<s>
A	O
geographic	B-General_Concept
data	I-General_Concept
model	I-Application
,	O
geospatial	B-General_Concept
data	I-General_Concept
model	I-Application
,	O
or	O
simply	O
data	B-Application
model	I-Application
in	O
the	O
context	O
of	O
geographic	B-Application
information	I-Application
systems	I-Application
,	O
is	O
a	O
mathematical	O
and	O
digital	O
structure	O
for	O
representing	O
phenomena	O
over	O
the	O
Earth	O
.	O
</s>
<s>
Generally	O
,	O
such	O
data	B-Application
models	I-Application
represent	O
various	O
aspects	O
of	O
these	O
phenomena	O
by	O
means	O
of	O
geographic	B-General_Concept
data	I-General_Concept
,	O
including	O
spatial	O
locations	O
,	O
attributes	O
,	O
change	O
over	O
time	O
,	O
and	O
identity	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
vector	O
data	B-Application
model	I-Application
represents	O
geography	O
as	O
collections	O
of	O
points	O
,	O
lines	O
,	O
and	O
polygons	O
,	O
and	O
the	O
raster	B-Algorithm
data	B-Application
model	I-Application
represent	O
geography	O
as	O
cell	O
matrices	O
that	O
store	O
numeric	O
values	O
.	O
</s>
<s>
Data	B-Application
models	I-Application
are	O
implemented	O
throughout	O
the	O
GIS	B-Application
ecosystem	O
,	O
including	O
the	O
software	O
tools	O
for	O
data	O
management	O
and	O
spatial	O
analysis	O
,	O
data	O
stored	O
in	O
a	O
variety	O
of	O
GIS	B-Application
file	O
formats	O
,	O
specifications	O
and	O
standards	O
,	O
and	O
specific	O
designs	O
for	O
GIS	B-Application
installations	O
.	O
</s>
<s>
While	O
the	O
unique	O
nature	O
of	O
spatial	B-General_Concept
information	I-General_Concept
has	O
led	O
to	O
its	O
own	O
set	O
of	O
model	O
structures	O
,	O
much	O
of	O
the	O
process	O
of	O
data	B-Application
modeling	I-Application
is	O
similar	O
to	O
the	O
rest	O
of	O
information	O
technology	O
,	O
including	O
the	O
progression	O
from	O
conceptual	B-Application
models	I-Application
to	O
logical	B-Application
models	I-Application
to	O
physical	B-Application
models	I-Application
,	O
and	O
the	O
difference	O
between	O
generic	B-Application
models	I-Application
and	O
application-specific	O
designs	O
.	O
</s>
<s>
The	O
earliest	O
computer	O
systems	O
that	O
represented	O
geographic	O
phenomena	O
were	O
quantitative	O
analysis	O
models	O
developed	O
during	O
the	O
quantitative	O
revolution	O
in	O
geography	O
in	O
the	O
1950s	O
and	O
1960s	O
;	O
these	O
could	O
not	O
be	O
called	O
a	O
geographic	B-Application
information	I-Application
system	I-Application
because	O
they	O
did	O
not	O
attempt	O
to	O
store	O
geographic	B-General_Concept
data	I-General_Concept
in	O
a	O
consistent	O
permanent	O
structure	O
,	O
but	O
were	O
usually	O
statistical	O
or	O
mathematical	O
models	O
.	O
</s>
<s>
The	O
first	O
true	O
GIS	B-Application
software	I-Application
modeled	O
spatial	B-General_Concept
information	I-General_Concept
using	O
data	B-Application
models	I-Application
that	O
would	O
come	O
to	O
be	O
known	O
as	O
raster	B-Algorithm
or	O
vector	O
:	O
</s>
<s>
SYMAP	O
(	O
by	O
Howard	O
Fisher	O
,	O
Harvard	O
Laboratory	O
for	O
Computer	O
Graphics	O
and	O
Spatial	O
Analysis	O
,	O
developed	O
1963	O
–	O
1967	O
)	O
produced	O
raster	B-Algorithm
maps	O
,	O
although	O
data	O
was	O
usually	O
entered	O
as	O
vector-like	O
region	O
outlines	O
or	O
sample	O
points	O
then	O
interpolated	O
into	O
a	O
raster	B-Algorithm
structure	O
for	O
output	O
.	O
</s>
<s>
The	O
GRID	O
package	O
,	O
developed	O
at	O
the	O
lab	O
in	O
1969	O
by	O
David	O
Sinton	O
,	O
was	O
based	O
on	O
SYMAP	O
but	O
was	O
more	O
focused	O
on	O
the	O
permanent	O
storage	O
and	O
analysis	O
of	O
gridded	O
data	O
,	O
thus	O
becoming	O
perhaps	O
the	O
first	O
general	O
purpose	O
raster	B-Algorithm
GIS	B-Application
software	I-Application
.	O
</s>
<s>
The	O
Canadian	O
Geographic	B-Application
Information	I-Application
System	I-Application
(	O
by	O
Roger	O
Tomlinson	O
,	O
Canada	O
Land	O
Inventory	O
,	O
developed	O
1963	O
–	O
1968	O
)	O
stored	O
natural	O
resource	O
data	O
as	O
"	O
faces	O
"	O
(	O
vector	O
polygons	O
)	O
,	O
although	O
these	O
were	O
typically	O
derived	O
from	O
raster	B-Algorithm
scans	O
of	O
paper	O
maps	O
.	O
</s>
<s>
Dual	O
Independent	O
Map	O
Encoding	O
(	O
DIME	O
,	O
US	O
Census	O
Bureau	O
,	O
1967	O
)	O
was	O
perhaps	O
the	O
first	O
robust	O
vector	O
data	B-Application
model	I-Application
incorporating	O
network	O
and	O
polygon	O
topology	O
and	O
attributes	O
sufficient	O
to	O
allow	O
address	B-Application
geocoding	I-Application
.	O
</s>
<s>
Like	O
the	O
CGIS	O
,	O
early	O
GIS	B-Application
installations	O
in	O
the	O
United	O
States	O
were	O
often	O
focused	O
on	O
inventories	O
of	O
land	O
use	O
and	O
natural	O
resources	O
,	O
including	O
the	O
Minnesota	O
Land	O
Management	O
Information	O
System	O
(	O
MLMIS	O
,	O
1969	O
)	O
,	O
the	O
Land	O
Use	O
and	O
Natural	O
Resources	O
Inventory	O
of	O
New	O
York	O
(	O
LUNR	O
,	O
1970	O
)	O
,	O
and	O
the	O
Oak	O
Ridge	O
Regional	O
Modelling	O
Information	O
System	O
(	O
ORRMIS	O
,	O
1973	O
)	O
.	O
</s>
<s>
Unlike	O
CGIS	O
,	O
these	O
were	O
all	O
raster	B-Algorithm
systems	O
inspired	O
by	O
SYMAP	O
,	O
although	O
the	O
MLMIS	O
was	O
based	O
on	O
subsections	O
of	O
the	O
Public	O
Land	O
Survey	O
System	O
,	O
which	O
is	O
not	O
a	O
perfect	O
regular	O
grid	O
.	O
</s>
<s>
Most	O
first-generation	O
GIS	B-Application
were	O
custom-built	O
for	O
specific	O
needs	O
,	O
with	O
data	B-Application
models	I-Application
designed	O
to	O
be	O
stored	O
and	O
processed	O
most	O
efficiently	O
using	O
the	O
technology	O
limitations	O
of	O
the	O
day	O
(	O
especially	O
punched	B-Architecture
cards	I-Architecture
and	O
limited	O
mainframe	O
processing	O
time	O
)	O
.	O
</s>
<s>
During	O
the	O
1970s	O
,	O
the	O
early	O
systems	O
had	O
produced	O
sufficient	O
results	O
to	O
compare	O
them	O
and	O
evaluate	O
the	O
effectiveness	O
of	O
their	O
underlying	O
data	B-Application
models	I-Application
.	O
</s>
<s>
This	O
led	O
to	O
efforts	O
at	O
the	O
Harvard	O
Lab	O
and	O
elsewhere	O
focused	O
on	O
developing	O
a	O
new	O
generation	O
of	O
generic	B-Application
data	I-Application
models	I-Application
,	O
such	O
as	O
the	O
POLYVRT	O
topological	O
vector	O
model	O
that	O
would	O
form	O
the	O
basis	O
for	O
commercial	O
software	O
and	O
data	O
such	O
as	O
the	O
Esri	O
Coverage	O
.	O
</s>
<s>
As	O
commercial	O
off-the-shelf	O
GIS	B-Application
software	I-Application
,	O
GIS	B-Application
installations	O
,	O
and	O
GIS	B-General_Concept
data	I-General_Concept
proliferated	O
in	O
the	O
1980s	O
,	O
scholars	O
began	O
to	O
look	O
for	O
conceptual	B-Application
models	I-Application
of	O
geographic	O
phenomena	O
that	O
seemed	O
to	O
underlay	O
the	O
common	O
data	B-Application
models	I-Application
,	O
trying	O
to	O
discover	O
why	O
the	O
raster	B-Algorithm
and	O
vector	O
data	B-Application
models	I-Application
seemed	O
to	O
make	O
common	O
sense	O
,	O
and	O
how	O
they	O
measured	O
and	O
represented	O
the	O
real	O
world	O
.	O
</s>
<s>
This	O
was	O
one	O
of	O
the	O
primary	O
threads	O
that	O
formed	O
the	O
subdiscipline	O
of	O
geographic	B-General_Concept
information	I-General_Concept
science	O
in	O
the	O
early	O
1990s	O
.	O
</s>
<s>
Further	O
developments	O
in	O
GIS	B-General_Concept
data	I-General_Concept
modeling	O
in	O
the	O
1990s	O
were	O
driven	O
by	O
rapid	O
increases	O
in	O
both	O
the	O
GIS	B-Application
user	O
base	O
and	O
computing	O
capability	O
.	O
</s>
<s>
Major	O
trends	O
included	O
1	O
)	O
the	O
development	O
of	O
extensions	O
to	O
the	O
traditional	O
data	B-Application
models	I-Application
to	O
handle	O
more	O
complex	O
needs	O
such	O
as	O
time	O
,	O
three-dimensional	O
structures	O
,	O
uncertainty	O
,	O
and	O
multimedia	O
;	O
and	O
2	O
)	O
the	O
need	O
to	O
efficiently	O
manage	O
exponentially	O
increasing	O
volumes	O
of	O
spatial	B-General_Concept
data	I-General_Concept
with	O
enterprise	O
needs	O
for	O
multiuser	O
access	O
and	O
security	O
.	O
</s>
<s>
These	O
trends	O
eventually	O
culminated	O
in	O
the	O
emergence	O
of	O
spatial	B-Algorithm
databases	I-Algorithm
incorporated	O
into	O
relational	B-Application
databases	I-Application
and	O
object-relational	B-General_Concept
databases	I-General_Concept
.	O
</s>
<s>
Because	O
the	O
world	O
is	O
much	O
more	O
complex	O
than	O
can	O
be	O
represented	O
in	O
a	O
computer	O
,	O
all	O
geospatial	B-General_Concept
data	I-General_Concept
are	O
incomplete	O
approximations	O
of	O
the	O
world	O
.	O
</s>
<s>
Thus	O
,	O
most	O
geospatial	B-General_Concept
data	I-General_Concept
models	O
encode	O
some	O
form	O
of	O
strategy	O
for	O
collecting	O
a	O
finite	O
sample	O
of	O
an	O
often	O
infinite	O
domain	O
,	O
and	O
a	O
structure	O
to	O
organize	O
the	O
sample	O
in	O
such	O
a	O
way	O
as	O
to	O
enable	O
interpolation	O
of	O
the	O
nature	O
of	O
the	O
unsampled	O
portion	O
.	O
</s>
<s>
The	O
process	O
of	O
designing	O
geospatial	B-General_Concept
data	I-General_Concept
models	O
is	O
similar	O
to	O
data	B-Application
modeling	I-Application
in	O
general	O
,	O
at	O
least	O
in	O
its	O
overall	O
pattern	O
.	O
</s>
<s>
Conceptual	B-Application
data	I-Application
model	I-Application
,	O
a	O
high-level	O
specification	O
of	O
how	O
information	O
is	O
organized	O
in	O
the	O
mind	O
and	O
in	O
enterprise	O
processes	O
,	O
without	O
regard	O
to	O
the	O
restrictions	O
of	O
GIS	B-Application
and	O
other	O
computer	O
systems	O
.	O
</s>
<s>
It	O
is	O
common	O
to	O
develop	O
and	O
represent	O
a	O
conceptual	O
model	O
visually	O
using	O
tools	O
such	O
as	O
an	O
entity-relationship	B-Architecture
model	I-Architecture
.	O
</s>
<s>
Logical	B-Application
data	I-Application
model	I-Application
,	O
a	O
broad	O
strategy	O
for	O
how	O
to	O
represent	O
the	O
conceptual	O
model	O
in	O
the	O
computer	O
,	O
sometimes	O
novel	O
but	O
often	O
within	O
the	O
framework	O
of	O
existing	O
software	O
,	O
hardware	O
,	O
and	O
standards	O
.	O
</s>
<s>
The	O
unified	B-Language
modeling	I-Language
language	I-Language
(	O
UML	B-Language
)	O
,	O
specifically	O
the	O
class	O
diagram	O
,	O
is	O
commonly	O
used	O
for	O
visually	O
developing	O
logical	O
and	O
physical	B-Application
models	I-Application
.	O
</s>
<s>
Physical	B-Application
data	I-Application
model	I-Application
,	O
the	O
detailed	O
specification	O
of	O
how	O
data	O
will	O
be	O
structured	O
in	O
memory	O
or	O
in	O
files	O
.	O
</s>
<s>
A	O
generic	B-Application
data	I-Application
model	I-Application
is	O
intended	O
to	O
be	O
employed	O
in	O
a	O
wide	O
variety	O
applications	O
,	O
by	O
discovering	O
consistent	O
patterns	O
in	O
the	O
ways	O
that	O
society	O
in	O
general	O
conceptualizes	O
information	O
and/or	O
structures	O
that	O
work	O
most	O
efficiently	O
in	O
computers	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
field	O
is	O
a	O
generic	O
conceptual	O
model	O
of	O
geographic	O
phenomena	O
,	O
the	O
relational	B-Application
database	I-Application
model	O
and	O
vector	O
are	O
generic	O
logical	B-Application
models	I-Application
,	O
while	O
the	O
shapefile	O
format	O
is	O
a	O
generic	O
physical	O
model	O
.	O
</s>
<s>
These	O
models	O
are	O
typically	O
implemented	O
directly	O
info	O
software	O
and	O
GIS	B-Application
file	O
formats	O
.	O
</s>
<s>
In	O
the	O
past	O
,	O
these	O
models	O
have	O
been	O
designed	O
by	O
academic	O
researchers	O
,	O
by	O
standards	O
bodies	O
such	O
as	O
the	O
Open	O
Geospatial	B-General_Concept
Consortium	O
,	O
and	O
by	O
software	O
vendors	O
such	O
as	O
Esri	O
.	O
</s>
<s>
While	O
academic	O
and	O
standard	O
models	O
are	O
public	O
(	O
and	O
sometimes	O
open	B-License
source	I-License
)	O
,	O
companies	O
may	O
choose	O
to	O
keep	O
the	O
details	O
of	O
their	O
model	O
a	O
secret	O
(	O
as	O
Esri	O
attempted	O
to	O
do	O
with	O
the	O
coverage	O
and	O
the	O
file	O
geodatabase	O
)	O
or	O
to	O
publish	O
them	O
openly	O
(	O
as	O
Esri	O
did	O
with	O
the	O
shapefile	O
)	O
.	O
</s>
<s>
A	O
specific	O
data	B-Application
model	I-Application
or	O
GIS	B-Application
design	O
is	O
a	O
specification	O
of	O
the	O
data	O
needed	O
for	O
a	O
particular	O
enterprise	O
or	O
project	O
GIS	B-Application
application	O
.	O
</s>
<s>
It	O
is	O
generally	O
created	O
within	O
the	O
constraints	O
of	O
chosen	O
generic	B-Application
data	I-Application
models	I-Application
,	O
so	O
that	O
existing	O
GIS	B-Application
software	I-Application
can	O
be	O
used	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
data	B-Application
model	I-Application
for	O
a	O
city	O
would	O
include	O
a	O
list	O
of	O
data	O
layers	O
to	O
be	O
included	O
(	O
e.g.	O
,	O
roads	O
,	O
buildings	O
,	O
parcels	O
,	O
zoning	O
)	O
,	O
with	O
each	O
being	O
specified	O
with	O
the	O
type	O
of	O
generic	O
spatial	B-General_Concept
data	I-General_Concept
model	I-Application
being	O
used	O
(	O
e.g.	O
</s>
<s>
raster	B-Algorithm
or	O
vector	O
)	O
,	O
choices	O
of	O
parameters	O
such	O
as	O
coordinate	O
system	O
,	O
and	O
its	O
attribute	O
columns	O
.	O
</s>
<s>
Generic	O
geospatial	B-General_Concept
conceptual	B-Application
models	I-Application
attempt	O
to	O
capture	O
both	O
the	O
physical	O
nature	O
of	O
geographic	O
phenomena	O
and	O
how	O
people	O
think	O
about	O
them	O
and	O
work	O
with	O
them	O
.	O
</s>
<s>
Contrary	O
to	O
the	O
standard	O
modeling	O
process	O
described	O
above	O
,	O
the	O
data	B-Application
models	I-Application
upon	O
which	O
GIS	B-Application
is	O
built	O
were	O
not	O
originally	O
designed	O
based	O
on	O
a	O
general	O
conceptual	O
model	O
of	O
geographic	O
phenomena	O
,	O
but	O
were	O
largely	O
designed	O
according	O
to	O
technical	O
expediency	O
,	O
likely	O
influenced	O
by	O
common	O
sense	O
conceptualizations	O
that	O
had	O
not	O
yet	O
been	O
documented	O
.	O
</s>
<s>
That	O
said	O
,	O
an	O
early	O
conceptual	O
framework	O
that	O
was	O
very	O
influential	O
in	O
early	O
GIS	B-Application
development	O
was	O
the	O
recognition	O
by	O
Brian	O
Berry	O
and	O
others	O
that	O
geographic	B-General_Concept
information	I-General_Concept
can	O
be	O
decomposed	O
into	O
the	O
description	O
of	O
three	O
very	O
different	O
aspects	O
of	O
each	O
phenomenon	O
:	O
space	O
,	O
time	O
,	O
and	O
attribute/property/theme	O
.	O
</s>
<s>
During	O
the	O
1980s	O
and	O
1990s	O
,	O
a	O
body	O
of	O
spatial	B-General_Concept
information	I-General_Concept
theories	O
gradually	O
emerged	O
as	O
a	O
major	O
subfield	O
of	O
geographic	B-General_Concept
information	I-General_Concept
science	O
,	O
incorporating	O
elements	O
of	O
philosophy	O
(	O
especially	O
ontology	B-Language
)	O
,	O
linguistics	O
,	O
and	O
sciences	O
of	O
spatial	O
cognition	O
.	O
</s>
<s>
These	O
two	O
conceptual	B-Application
models	I-Application
are	O
not	O
meant	O
to	O
represent	O
different	O
phenomena	O
,	O
but	O
often	O
are	O
different	O
ways	O
of	O
conceptualizing	O
and	O
describing	O
the	O
same	O
phenomenon	O
.	O
</s>
<s>
Each	O
geometric	O
shape	O
is	O
represented	O
using	O
coordinate	O
geometry	O
,	O
by	O
a	O
structured	O
set	O
of	O
coordinates	O
(	O
x	O
,	O
y	O
)	O
in	O
a	O
geographic	O
coordinate	O
system	O
,	O
selected	O
from	O
a	O
set	O
of	O
available	O
geometric	B-Algorithm
primitives	I-Algorithm
,	O
such	O
as	O
points	O
,	O
lines	O
,	O
and	O
polygons	O
.	O
</s>
<s>
Although	O
there	O
are	O
dozens	O
of	O
vector	O
file	O
formats	O
(	O
i.e.	O
,	O
physical	B-Application
data	I-Application
models	I-Application
)	O
used	O
in	O
various	O
GIS	B-Application
software	I-Application
,	O
most	O
conform	O
to	O
the	O
Simple	O
Feature	O
Access	O
(	O
SFA	O
)	O
specification	O
from	O
the	O
Open	O
Geospatial	B-General_Concept
Consortium	O
(	O
OGC	O
)	O
.	O
</s>
<s>
It	O
was	O
developed	O
in	O
the	O
1990s	O
by	O
finding	O
common	O
ground	O
between	O
existing	O
vector	O
models	O
,	O
and	O
is	O
now	O
enshrined	O
as	O
ISO	O
19125	O
,	O
the	O
reference	O
standard	O
for	O
the	O
vector	O
data	B-Application
model	I-Application
.	O
</s>
<s>
OGC-SFA	O
includes	O
the	O
following	O
vector	O
geometric	B-Algorithm
primitives	I-Algorithm
:	O
</s>
<s>
GIS	B-Application
software	I-Application
distinguishes	O
the	O
interior	O
and	O
the	O
exterior	O
by	O
requiring	O
that	O
the	O
line	O
be	O
ordered	O
counter-clockwise	O
,	O
so	O
the	O
interior	O
is	O
always	O
on	O
the	O
left	O
side	O
of	O
the	O
boundary	O
.	O
</s>
<s>
Text	B-Application
(	O
alternatively	O
called	O
annotation	O
)	O
:	O
a	O
minority	O
of	O
vector	O
data	O
formats	O
,	O
including	O
the	O
Esri	O
geodatabase	O
and	O
Autodesk	O
.dwg	O
,	O
support	O
the	O
storage	O
of	O
text	B-Application
in	O
the	O
database	O
.	O
</s>
<s>
An	O
annotation	O
is	O
usually	O
represented	O
as	O
a	O
point	O
or	O
curve	O
(	O
the	O
baseline	O
)	O
with	O
a	O
set	O
of	O
attributes	O
giving	O
the	O
text	B-Application
content	O
and	O
design	O
characteristics	O
(	O
font	O
,	O
size	O
,	O
spacing	O
,	O
etc	O
.	O
</s>
<s>
Based	O
on	O
this	O
basic	O
strategy	O
of	O
geometric	O
shapes	O
and	O
attributes	O
,	O
vector	O
data	B-Application
models	I-Application
use	O
a	O
variety	O
of	O
structures	O
to	O
collect	O
these	O
into	O
a	O
single	O
data	O
set	O
(	O
often	O
called	O
a	O
layer	O
)	O
,	O
usually	O
containing	O
a	O
set	O
of	O
related	O
features	O
(	O
e.g.	O
,	O
roads	O
)	O
.	O
</s>
<s>
The	O
georelational	B-Application
data	I-Application
model	I-Application
was	O
the	O
basis	O
for	O
most	O
early	O
vector	O
GIS	B-Application
software	I-Application
.	O
</s>
<s>
The	O
geometric	O
data	O
and	O
the	O
attribute	O
data	O
are	O
stored	O
separately	O
;	O
this	O
was	O
originally	O
because	O
the	O
geometric	O
data	O
required	O
GIS-specific	O
code	O
to	O
process	O
it	O
,	O
but	O
existing	O
relational	B-Application
database	I-Application
software	O
(	O
RDBMS	O
)	O
could	O
be	O
used	O
to	O
manage	O
the	O
attributes	O
.	O
</s>
<s>
For	O
example	O
,	O
Esri	O
ARC/INFO	B-Application
(	O
later	O
ArcInfo	B-Application
)	O
was	O
originally	O
composed	O
of	O
two	O
separate	O
programs	O
:	O
ARC	O
was	O
written	O
by	O
Esri	O
for	O
spatial	O
management	O
and	O
analysis	O
,	O
while	O
INFO	O
was	O
a	O
licensed	O
commercial	O
RDBMS	O
program	O
.	O
</s>
<s>
It	O
was	O
termed	O
"	O
georelational	O
"	O
because	O
in	O
keeping	O
with	O
the	O
principles	O
of	O
relational	B-Application
databases	I-Application
,	O
the	O
geometry	O
and	O
attributes	O
could	O
be	O
joined	O
by	O
matching	O
each	O
shape	O
with	O
a	O
row	O
in	O
the	O
table	O
using	O
a	O
key	O
,	O
such	O
as	O
the	O
row	O
number	O
or	O
an	O
ID	O
number	O
.	O
</s>
<s>
The	O
spatial	B-Algorithm
database	I-Algorithm
(	O
also	O
called	O
the	O
object-based	O
model	O
)	O
first	O
appeared	O
in	O
the	O
1990s	O
.	O
</s>
<s>
It	O
also	O
leverages	O
the	O
maturity	O
of	O
relational	B-Application
database	I-Application
management	I-Application
systems	I-Application
,	O
especially	O
for	O
their	O
ability	O
to	O
manage	O
extremely	O
large	O
enterprise	O
databases	O
.	O
</s>
<s>
Instead	O
of	O
storing	O
geometric	O
data	O
separately	O
,	O
the	O
spatial	B-Algorithm
database	I-Algorithm
defines	O
a	O
geometry	O
data	O
type	O
,	O
allowing	O
the	O
shapes	O
to	O
be	O
stored	O
in	O
a	O
column	O
in	O
the	O
same	O
table	O
as	O
the	O
attributes	O
,	O
creating	O
a	O
single	O
unified	O
data	O
set	O
for	O
each	O
layer	O
.	O
</s>
<s>
Most	O
RDBMS	O
software	O
(	O
both	O
commercial	O
and	O
open-source	B-License
)	O
have	O
spatial	O
extensions	O
to	O
enable	O
the	O
storage	O
and	O
query	O
of	O
geometric	O
data	O
,	O
usually	O
based	O
on	O
the	O
Simple	O
Features-SQL	O
standard	O
from	O
the	O
Open	O
Geospatial	B-General_Concept
Consortium	O
.	O
</s>
<s>
Some	O
non-database	O
data	O
formats	O
also	O
integrate	O
geometric	O
and	O
attribute	O
data	O
for	O
each	O
object	O
into	O
a	O
single	O
structure	O
,	O
such	O
as	O
GeoJSON	B-General_Concept
.	O
</s>
<s>
Vector	O
data	B-General_Concept
structures	I-General_Concept
can	O
also	O
be	O
classified	O
by	O
how	O
they	O
manage	O
topological	O
relationships	O
between	O
objects	O
in	O
a	O
dataset	O
:	O
</s>
<s>
A	O
topological	O
data	B-Application
model	I-Application
incorporates	O
topological	O
relationships	O
as	O
a	O
core	O
part	O
of	O
the	O
model	O
design	O
.	O
</s>
<s>
The	O
GBF/DIME	O
format	O
from	O
the	O
U.S.	O
Census	O
Bureau	O
was	O
probably	O
the	O
first	O
topological	O
data	B-Application
model	I-Application
;	O
another	O
early	O
example	O
was	O
POLYVRT	O
,	O
developed	O
at	O
the	O
Harvard	O
Laboratory	O
for	O
Computer	O
Graphics	O
and	O
Spatial	O
Analysis	O
in	O
the	O
1970s	O
,	O
eventually	O
evolving	O
into	O
the	O
Esri	O
ARC/INFO	B-Application
Coverage	O
format	O
.	O
</s>
<s>
This	O
structure	O
was	O
designed	O
to	O
enable	O
composite	O
line-polygon	O
structures	O
(	O
e.g.	O
,	O
the	O
census	O
block	O
)	O
,	O
address	B-Application
geocoding	I-Application
,	O
and	O
transport	O
network	O
analysis	O
.	O
</s>
<s>
However	O
,	O
it	O
is	O
a	O
fairly	O
complicated	O
data	B-General_Concept
structure	I-General_Concept
.	O
</s>
<s>
Almost	O
all	O
topological	O
data	B-Application
models	I-Application
are	O
also	O
geo-relational	O
.	O
</s>
<s>
A	O
spaghetti	O
data	B-Application
model	I-Application
does	O
not	O
include	O
any	O
information	O
about	O
topology	O
(	O
so-called	O
because	O
the	O
individual	O
strands	O
in	O
a	O
bowl	O
of	O
spaghetti	O
may	O
overlap	O
without	O
connecting	O
)	O
.	O
</s>
<s>
It	O
was	O
common	O
in	O
early	O
GIS	B-Application
systems	O
such	O
as	O
the	O
Map	B-Application
Overlay	I-Application
and	I-Application
Statistical	I-Application
System	I-Application
(	O
MOSS	O
)	O
as	O
well	O
as	O
most	O
recent	O
data	O
formats	O
,	O
such	O
as	O
the	O
Esri	O
shapefile	O
,	O
geography	O
markup	O
language	O
(	O
GML	O
)	O
,	O
and	O
almost	O
all	O
spatial	B-Algorithm
databases	I-Algorithm
.	O
</s>
<s>
Despite	O
the	O
increased	O
data	O
volume	O
and	O
potential	O
for	O
error	O
over	O
topological	O
data	O
,	O
this	O
model	O
has	O
dominated	O
GIS	B-Application
since	O
2000	O
,	O
largely	O
due	O
to	O
its	O
conceptual	O
simplicity	O
.	O
</s>
<s>
Some	O
GIS	B-Application
software	I-Application
has	O
tools	O
for	O
validating	O
topological	O
integrity	O
rules	O
(	O
e.g.	O
</s>
<s>
A	O
hybrid	O
topological	O
data	B-Application
model	I-Application
has	O
the	O
option	O
of	O
storing	O
topological	O
relationship	O
information	O
as	O
a	O
separate	O
layer	O
built	O
on	O
top	O
of	O
a	O
spaghetti	O
data	O
set	O
.	O
</s>
<s>
The	O
raster	B-Algorithm
logical	O
model	O
represents	O
a	O
field	O
using	O
a	O
tessellation	B-Algorithm
of	O
geographic	O
space	O
into	O
a	O
regularly	O
spaced	O
two-dimensional	O
array	O
of	O
locations	O
(	O
each	O
called	O
a	O
cell	O
)	O
,	O
with	O
a	O
single	O
attribute	O
value	O
for	O
each	O
cell	O
(	O
or	O
more	O
than	O
one	O
value	O
in	O
a	O
multi-band	O
raster	B-Algorithm
)	O
.	O
</s>
<s>
Typically	O
,	O
each	O
cell	O
either	O
represents	O
a	O
single	O
central	O
point	O
sample	O
(	O
in	O
which	O
the	O
measurement	O
model	O
for	O
the	O
entire	O
raster	B-Algorithm
is	O
called	O
a	O
lattice	O
)	O
or	O
it	O
represents	O
a	O
summary	O
(	O
usually	O
the	O
mean	O
)	O
of	O
the	O
field	O
variable	O
over	O
the	O
square	O
area	O
(	O
in	O
which	O
the	O
model	O
is	O
called	O
a	O
grid	O
)	O
.	O
</s>
<s>
The	O
general	O
data	B-Application
model	I-Application
is	O
essentially	O
the	O
same	O
as	O
that	O
used	O
for	O
images	O
and	O
other	O
raster	B-Algorithm
graphics	I-Algorithm
,	O
with	O
the	O
addition	O
of	O
capabilities	O
for	O
the	O
geographic	O
context	O
.	O
</s>
<s>
To	O
represent	O
a	O
raster	B-Algorithm
grid	O
in	O
a	O
computer	O
file	O
,	O
it	O
must	O
be	O
serialized	O
into	O
a	O
single	O
(	O
one-dimensional	O
)	O
list	O
of	O
values	O
.	O
</s>
<s>
While	O
the	O
raster	B-Algorithm
model	O
is	O
closely	O
tied	O
to	O
the	O
field	O
conceptual	O
model	O
,	O
objects	O
can	O
also	O
be	O
represented	O
in	O
raster	B-Algorithm
,	O
essentially	O
by	O
transforming	O
an	O
object	O
X	O
into	O
a	O
discrete	O
(	O
Boolean	B-General_Concept
)	O
field	O
of	O
presence/absence	O
of	O
X	O
.	O
Alternatively	O
,	O
a	O
layer	O
of	O
objects	O
(	O
usually	O
polygons	O
)	O
could	O
be	O
transformed	O
into	O
a	O
discrete	O
field	O
of	O
object	O
identifiers	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
some	O
raster	B-Algorithm
file	O
formats	O
allow	O
a	O
vector-like	O
table	O
of	O
attributes	O
to	O
be	O
joined	O
to	O
the	O
raster	B-Algorithm
by	O
matching	O
the	O
ID	O
values	O
.	O
</s>
<s>
Raster	B-Algorithm
representations	O
of	O
objects	O
are	O
often	O
temporary	O
,	O
only	O
created	O
and	O
used	O
as	O
part	O
of	O
a	O
modelling	O
procedure	O
,	O
rather	O
than	O
in	O
a	O
permanent	O
data	O
store	O
.	O
</s>
<s>
To	O
be	O
useful	O
in	O
GIS	B-Application
,	O
a	O
raster	B-Algorithm
file	O
must	O
be	O
georeferenced	O
to	O
correspond	O
to	O
real	O
world	O
locations	O
,	O
as	O
a	O
raw	O
raster	B-Algorithm
can	O
only	O
express	O
locations	O
in	O
terms	O
of	O
rows	O
and	O
columns	O
.	O
</s>
<s>
This	O
is	O
typically	O
done	O
with	O
a	O
set	O
of	O
metadata	O
parameters	O
,	O
either	O
in	O
the	O
file	O
header	O
(	O
such	O
as	O
the	O
GeoTIFF	B-Application
format	O
)	O
or	O
in	O
a	O
sidecar	O
file	O
(	O
such	O
as	O
a	O
world	O
file	O
)	O
.	O
</s>
<s>
A	O
linear	O
Affine	B-Algorithm
transformation	I-Algorithm
is	O
the	O
most	O
common	O
type	O
of	O
georeferencing	O
,	O
allowing	O
rotation	O
and	O
rectangular	O
cells	O
.	O
</s>
<s>
Raster	B-Algorithm
data	O
sets	O
can	O
be	O
very	O
large	O
,	O
so	O
image	B-General_Concept
compression	I-General_Concept
techniques	O
are	O
often	O
used	O
.	O
</s>
<s>
In	O
most	O
GIS	B-Application
applications	O
,	O
lossless	B-Algorithm
compression	I-Algorithm
algorithms	O
(	O
e.g.	O
,	O
Lempel-Ziv	O
)	O
are	O
preferred	O
over	O
lossy	O
ones	O
(	O
e.g.	O
,	O
JPEG	O
)	O
,	O
because	O
the	O
complete	O
original	O
data	O
are	O
needed	O
,	O
not	O
an	O
interpolation	O
.	O
</s>
<s>
Starting	O
in	O
the	O
1990s	O
,	O
as	O
the	O
original	O
data	B-Application
models	I-Application
and	O
GIS	B-Application
software	I-Application
matured	O
,	O
one	O
of	O
the	O
primary	O
foci	O
of	O
data	B-Application
modeling	I-Application
research	O
was	O
on	O
developing	O
extensions	O
to	O
the	O
traditional	O
models	O
to	O
handle	O
more	O
complex	O
geographic	B-General_Concept
information	I-General_Concept
.	O
</s>
<s>
In	O
the	O
dawn	O
of	O
the	O
GIScience	O
era	O
of	O
the	O
early	O
1990s	O
,	O
the	O
work	O
of	O
Gail	O
Langran	O
opened	O
the	O
doors	O
to	O
research	O
into	O
methods	O
of	O
explicitly	O
representing	O
change	O
over	O
time	O
in	O
GIS	B-General_Concept
data	I-General_Concept
;	O
this	O
led	O
to	O
many	O
conceptual	O
and	O
data	B-Application
models	I-Application
emerging	O
in	O
the	O
decades	O
since	O
.	O
</s>
<s>
Some	O
forms	O
of	O
temporal	O
data	O
began	O
to	O
be	O
supported	O
in	O
off-the-shelf	O
GIS	B-Application
software	I-Application
by	O
2010	O
.	O
</s>
<s>
Several	O
common	O
models	O
for	O
representing	O
time	O
in	O
vector	O
and	O
raster	B-Algorithm
GIS	B-General_Concept
data	I-General_Concept
include	O
:	O
</s>
<s>
Some	O
GIS	B-Application
software	I-Application
,	O
such	O
as	O
ArcGIS	B-Application
Pro	O
,	O
natively	O
supports	O
this	O
model	O
,	O
with	O
functionality	O
including	O
animation	O
.	O
</s>
<s>
Time-stamped	O
boundaries	O
,	O
using	O
the	O
topological	O
vector	O
data	B-Application
model	I-Application
to	O
decompose	O
polygons	O
into	O
boundary	O
segments	O
,	O
and	O
stamping	O
each	O
segment	O
by	O
the	O
time	O
during	O
which	O
it	O
was	O
valid	O
.	O
</s>
<s>
This	O
method	O
was	O
pioneered	O
by	O
the	O
Great	O
Britain	O
Historical	O
GIS	B-Application
.	O
</s>
<s>
Time	O
as	O
dimension	O
,	O
which	O
treats	O
time	O
as	O
another	O
(	O
3rd	O
or	O
4th	O
)	O
spatial	O
dimension	O
,	O
and	O
using	O
multidimensional	O
vector	O
or	O
raster	B-Algorithm
structures	O
to	O
create	O
geometries	O
incorporating	O
time	O
.	O
</s>
<s>
Hägerstrand	O
visualized	O
his	O
time	O
geography	O
this	O
way	O
,	O
and	O
some	O
GIS	B-Application
models	O
based	O
on	O
it	O
use	O
this	O
approach	O
.	O
</s>
<s>
The	O
NetCDF	B-Application
format	O
supports	O
managing	O
temporal	O
raster	B-Algorithm
data	O
as	O
a	O
dimension	O
.	O
</s>
<s>
There	O
are	O
several	O
approaches	O
for	O
representing	O
three-dimensional	O
map	O
information	O
,	O
and	O
for	O
managing	O
it	O
in	O
the	O
data	B-Application
model	I-Application
.	O
</s>
<s>
Some	O
of	O
these	O
were	O
developed	O
specifically	O
for	O
GIS	B-Application
,	O
while	O
others	O
have	O
been	O
adopted	O
from	O
3D	O
computer	O
graphics	O
or	O
computer-aided	B-Application
drafting	I-Application
(	O
CAD	B-Application
)	O
.	O
</s>
<s>
Height	B-Data_Structure
fields	I-Data_Structure
(	O
also	O
known	O
as	O
"	O
2	O
1/2	O
dimensional	O
surfaces	O
"	O
)	O
model	O
three-dimensional	O
phenomena	O
by	O
a	O
single	O
functional	O
surface	O
,	O
in	O
which	O
elevation	O
is	O
a	O
function	O
of	O
two-dimensional	O
location	O
,	O
allowing	O
it	O
to	O
be	O
represented	O
using	O
field	O
techniques	O
such	O
as	O
isolated	O
points	O
,	O
contour	O
lines	O
,	O
raster	B-Algorithm
(	O
the	O
digital	B-Application
elevation	I-Application
model	I-Application
)	O
,	O
and	O
triangulated	B-Algorithm
irregular	I-Algorithm
networks	I-Algorithm
.	O
</s>
<s>
A	O
polygon	B-Algorithm
mesh	I-Algorithm
(	O
related	O
to	O
the	O
mathematical	O
polyhedron	O
)	O
is	O
a	O
logical	O
extension	O
of	O
the	O
vector	O
data	B-Application
model	I-Application
,	O
and	O
is	O
probably	O
the	O
3-D	O
model	O
type	O
most	O
widely	O
supported	O
in	O
GIS	B-Application
.	O
</s>
<s>
The	O
voxel	B-Algorithm
model	O
is	O
the	O
logical	O
extension	O
of	O
the	O
raster	B-Algorithm
data	B-Application
model	I-Application
,	O
by	O
tessellating	O
three-dimensional	O
space	O
into	O
cubes	O
called	O
voxels	B-Algorithm
(	O
a	O
portmanteau	O
of	O
volume	O
and	O
pixel	O
,	O
the	O
latter	O
being	O
itself	O
a	O
portmanteau	O
)	O
.	O
</s>
<s>
NetCDF	B-Application
is	O
one	O
of	O
the	O
most	O
common	O
data	O
formats	O
that	O
supports	O
3-D	O
cells	O
.	O
</s>
<s>
Vector-based	O
stack-unit	O
maps	O
depict	O
the	O
vertical	O
succession	O
of	O
geologic	O
units	O
to	O
a	O
specified	O
depth	O
(	O
here	O
,	O
the	O
base	O
of	O
the	O
block	B-Application
diagram	I-Application
)	O
.	O
</s>
<s>
Raster-based	O
stacked	O
surfaces	O
depict	O
the	O
surface	O
of	O
each	O
buried	O
geologic	O
unit	O
,	O
and	O
can	O
accommodate	O
data	O
on	O
lateral	O
variations	O
of	O
physical	O
properties	O
.	O
</s>
<s>
In	O
this	O
example	O
from	O
Soller	O
and	O
others	O
(	O
1999	O
)	O
,	O
the	O
upper	O
surface	O
of	O
each	O
buried	O
geologic	O
unit	O
was	O
represented	O
in	O
raster	B-Algorithm
format	I-Algorithm
as	O
an	O
ArcInfo	B-Application
Grid	O
file	O
.	O
</s>
<s>
Each	O
geologic	O
unit	O
in	O
raster	B-Algorithm
format	I-Algorithm
can	O
be	O
managed	O
in	O
the	O
data	B-Application
model	I-Application
,	O
in	O
a	O
manner	O
not	O
dissimilar	O
from	O
that	O
shown	O
for	O
the	O
stack-unit	O
map	O
.	O
</s>
<s>
The	O
Mahomet	O
Sand	O
is	O
continuous	O
in	O
this	O
area	O
,	O
and	O
represents	O
one	O
occurrence	O
of	O
this	O
unit	O
in	O
the	O
data	B-Application
model	I-Application
.	O
</s>
<s>
Each	O
raster	B-Algorithm
,	O
or	O
pixel	O
,	O
on	O
the	O
Mahomet	O
Sand	O
surface	O
has	O
a	O
set	O
of	O
map	O
coordinates	O
that	O
are	O
recorded	O
in	O
a	O
GIS	B-Application
(	O
in	O
the	O
data	B-Application
model	I-Application
bin	O
that	O
is	O
labeled	O
"	O
pixel	O
coordinates	O
"	O
,	O
which	O
is	O
the	O
raster	B-Algorithm
corollary	O
of	O
the	O
"	O
geometry	O
"	O
bin	O
for	O
vector	O
map	O
data	O
)	O
.	O
</s>
