Geografic-Information-System/raster/r.walk/r.walk.html

<h2>DESCRIPTION</h2>

<em>r.walk</em> outputs 1) a raster map showing the lowest
cumulative cost of moving between each cell and the user-specified
starting points and 2) a second raster map showing the movement 
direction to the next cell on the path back to the start point (see 
<a href="#move">Movement Direction</a>). It uses an input elevation 
raster map whose cell category values represent elevation, 
combined with a second input raster map whose cell values 
represent friction costs.

<p>
This function is similar to <em><a href="r.cost.html">r.cost</a></em>,
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.

<h2>NOTES</h2>

<p>
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:

<div class="code"><pre>
T= [(a)*(Delta S)] + [(b)*(Delta H uphill)] + [(c)*(Delta H moderate downhill)] + [(d)*(Delta H steep downhill)]
</pre></div>

where:
<ul>
  <li><tt>T</tt> is time of movement in seconds,</li>
  <li><tt>Delta S</tt> is the distance covered in meters,</li>
  <li><tt>Delta H</tt> is the altitude difference in meter.</li>
</ul>

<p>
The a, b, c, d <b>walk_coeff</b> parameters take in account
movement speed in the different conditions and are linked to:

<ul>
  <li>a: underfoot condition (a=1/walking_speed)</li>
  <li>b: underfoot condition and cost associated to movement uphill</li>
  <li>c: underfoot condition and cost associated to movement moderate downhill</li>
  <li>d: underfoot condition and cost associated to movement steep downhill</li>
</ul>

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 (<b>slope_factor</b>) is -0.2125, corresponding
to tan(-12), calibrated on human behaviour (&gt;5 and &lt;12 degrees:
moderate downhill; &gt;12 degrees: steep downhill). The default values
for a, b, c, d <b>walk_coeff</b> parameters are those proposed by
Langmuir (0.72, 6.0, 1.9998, -1.9998), based on man walking effort in
standard conditions.

<p>The <b>lambda</b> parameter of the linear equation
combining movement and friction costs:<br>
<div class="code"><pre>
total cost = movement time cost + (lambda) * friction costs
</pre></div>
must be set in the option section of <em>r.walk</em>.
<p>
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.

<div class="code"><pre>
  K   K 
K x x x K
  x O x
K x x x K
  K   K
</pre></div>

<p>The minimum cumulative costs are computed using Dijkstra's
algorithm, that find an optimum solution (for more details see
<em>r.cost</em>, that uses the same algorithm).
<a name="move"></a>
<h2>Movement Direction</h2>
<p>The movement direction surface is created to record the sequence of
movements that created the cost accumulation surface. Without it 
<em><a href="r.drain.html">r.drain</a></em> would not correctly create a path from an end point 
back to the start point. The direction of each cell points towards 
the next cell. The directions are recorded as degrees CCW from East:
<div class="code"><pre>
       112.5      67.5         i.e. a cell with the value 135 
157.5  135   90   45   22.5    means the next cell is to the north-west
       180   x   360           
202.5  225  270  315  337.5
       247.5     292.5
</pre></div>

<p>
Once <em>r.walk</em> 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), <em><a href="r.drain.html">r.drain</a></em> can be used to
find the minimum cost path. Make sure to use the <b>-d</b> flag and
the movement direction raster map when
running <em><a href="r.drain.html">r.drain</a></em> to ensure the path
is computed according to the proper movement directions.


<h2>REFERENCES</h2>

<ul>
<li>Aitken, R. 1977. Wilderness areas in Scotland. Unpublished Ph.D. thesis.
 University of Aberdeen.
<li> Steno Fontanari, University of Trento, Italy, Ingegneria per l'Ambiente e
 il Territorio, 2000-2001.
 Svilluppo di metodologie GIS per la determinazione dell'accessibilità
 territoriale come supporto alle decisioni nella gestione ambientale.
<li>Langmuir, E. 1984. Mountaincraft and leadership. The Scottish
 Sports Council/MLTB. Cordee, Leicester.
</ul>

<h2>SEE ALSO</h2>

<em>
<a href="r.cost.html">r.cost</a>,
<a href="r.drain.html">r.drain</a>,
<a href="r.in.ascii.html">r.in.ascii</a>,
<a href="r.mapcalc.html">r.mapcalc</a>,
<a href="r.out.ascii.html">r.out.ascii</a>
</em>


<h2>AUTHORS</h2>

<b>Based on r.cost written by :</b><br>
Antony Awaida, Intelligent Engineering, Systems Laboratory, M.I.T.<br>
James Westervelt, U.S.Army Construction Engineering Research Laboratory<br>
Updated for Grass 5 by Pierre de Mouveaux (pmx@audiovu.com)

<p><b>Initial version of r.walk:</b><br>
Steno Fontanari, 2002

<p><b>Current version of r.walk:</b><br>
Franceschetti Simone, Sorrentino Diego, Mussi Fabiano and Pasolli Mattia<br>
Correction by: Fontanari Steno, Napolitano Maurizio and  Flor Roberto<br>
In collaboration with: Franchi Matteo, Vaglia Beatrice, Bartucca Luisa, Fava Valentina and Tolotti Mathias, 2004

<p><b>Updated for Grass 6.1:</b><br>
Roberto Flor and Markus Neteler

<p>
<i>Last changed: $Date$</i>