make sure to use the -d flag and the movement direction raster map when running r.drain to ensure the path is computed according to the proper movement directions.

SEE ALSO¶

r.cost, r.drain, r.in.ascii, r.mapcalc, r.out.ascii

REFERENCES¶

AUTHORS¶

Based on r.cost written by : Antony Awaida, Intelligent Engineering Systems Laboratory, M.I.T. James Westervelt, U.S.Army Construction Engineering Research Laboratory Updated for Grass 5 Pierre de Mouveaux (pmx@audiovu.com) Initial version of r.walk: Steno Fontanari, 2002 Current version of r.walk: Franceschetti Simone, Sorrentino Diego, Mussi Fabiano and Pasolli Mattia Correction by: Fontanari Steno, Napolitano Maurizio and Flor Roberto In collaboration with: Franchi Matteo, Vaglia Beatrice, Bartucca Luisa, Fava Valentina and Tolotti Mathias, 2004 Updated for Grass 6.1 Roberto Flor and Markus Neteler Last changed: $Date: 2012-12-31 13:29:35 +0100 (Mon, 31 Dec 2012) $ Full index © 2003-2014 GRASS Development Team