TODO/PROPOSAL
(proposed by Ferdinando Urbano 15-Dec-2005)

r.walk was born to compute the minimum cumulative "travel time" (in
seconds) between each cell and the user-specified starting points.  as
it is implemented now, combining the "travel time" (in seconds) and a
"friction" map, the output value has no physical meaning and it is
useful just to calculate the minimum "generic, undimensioned cost"
path, because "cost" right now is ("time travel in seconds" + Lamba *
"friction cost").

it would be interesting to model all the aspects that influence the
speed movement "inside" the a,b,c,d (see the r.walk documentation)
parameters going back to a physical meaning (speed in a specific
condition) of the formula (the real time in second that the subject
need to move between two points).

For man walking on a marked path, a,b,c,d can be considered constant
in space, but they can be very different for man walking in wilderness
or animals moving in their home range, where so many different
environments and condition can be found (swamp, grassland, dense
forest, lakes, rivers, ...). The walking speed in a lake is very slow,
and in a dense forest is slower than in a grassland. To consider these
spatial differences, a,b,c,d should be passed as 4 grids, with a
specific value of each parameters in each cell of the grid depending
on the environmental attribute of each cell.  Instead, right now,
r.walk do not consider spatial variation in walking speed in different
conditions (except for slope).

To consider the "friction" map, another function based on this more
complete version of r.walk could be developed.  The "friction" map
should be viewed as "suitability" or "environmental preference" of the
subject for each cell, not linked to time travel.  For example, a wild
bear could prefer to move inside a forest rather than in an open
grassland because it is more protected, even if the movement can be
quicker in the latter case; or a man could prefer to walk a little bit
more along a river to reach a bridge instead of crossing the water,
not because it is more time consuming but just because it is more
comfortable.  In this case a function combining time travel and
"environmental preference" together, would find an optimized "minimum
cumulative cost" that optimize the difference between the
"environmental preference" gain and the time to get it.  This is very
interesting but it is different from the original philosophy of
r.walk, that have a specific application.
