<s>
Vector	B-Application
overlay	I-Application
is	O
an	O
operation	O
(	O
or	O
class	O
of	O
operations	O
)	O
in	O
a	O
geographic	B-Application
information	I-Application
system	I-Application
(	O
GIS	B-Application
)	O
for	O
integrating	O
two	O
or	O
more	O
vector	O
spatial	O
data	O
sets	O
.	O
</s>
<s>
Terms	O
such	O
as	O
polygon	B-Application
overlay	I-Application
,	O
map	O
overlay	B-Application
,	O
and	O
topological	O
overlay	B-Application
are	O
often	O
used	O
synonymously	O
,	O
although	O
they	O
are	O
not	O
identical	O
in	O
the	O
range	O
of	O
operations	O
they	O
include	O
.	O
</s>
<s>
Overlay	B-Application
has	O
been	O
one	O
of	O
the	O
core	O
elements	O
of	O
spatial	O
analysis	O
in	O
GIS	B-Application
since	O
its	O
early	O
development	O
.	O
</s>
<s>
Some	O
overlay	B-Application
operations	O
,	O
especially	O
Intersect	B-Application
and	O
Union	O
,	O
are	O
implemented	O
in	O
all	O
GIS	B-Application
software	I-Application
and	O
are	O
used	O
in	O
a	O
wide	O
variety	O
of	O
analytical	O
applications	O
,	O
while	O
others	O
are	O
less	O
common	O
.	O
</s>
<s>
Overlay	B-Application
is	O
based	O
on	O
the	O
fundamental	O
principle	O
of	O
geography	O
known	O
as	O
areal	O
integration	O
,	O
in	O
which	O
different	O
topics	O
(	O
say	O
,	O
climate	O
,	O
topography	O
,	O
and	O
agriculture	O
)	O
can	O
be	O
directly	O
compared	O
based	O
on	O
a	O
common	O
location	O
.	O
</s>
<s>
The	O
basic	O
approach	O
of	O
a	O
vector	B-Application
overlay	I-Application
operation	O
is	O
to	O
take	O
in	O
two	O
or	O
more	O
layers	O
composed	O
of	O
vector	O
shapes	O
,	O
and	O
output	O
a	O
layer	O
consisting	O
of	O
new	O
shapes	O
created	O
from	O
the	O
topological	O
relationships	O
discovered	O
between	O
the	O
input	O
shapes	O
.	O
</s>
<s>
Prior	O
to	O
the	O
advent	O
of	O
GIS	B-Application
,	O
the	O
overlay	B-Application
principle	O
had	O
developed	O
as	O
a	O
method	O
of	O
literally	O
superimposing	O
different	O
thematic	O
maps	O
(	O
typically	O
an	O
isarithmic	O
map	O
or	O
a	O
chorochromatic	O
map	O
)	O
drawn	O
on	O
transparent	O
film	O
(	O
e.g.	O
,	O
cellulose	O
acetate	O
)	O
to	O
see	O
the	O
interactions	O
and	O
find	O
locations	O
with	O
specific	O
combinations	O
of	O
characteristics	O
.	O
</s>
<s>
The	O
first	O
true	O
GIS	B-Application
,	O
the	O
Canada	O
Geographic	B-Application
Information	I-Application
System	I-Application
(	O
CGIS	O
)	O
,	O
developed	O
during	O
the	O
1960s	O
and	O
completed	O
in	O
1971	O
,	O
was	O
based	O
on	O
a	O
rudimentary	O
vector	O
data	O
model	O
,	O
and	O
one	O
of	O
the	O
earliest	O
functions	O
was	O
polygon	B-Application
overlay	I-Application
.	O
</s>
<s>
Another	O
early	O
vector	O
GIS	B-Application
,	O
the	O
Polygon	O
Information	O
Overlay	B-Application
System	O
(	O
PIOS	O
)	O
,	O
developed	O
by	O
ESRI	O
for	O
San	O
Diego	O
County	O
,	O
California	O
in	O
1971	O
,	O
also	O
supported	O
polygon	B-Application
overlay	I-Application
.	O
</s>
<s>
Unfortunately	O
,	O
the	O
results	O
of	O
overlay	B-Application
in	O
these	O
early	O
systems	O
was	O
often	O
prone	O
to	O
error	O
.	O
</s>
<s>
Carl	O
Steinitz	O
,	O
a	O
landscape	O
architect	O
,	O
helped	O
found	O
the	O
Harvard	O
Laboratory	O
for	O
Computer	O
Graphics	O
and	O
Spatial	O
Analysis	O
,	O
in	O
part	O
to	O
develop	O
GIS	B-Application
as	O
a	O
digital	O
tool	O
to	O
implement	O
McHarg	O
's	O
methods	O
.	O
</s>
<s>
Chrisman	O
and	O
James	O
Dougenik	O
implemented	O
this	O
strategy	O
in	O
the	O
WHIRLPOOL	O
program	O
,	O
released	O
in	O
1979	O
as	O
part	O
of	O
the	O
Odyssey	O
project	O
to	O
develop	O
a	O
general-purpose	O
GIS	B-Application
.	O
</s>
<s>
This	O
system	O
implemented	O
several	O
improvements	O
over	O
the	O
earlier	O
approaches	O
in	O
CGIS	O
and	O
PIOS	O
,	O
and	O
its	O
algorithm	O
became	O
part	O
of	O
the	O
core	O
of	O
GIS	B-Application
software	I-Application
for	O
decades	O
to	O
come	O
.	O
</s>
<s>
The	O
goal	O
of	O
all	O
overlay	B-Application
operations	O
is	O
to	O
take	O
in	O
vector	O
layers	O
,	O
and	O
create	O
a	O
layer	O
that	O
integrates	O
both	O
the	O
geometry	O
and	O
the	O
attributes	O
of	O
the	O
inputs	O
.	O
</s>
<s>
Since	O
the	O
original	O
implementation	O
,	O
the	O
basic	O
strategy	O
of	O
the	O
polygon	B-Application
overlay	I-Application
algorithm	O
has	O
remained	O
the	O
same	O
,	O
although	O
the	O
vector	O
data	O
structures	O
that	O
are	O
used	O
have	O
evolved	O
.	O
</s>
<s>
In	O
early	O
topological	O
data	O
structures	O
such	O
as	O
POLYVRT	O
and	O
the	O
ARC/INFO	B-Application
coverage	O
,	O
the	O
data	O
was	O
natively	O
stored	O
this	O
way	O
,	O
so	O
this	O
step	O
was	O
unnecessary	O
.	O
</s>
<s>
Any	O
pair	O
of	O
lines	O
that	O
stay	O
within	O
this	O
distance	O
of	O
each	O
other	O
are	O
collapsed	O
into	O
a	O
single	O
line	O
,	O
avoiding	O
unwanted	O
narrow	O
sliver	B-Application
polygons	I-Application
that	O
can	O
occur	O
when	O
lines	O
that	O
should	O
be	O
coincident	O
(	O
for	O
example	O
,	O
a	O
river	O
and	O
a	O
boundary	O
that	O
should	O
follow	O
it	O
de	O
jure	O
)	O
are	O
digitized	O
separately	O
with	O
slightly	O
different	O
vertices	O
.	O
</s>
<s>
These	O
different	O
overlay	B-Application
operators	O
are	O
used	O
to	O
answer	O
a	O
variety	O
of	O
questions	O
,	O
although	O
some	O
are	O
far	O
more	O
commonly	O
implemented	O
and	O
used	O
than	O
others	O
.	O
</s>
<s>
As	O
in	O
these	O
algebraic	O
systems	O
,	O
the	O
overlay	B-Application
operators	O
may	O
be	O
commutative	O
(	O
giving	O
the	O
same	O
result	O
regardless	O
of	O
order	O
)	O
and/or	O
associative	O
(	O
more	O
than	O
two	O
inputs	O
giving	O
the	O
same	O
result	O
regardless	O
of	O
the	O
order	O
in	O
which	O
they	O
are	O
paired	O
)	O
.	O
</s>
<s>
Intersect	B-Application
(	O
ArcGIS	O
,	O
QGIS	B-Application
,	O
Manifold	O
,	O
TNTmips	B-Application
;	O
AND	O
in	O
GRASS	O
)	O
:	O
The	O
result	O
includes	O
only	O
the	O
LCGUs	O
where	O
the	O
two	O
input	O
layers	O
intersect	B-Application
(	O
overlap	O
)	O
;	O
that	O
is	O
,	O
those	O
with	O
both	O
"	O
parents.	O
"	O
</s>
<s>
Intersect	B-Application
is	O
probably	O
the	O
most	O
commonly	O
used	O
operator	O
in	O
this	O
list	O
.	O
</s>
<s>
Union	O
(	O
ArcGIS	O
,	O
QGIS	B-Application
,	O
Manifold	O
,	O
TNTmips	B-Application
;	O
or	O
in	O
GRASS	O
)	O
:	O
The	O
result	O
includes	O
all	O
of	O
the	O
LCGUs	O
,	O
both	O
those	O
where	O
the	O
inputs	O
intersect	B-Application
and	O
where	O
they	O
do	O
not	O
.	O
</s>
<s>
Subtract	O
(	O
TNTmips	B-Application
;	O
Erase	O
in	O
ArcGIS	O
;	O
Difference	O
in	O
QGIS	B-Application
;	O
not	O
in	O
GRASS	O
;	O
missing	O
from	O
Manifold	O
)	O
:	O
The	O
result	O
includes	O
only	O
the	O
portions	O
of	O
polygons	O
in	O
one	O
layer	O
that	O
do	O
not	O
overlap	O
with	O
the	O
other	O
layer	O
;	O
that	O
is	O
,	O
the	O
LCGUs	O
that	O
have	O
no	O
parent	O
from	O
the	O
other	O
layer	O
.	O
</s>
<s>
Exclusive	O
or	O
(	O
Symmetrical	O
Difference	O
in	O
ArcGIS	O
,	O
QGIS	B-Application
;	O
Exclusive	O
Union	O
in	O
TNTmips	B-Application
;	O
XOR	O
in	O
GRASS	O
;	O
missing	O
from	O
Manifold	O
)	O
:	O
The	O
result	O
includes	O
the	O
portions	O
of	O
polygons	O
in	O
both	O
layers	O
that	O
do	O
not	O
overlap	O
;	O
that	O
is	O
,	O
all	O
LCGUs	O
that	O
have	O
one	O
parent	O
.	O
</s>
<s>
Clip	O
(	O
ArcGIS	O
,	O
QGIS	B-Application
,	O
GRASS	O
,	O
Manifold	O
;	O
Extract	O
Inside	O
in	O
TNTmips	B-Application
)	O
:	O
The	O
result	O
includes	O
the	O
portions	O
of	O
polygons	O
of	O
one	O
layer	O
where	O
they	O
intersect	B-Application
the	O
other	O
layer	O
.	O
</s>
<s>
Cover	O
(	O
Update	O
in	O
ArcGIS	O
and	O
Manifold	O
;	O
Replace	O
in	O
TNTmips	B-Application
;	O
not	O
in	O
QGIS	B-Application
or	O
GRASS	O
)	O
:	O
The	O
result	O
includes	O
one	O
layer	O
intact	O
,	O
with	O
the	O
portions	O
of	O
the	O
polygons	O
of	O
the	O
other	O
layer	O
only	O
where	O
the	O
two	O
layers	O
do	O
not	O
intersect	B-Application
.	O
</s>
<s>
Divide	O
(	O
Identity	O
in	O
ArcGIS	O
and	O
Manifold	O
;	O
not	O
in	O
QGIS	B-Application
,	O
TNTmips	B-Application
,	O
or	O
GRASS	O
)	O
:	O
The	O
result	O
includes	O
all	O
of	O
the	O
LCGUs	O
that	O
cover	O
one	O
of	O
the	O
input	O
layers	O
,	O
excluding	O
those	O
that	O
are	O
only	O
in	O
the	O
other	O
layer	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
common	O
uses	O
of	O
polygon	B-Application
overlay	I-Application
is	O
to	O
perform	O
a	O
suitability	B-Application
analysis	I-Application
,	O
also	O
known	O
as	O
a	O
suitability	O
model	O
or	O
multi-criteria	O
evaluation	O
.	O
</s>
<s>
Each	O
of	O
the	O
criteria	O
can	O
be	O
considered	O
boolean	O
in	O
the	O
sense	O
of	O
Boolean	O
logic	O
,	O
because	O
for	O
any	O
point	O
in	O
space	O
,	O
each	O
criterion	O
is	O
either	O
present	O
or	O
not	O
present	O
,	O
and	O
the	O
point	O
is	O
either	O
in	O
the	O
final	O
habitat	O
area	O
or	O
it	O
is	O
not	O
(	O
acknowledging	O
that	O
the	O
criteria	O
may	O
be	O
vague	O
,	O
but	O
this	O
requires	O
more	O
complex	O
fuzzy	O
suitability	B-Application
analysis	I-Application
methods	O
)	O
.	O
</s>
<s>
In	O
a	O
task	O
such	O
as	O
this	O
,	O
the	O
overlay	B-Application
procedure	O
can	O
be	O
simplified	O
because	O
the	O
individual	O
polygons	O
within	O
each	O
layer	O
are	O
not	O
important	O
,	O
and	O
can	O
be	O
dissolved	O
into	O
a	O
single	O
boolean	O
region	O
(	O
consisting	O
of	O
one	O
or	O
more	O
disjoint	O
polygons	O
but	O
no	O
adjacent	O
polygons	O
)	O
representing	O
the	O
region	O
that	O
meets	O
the	O
criterion	O
.	O
</s>
<s>
With	O
these	O
inputs	O
,	O
each	O
of	O
the	O
operators	O
of	O
Boolean	O
logic	O
corresponds	O
exactly	O
to	O
one	O
of	O
the	O
polygon	B-Application
overlay	I-Application
operators	O
:	O
intersect	B-Application
=	O
AND	O
,	O
union	O
=	O
OR	O
,	O
subtract	O
=	O
AND	O
NOT	O
,	O
exclusive	O
or	O
=	O
XOR	O
.	O
</s>
<s>
Thus	O
,	O
this	O
particular	O
use	O
of	O
polygon	B-Application
overlay	I-Application
can	O
be	O
treated	O
as	O
an	O
algebra	O
that	O
is	O
homomorphic	O
to	O
Boolean	O
logic	O
.	O
</s>
<s>
This	O
enables	O
the	O
use	O
of	O
GIS	B-Application
to	O
solve	O
many	O
spatial	O
tasks	O
that	O
can	O
be	O
reduced	O
to	O
simple	O
logic	O
.	O
</s>
<s>
Vector	B-Application
overlay	I-Application
is	O
most	O
commonly	O
performed	O
using	O
two	O
polygon	O
layers	O
as	O
input	O
and	O
creating	O
a	O
third	O
polygon	O
layer	O
.	O
</s>
<s>
The	O
following	O
operations	O
are	O
typically	O
supported	O
in	O
GIS	B-Application
software	I-Application
:	O
</s>
<s>
Intersect	B-Application
:	O
The	O
output	O
will	O
be	O
of	O
the	O
same	O
dimension	O
as	O
the	O
lower	O
of	O
the	O
inputs	O
:	O
Points	O
*	O
{	O
Points	O
,	O
Lines	O
,	O
Polygons}	O
=	O
Points	O
,	O
Lines	O
*	O
{	O
Lines	O
,	O
Polygons}	O
=	O
Lines	O
.	O
</s>
<s>
QGIS	B-Application
has	O
separate	O
operations	O
for	O
computing	O
a	O
line	O
intersection	O
as	O
lines	O
(	O
to	O
find	O
coincident	O
lines	O
)	O
and	O
as	O
points	O
.	O
</s>
<s>
This	O
operation	O
might	O
also	O
be	O
considered	O
a	O
form	O
of	O
spatial	B-Language
query	I-Language
,	O
as	O
it	O
retains	O
the	O
features	O
of	O
one	O
layer	O
based	O
on	O
its	O
topological	O
relationship	O
to	O
another	O
.	O
</s>
<s>
Vector	B-Application
Overlay	I-Application
is	O
included	O
in	O
some	O
form	O
in	O
virtually	O
every	O
GIS	B-Application
software	I-Application
package	O
that	O
supports	O
vector	O
analysis	O
,	O
although	O
the	O
interface	O
and	O
underlying	O
algorithms	O
vary	O
significantly	O
.	O
</s>
<s>
Esri	O
GIS	B-Application
software	I-Application
has	O
included	O
polygon	B-Application
overlay	I-Application
since	O
the	O
first	O
release	O
of	O
ARC/INFO	B-Application
in	O
1982	O
.	O
</s>
<s>
Each	O
generation	O
of	O
Esri	O
software	O
(	O
ARC/INFO	B-Application
,	O
ArcGIS	O
,	O
ArcGIS	O
Pro	O
)	O
has	O
included	O
a	O
set	O
of	O
separate	O
tools	O
for	O
each	O
of	O
the	O
overlay	B-Application
operators	O
(	O
Intersect	B-Application
,	O
Union	O
,	O
Clip	O
,	O
etc	O
.	O
)	O
.	O
</s>
<s>
GRASS	B-Application
GIS	I-Application
(	O
open	O
source	O
)	O
,	O
although	O
it	O
was	O
originally	O
raster-based	O
,	O
has	O
included	O
overlay	B-Application
as	O
part	O
of	O
its	O
vector	O
system	O
since	O
GRASS	O
3.0	O
(	O
1988	O
)	O
.	O
</s>
<s>
Most	O
of	O
the	O
polygon	B-Application
overlay	I-Application
operators	O
are	O
collected	O
into	O
a	O
single	O
command	O
,	O
with	O
as	O
a	O
separate	O
command	O
.	O
</s>
<s>
QGIS	B-Application
(	O
open	O
source	O
)	O
originally	O
incorporated	O
GRASS	O
as	O
its	O
analytical	O
engine	O
,	O
but	O
has	O
gradually	O
developed	O
its	O
own	O
processing	O
framework	O
,	O
including	O
.	O
</s>
<s>
Manifold	B-Application
System	I-Application
implements	O
overlay	B-Application
in	O
its	O
system	O
.	O
</s>
<s>
The	O
Javascript	O
API	O
includes	O
the	O
most	O
common	O
overlay	B-Application
methods	O
,	O
although	O
these	O
operate	O
on	O
individual	O
input	O
polygon	O
objects	O
,	O
not	O
on	O
entire	O
layers	O
.	O
</s>
<s>
TNTmips	B-Application
includes	O
several	O
tools	O
for	O
among	O
its	O
vector	O
analysis	O
process	O
.	O
</s>
