<s>
In	O
spatial	O
analysis	O
and	O
geographic	B-Application
information	I-Application
systems	I-Application
,	O
cost	B-Application
distance	I-Application
analysis	I-Application
or	O
cost	B-Application
path	I-Application
analysis	I-Application
is	O
a	O
method	O
for	O
determining	O
one	O
or	O
more	O
optimal	O
routes	O
of	O
travel	O
through	O
unconstrained	O
(	O
two-dimensional	O
)	O
space	O
.	O
</s>
<s>
It	O
is	O
an	O
optimization	O
problem	O
with	O
multiple	O
deterministic	B-General_Concept
algorithm	I-General_Concept
solutions	O
,	O
implemented	O
in	O
most	O
GIS	B-Application
software	I-Application
.	O
</s>
<s>
The	O
various	O
problems	O
,	O
algorithms	O
,	O
and	O
tools	O
of	O
cost	B-Application
distance	I-Application
analysis	I-Application
operate	O
over	O
an	O
unconstrained	O
two-dimensional	O
space	O
,	O
meaning	O
that	O
a	O
path	O
could	O
be	O
of	O
any	O
shape	O
.	O
</s>
<s>
The	O
collection	O
of	O
GIS	B-Application
tools	O
for	O
solving	O
these	O
problems	O
are	O
called	O
network	O
analysis	O
.	O
</s>
<s>
In	O
1957	O
,	O
during	O
the	O
Quantitative	O
revolution	O
in	O
Geography	O
,	O
with	O
its	O
propensity	O
to	O
adopt	O
principles	O
or	O
mathematical	O
formalisms	O
from	O
the	O
"	O
hard	O
"	O
sciences	O
(	O
known	O
as	O
social	B-General_Concept
physics	I-General_Concept
)	O
,	O
William	O
Warntz	O
used	O
refraction	O
as	O
an	O
analogy	O
for	O
how	O
minimizing	O
travel	O
cost	O
will	O
make	O
transportation	O
routes	O
change	O
direction	O
at	O
the	O
boundary	O
between	O
two	O
landscapes	O
with	O
very	O
different	O
friction	O
of	O
distance	O
(	O
e.g.	O
,	O
emerging	O
from	O
a	O
forest	O
into	O
a	O
prairie	O
)	O
.	O
</s>
<s>
Raster	O
GIS	B-Application
provided	O
the	O
first	O
feasible	O
platform	O
for	O
implementing	O
the	O
theoretical	O
solution	O
by	O
converting	O
the	O
continuous	O
integration	O
into	O
a	O
discrete	O
summation	O
procedure	O
.	O
</s>
<s>
Dana	O
Tomlin	O
implemented	O
cost	B-Application
distance	I-Application
analysis	I-Application
in	O
his	O
Map	O
Analysis	O
Package	O
by	O
1986	O
,	O
and	O
Ronald	O
Eastman	O
added	O
it	O
to	O
IDRISI	B-Application
by	O
1989	O
,	O
with	O
a	O
more	O
efficient	O
"	O
pushbroom	O
"	O
cost	O
accumulation	O
algorithm	O
.	O
</s>
<s>
Douglas	O
(	O
1994	O
)	O
further	O
refined	O
the	O
accumulation	O
algorithm	O
,	O
which	O
is	O
basically	O
what	O
is	O
implemented	O
in	O
most	O
current	O
GIS	B-Application
software	I-Application
.	O
</s>
<s>
The	O
primary	O
data	O
set	O
used	O
in	O
cost	B-Application
distance	I-Application
analysis	I-Application
is	O
the	O
cost	O
raster	O
,	O
sometimes	O
called	O
the	O
cost-of-passage	O
surface	O
,	O
the	O
friction	O
image	O
,	O
the	O
cost-rate	O
field	O
,	O
or	O
cost	O
surface	O
.	O
</s>
<s>
It	O
is	O
thus	O
a	O
discretization	B-Algorithm
of	O
a	O
field	O
of	O
cost	O
rate	O
(	O
cost	O
per	O
linear	O
unit	O
)	O
,	O
a	O
spatially	O
intensive	O
property	O
.	O
</s>
<s>
An	O
important	O
part	O
of	O
the	O
creation	O
of	O
an	O
index	O
model	O
like	O
this	O
is	O
Calibration	B-General_Concept
(	O
statistics	O
)	O
,	O
adjusting	O
the	O
parameters	O
of	O
the	O
formula(s )	O
to	O
make	O
the	O
modeled	O
relative	O
cost	O
match	O
real-world	O
costs	O
,	O
using	O
methods	O
such	O
as	O
the	O
Analytic	O
hierarchy	O
process	O
.	O
</s>
<s>
The	O
index	O
model	O
formula	O
is	O
typically	O
implemented	O
in	O
a	O
raster	O
GIS	B-Application
using	O
map	O
algebra	O
tools	O
from	O
raster	O
grids	O
representing	O
each	O
cost	O
factor	O
,	O
resulting	O
in	O
a	O
single	O
cost	O
raster	O
grid	O
.	O
</s>
<s>
Some	O
research	O
has	O
been	O
done	O
on	O
extending	O
cost	B-Application
distance	I-Application
analysis	I-Application
algorithms	O
to	O
incorporate	O
directional	O
cost	O
,	O
but	O
it	O
is	O
not	O
yet	O
widely	O
implemented	O
in	O
GIS	B-Application
software	I-Application
.	O
</s>
<s>
IDRISI	B-Application
has	O
some	O
support	O
for	O
anisotropy	O
.	O
</s>
<s>
The	O
algorithm	O
must	O
also	O
take	O
into	O
account	O
that	O
indirect	O
routes	O
may	O
have	O
lower	O
cost	O
,	O
often	O
using	O
a	O
hash	B-Algorithm
table	I-Algorithm
to	O
keep	O
track	O
of	O
temporary	O
cost	O
values	O
along	O
the	O
expanding	O
fringe	O
of	O
computation	O
that	O
can	O
be	O
reconsidered	O
.	O
</s>
<s>
A	O
slightly	O
different	O
version	O
of	O
the	O
least-cost	B-Application
path	I-Application
problem	O
,	O
which	O
could	O
be	O
considered	O
a	O
fuzzy	O
version	O
of	O
it	O
,	O
is	O
to	O
look	O
for	O
corridors	O
more	O
than	O
one	O
cell	O
in	O
width	O
,	O
thus	O
providing	O
some	O
flexibility	O
in	O
applying	O
the	O
results	O
.	O
</s>
<s>
This	O
can	O
be	O
accomplished	O
using	O
the	O
cost	O
accumulation	O
tool	O
above	O
,	O
along	O
with	O
a	O
map	O
algebra	O
tool	O
,	O
although	O
ArcGIS	B-Application
provides	O
a	O
tool	O
that	O
automates	O
the	O
process	O
.	O
</s>
<s>
They	O
are	O
directly	O
related	O
to	O
a	O
voronoi	B-Architecture
diagram	I-Architecture
,	O
which	O
is	O
essentially	O
an	O
allocation	O
over	O
a	O
space	O
with	O
constant	O
cost	O
.	O
</s>
<s>
They	O
are	O
also	O
conceptually	O
(	O
if	O
not	O
computationally	O
)	O
similar	O
to	O
location-allocation	B-Application
tools	O
for	O
network	O
analysis	O
.	O
</s>
<s>
This	O
is	O
the	O
approach	O
taken	O
in	O
ArcGIS	B-Application
Pro	I-Application
.	O
</s>
<s>
GRASS	B-Application
GIS	I-Application
uses	O
this	O
approach	O
;	O
in	O
fact	O
,	O
the	O
same	O
tool	O
is	O
used	O
as	O
for	O
computing	O
watersheds	O
from	O
terrain	O
.	O
</s>
<s>
Cost	O
distance	O
tools	O
are	O
available	O
in	O
most	O
raster	O
GIS	B-Application
software	I-Application
:	O
</s>
<s>
ArcGIS	B-Application
Desktop	I-Application
and	O
ArcGIS	B-Application
Pro	I-Application
,	O
with	O
separate	O
accumulation	O
(	O
)	O
and	O
drain	O
(	O
)	O
geoprocessing	O
tools	O
,	O
as	O
well	O
as	O
generation	O
.	O
</s>
<s>
Recently	O
,	O
starting	O
with	O
ArcGIS	B-Application
Pro	I-Application
version	O
2.5	O
,	O
a	O
new	O
set	O
of	O
cost	O
distance	O
tools	O
was	O
introduced	O
,	O
using	O
more	O
advanced	O
algorithms	O
with	O
more	O
flexible	O
options	O
.	O
</s>
<s>
TerrSet	B-Application
(	O
formerly	O
Idrisi	B-Application
)	O
has	O
several	O
tools	O
,	O
implementing	O
a	O
variety	O
of	O
algorithms	O
to	O
solve	O
different	O
kinds	O
of	O
cost	O
distance	O
problems	O
,	O
including	O
anisotropic	O
(	O
directional	O
)	O
cost	O
.	O
</s>
