<s>
A	O
cartogram	B-Application
(	O
also	O
called	O
a	O
value-area	O
map	O
or	O
an	O
anamorphic	O
map	O
,	O
the	O
latter	O
common	O
among	O
German-speakers	O
)	O
is	O
a	O
thematic	B-Application
map	I-Application
of	O
a	O
set	O
of	O
features	O
(	O
countries	O
,	O
provinces	O
,	O
etc	O
.	O
</s>
<s>
They	O
are	O
primarily	O
used	O
to	O
display	O
emphasis	O
and	O
for	O
analysis	O
as	O
nomographs	B-Application
.	O
</s>
<s>
Cartograms	B-Application
leverage	O
the	O
fact	O
that	O
size	O
is	O
the	O
most	O
intuitive	O
visual	O
variable	O
for	O
representing	O
a	O
total	O
amount	O
.	O
</s>
<s>
In	O
this	O
,	O
it	O
is	O
a	O
strategy	O
that	O
is	O
similar	O
to	O
proportional	O
symbol	O
maps	O
,	O
which	O
scale	O
point	O
features	O
,	O
and	O
many	O
flow	B-Application
maps	I-Application
,	O
which	O
scale	O
the	O
weight	O
of	O
linear	O
features	O
.	O
</s>
<s>
However	O
,	O
these	O
two	O
techniques	O
only	O
scale	O
the	O
map	O
symbol	O
,	O
not	O
space	O
itself	O
;	O
a	O
map	O
that	O
stretches	O
the	O
length	O
of	O
linear	O
features	O
is	O
considered	O
a	O
linear	O
cartogram	B-Application
(	O
although	O
additional	O
flow	B-Application
map	I-Application
techniques	O
may	O
be	O
added	O
)	O
.	O
</s>
<s>
Once	O
constructed	O
,	O
cartograms	B-Application
are	O
often	O
used	O
as	O
a	O
base	O
for	O
other	O
thematic	O
mapping	O
techniques	O
to	O
visualize	O
additional	O
variables	O
,	O
such	O
as	O
choropleth	O
mapping	O
.	O
</s>
<s>
The	O
cartogram	B-Application
was	O
developed	O
later	O
than	O
other	O
types	O
of	O
thematic	B-Application
maps	I-Application
,	O
but	O
followed	O
the	O
same	O
tradition	O
of	O
innovation	O
in	O
France	O
.	O
</s>
<s>
The	O
earliest	O
known	O
cartogram	B-Application
was	O
published	O
in	O
1876	O
by	O
French	O
statistician	O
and	O
geographer	O
Pierre	O
Émile	O
Levasseur	O
,	O
who	O
created	O
a	O
series	O
of	O
maps	O
that	O
represented	O
the	O
countries	O
of	O
Europe	O
as	O
squares	O
,	O
sized	O
according	O
to	O
a	O
variable	O
and	O
arranged	O
in	O
their	O
general	O
geographical	O
position	O
(	O
with	O
separate	O
maps	O
scaled	O
by	O
area	O
,	O
population	O
,	O
religious	O
adherents	O
,	O
and	O
national	O
budget	O
)	O
.	O
</s>
<s>
Later	O
reviewers	O
have	O
called	O
his	O
figures	O
a	O
statistical	O
diagram	O
rather	O
than	O
a	O
map	O
,	O
but	O
Levasseur	O
referred	O
to	O
it	O
as	O
a	O
carte	O
figurative	O
,	O
the	O
common	O
term	O
then	O
in	O
use	O
for	O
any	O
thematic	B-Application
map	I-Application
.	O
</s>
<s>
The	O
next	O
notable	O
development	O
was	O
a	O
pair	O
of	O
maps	O
by	O
Hermann	O
Haack	O
and	O
Hugo	O
Weichel	O
of	O
the	O
1898	O
election	O
results	O
for	O
the	O
German	O
Reichstag	O
in	O
preparation	O
for	O
the	O
1903	O
election	O
,	O
the	O
earliest	O
known	O
contiguous	O
cartogram	B-Application
.	O
</s>
<s>
The	O
subsequent	O
expansion	O
of	O
densely	O
populated	O
areas	O
around	O
Berlin	O
,	O
Hamburg	O
,	O
and	O
Saxony	O
was	O
intended	O
to	O
visualize	O
the	O
controversial	O
tendency	O
of	O
the	O
mainly	O
urban	O
Social	O
Democrats	O
to	O
win	O
the	O
popular	O
vote	O
,	O
while	O
the	O
mainly	O
rural	O
Zentrum	O
won	O
more	O
seats	O
(	O
thus	O
presaging	O
the	O
modern	O
popularity	O
of	O
cartograms	B-Application
for	O
showing	O
the	O
same	O
tendencies	O
in	O
recent	O
elections	O
in	O
the	O
United	O
States	O
)	O
.	O
</s>
<s>
The	O
continuous	O
cartogram	B-Application
emerged	O
soon	O
after	O
in	O
the	O
United	O
States	O
,	O
where	O
a	O
variety	O
appeared	O
in	O
the	O
popular	O
media	O
after	O
1911	O
.	O
</s>
<s>
Most	O
were	O
rather	O
crudely	O
drawn	O
compared	O
to	O
Haack	O
and	O
Weichel	O
,	O
with	O
the	O
exception	O
of	O
the	O
"	O
rectangular	O
statistical	O
cartograms	B-Application
"	O
by	O
the	O
American	O
master	O
cartographer	O
Erwin	O
Raisz	O
,	O
who	O
claimed	O
to	O
have	O
invented	O
the	O
technique	O
.	O
</s>
<s>
When	O
Haack	O
and	O
Weichel	O
referred	O
to	O
their	O
map	O
as	O
a	O
kartogramm	O
,	O
this	O
term	O
was	O
commonly	O
being	O
used	O
to	O
refer	O
to	O
all	O
thematic	B-Application
maps	I-Application
,	O
especially	O
in	O
Europe	O
.	O
</s>
<s>
It	O
was	O
not	O
until	O
Raisz	O
and	O
other	O
academic	O
cartographers	O
stated	O
their	O
preference	O
for	O
a	O
restricted	O
use	O
of	O
the	O
term	O
in	O
their	O
textbooks	O
(	O
Raisz	O
initially	O
espousing	O
value-area	O
cartogram	B-Application
)	O
that	O
the	O
current	O
meaning	O
was	O
gradually	O
adopted	O
.	O
</s>
<s>
The	O
primary	O
challenge	O
of	O
cartograms	B-Application
has	O
always	O
been	O
the	O
drafting	O
of	O
the	O
distorted	O
shapes	O
,	O
making	O
them	O
a	O
prime	O
target	O
for	O
computer	O
automation	O
.	O
</s>
<s>
Since	O
then	O
,	O
a	O
wide	O
variety	O
of	O
algorithms	O
have	O
been	O
developed	O
(	O
see	O
below	O
)	O
,	O
although	O
it	O
is	O
still	O
common	O
to	O
craft	O
cartograms	B-Application
manually	O
.	O
</s>
<s>
Since	O
the	O
early	O
days	O
of	O
the	O
academic	O
study	O
of	O
cartograms	B-Application
,	O
they	O
have	O
been	O
compared	O
to	O
map	B-Application
projections	I-Application
in	O
many	O
ways	O
,	O
in	O
that	O
both	O
methods	O
transform	O
(	O
and	O
thus	O
distort	O
)	O
space	O
itself	O
.	O
</s>
<s>
The	O
goal	O
of	O
designing	O
a	O
cartogram	B-Application
or	O
a	O
map	B-Application
projection	I-Application
is	O
therefore	O
to	O
represent	O
one	O
or	O
more	O
aspects	O
of	O
geographic	O
phenomena	O
as	O
accurately	O
as	O
possible	O
,	O
while	O
minimizing	O
the	O
collateral	O
damage	O
of	O
distortion	O
in	O
other	O
aspects	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
cartograms	B-Application
,	O
by	O
scaling	O
features	O
to	O
have	O
a	O
size	O
proportional	O
to	O
a	O
variable	O
other	O
than	O
their	O
actual	O
size	O
,	O
the	O
danger	O
is	O
that	O
the	O
features	O
will	O
be	O
distorted	O
to	O
the	O
degree	O
that	O
they	O
are	O
no	O
longer	O
recognizable	O
to	O
map	O
readers	O
,	O
making	O
them	O
less	O
useful	O
.	O
</s>
<s>
As	O
with	O
map	B-Application
projections	I-Application
,	O
the	O
tradeoffs	O
inherent	O
in	O
cartograms	B-Application
have	O
led	O
to	O
a	O
wide	O
variety	O
of	O
strategies	O
,	O
including	O
manual	O
methods	O
and	O
dozens	O
of	O
computer	O
algorithms	O
that	O
produce	O
very	O
different	O
results	O
from	O
the	O
same	O
source	O
data	O
.	O
</s>
<s>
The	O
quality	O
of	O
each	O
type	O
of	O
cartogram	B-Application
is	O
typically	O
judged	O
on	O
how	O
accurately	O
it	O
scales	O
each	O
feature	O
,	O
as	O
well	O
as	O
on	O
how	O
(	O
and	O
how	O
well	O
)	O
it	O
attempts	O
to	O
preserve	O
some	O
form	O
of	O
recognizability	O
in	O
the	O
features	O
,	O
usually	O
in	O
two	O
aspects	O
:	O
shape	O
and	O
topological	O
relationship	O
(	O
i.e.	O
,	O
retained	O
adjacency	O
of	O
neighboring	O
features	O
)	O
.	O
</s>
<s>
It	O
is	O
likely	O
impossible	O
to	O
preserve	O
both	O
of	O
these	O
,	O
so	O
some	O
cartogram	B-Application
methods	O
attempt	O
to	O
preserve	O
one	O
at	O
the	O
expense	O
of	O
the	O
other	O
,	O
some	O
attempt	O
a	O
compromise	O
solution	O
of	O
balancing	O
the	O
distortion	O
of	O
both	O
,	O
and	O
other	O
methods	O
do	O
not	O
attempt	O
to	O
preserve	O
either	O
one	O
,	O
sacrificing	O
all	O
recognizability	O
to	O
achieve	O
another	O
goal	O
.	O
</s>
<s>
The	O
area	O
cartogram	B-Application
is	O
by	O
far	O
the	O
most	O
common	O
form	O
;	O
it	O
scales	O
a	O
set	O
of	O
region	O
features	O
,	O
usually	O
administrative	O
districts	O
such	O
as	O
counties	O
or	O
countries	O
,	O
such	O
that	O
the	O
area	O
of	O
each	O
district	O
is	O
directly	O
proportional	O
to	O
a	O
given	O
variable	O
.	O
</s>
<s>
The	O
various	O
taxonomies	O
tend	O
to	O
agree	O
on	O
the	O
following	O
general	O
types	O
of	O
area	O
cartograms	B-Application
.	O
</s>
<s>
This	O
is	O
a	O
type	O
of	O
contiguous	O
cartogram	B-Application
that	O
uses	O
a	O
single	O
parametric	O
mathematical	O
formula	O
(	O
such	O
as	O
a	O
polynomial	O
curved	O
surface	O
)	O
to	O
distort	O
space	O
itself	O
to	O
equalize	O
the	O
spatial	O
distribution	O
of	O
the	O
chosen	O
variable	O
,	O
rather	O
than	O
distorting	O
the	O
individual	O
features	O
.	O
</s>
<s>
Because	O
of	O
this	O
distinction	O
,	O
some	O
have	O
preferred	O
to	O
call	O
the	O
result	O
a	O
pseudo-cartogram	O
.	O
</s>
<s>
Tobler	O
's	O
first	O
computer	O
cartogram	B-Application
algorithm	O
was	O
based	O
on	O
this	O
strategy	O
,	O
for	O
which	O
he	O
developed	O
the	O
general	O
mathematical	O
construct	O
on	O
which	O
his	O
and	O
subsequent	O
algorithms	O
are	O
based	O
.	O
</s>
<s>
This	O
approach	O
first	O
models	O
the	O
distribution	O
of	O
the	O
chosen	O
variable	O
as	O
a	O
continuous	O
density	O
function	O
(	O
usually	O
using	O
a	O
least	B-Algorithm
squares	I-Algorithm
fitting	I-Algorithm
)	O
,	O
then	O
uses	O
the	O
inverse	O
of	O
that	O
function	O
to	O
adjust	O
the	O
space	O
such	O
that	O
the	O
density	O
is	O
equalized	O
.	O
</s>
<s>
Also	O
called	O
irregular	O
cartograms	B-Application
or	O
deformation	O
cartograms	B-Application
,	O
This	O
is	O
a	O
family	O
of	O
very	O
different	O
algorithms	O
that	O
scale	O
and	O
deform	O
the	O
shape	O
of	O
each	O
district	O
while	O
maintaining	O
adjacent	O
edges	O
.	O
</s>
<s>
This	O
approach	O
has	O
its	O
roots	O
in	O
the	O
early	O
20th	O
Century	O
cartograms	B-Application
of	O
Haack	O
and	O
Weichel	O
and	O
others	O
,	O
although	O
these	O
were	O
rarely	O
as	O
mathematically	O
precise	O
as	O
current	O
computerized	O
versions	O
.	O
</s>
<s>
This	O
is	O
perhaps	O
the	O
simplest	O
method	O
for	O
constructing	O
a	O
cartogram	B-Application
,	O
in	O
which	O
each	O
district	O
is	O
simply	O
reduced	O
or	O
enlarged	O
in	O
size	O
according	O
to	O
the	O
variable	O
without	O
altering	O
its	O
shape	O
at	O
all	O
.	O
</s>
<s>
Although	O
they	O
are	O
usually	O
referred	O
to	O
as	O
Dorling	O
cartograms	B-Application
after	O
Daniel	O
Dorling	O
's	O
1996	O
algorithm	O
first	O
facilitated	O
their	O
construction	O
,	O
these	O
are	O
actually	O
the	O
original	O
form	O
of	O
cartogram	B-Application
,	O
dating	O
back	O
to	O
Levasseur	O
(	O
1876	O
)	O
and	O
Raisz	O
(	O
1934	O
)	O
.	O
</s>
<s>
These	O
often	O
look	O
like	O
proportional	O
symbol	O
maps	O
,	O
and	O
some	O
consider	O
them	O
to	O
be	O
a	O
hybrid	O
between	O
the	O
two	O
types	O
of	O
thematic	B-Application
map	I-Application
.	O
</s>
<s>
The	O
result	O
looks	O
much	O
like	O
a	O
treemap	B-Application
diagram	I-Application
,	O
although	O
the	O
latter	O
is	O
generally	O
sorted	O
by	O
size	O
rather	O
than	O
geography	O
.	O
</s>
<s>
In	O
this	O
approach	O
(	O
also	O
called	O
block	O
or	O
regular	O
cartograms	B-Application
)	O
,	O
each	O
shape	O
is	O
not	O
just	O
scaled	O
or	O
warped	O
,	O
but	O
is	O
reconstructed	O
from	O
a	O
discrete	O
tessellation	B-Algorithm
of	O
space	O
,	O
usually	O
into	O
squares	O
or	O
hexagons	O
.	O
</s>
<s>
Each	O
cell	O
of	O
the	O
tessellation	B-Algorithm
represents	O
a	O
constant	O
value	O
of	O
the	O
variable	O
(	O
e.g.	O
,	O
5000	O
residents	O
)	O
,	O
so	O
the	O
number	O
of	O
whole	O
cells	O
to	O
be	O
occupied	O
can	O
be	O
calculated	O
(	O
although	O
rounding	O
error	O
often	O
means	O
that	O
the	O
final	O
area	O
is	O
not	O
exactly	O
proportional	O
to	O
the	O
variable	O
)	O
.	O
</s>
<s>
Thus	O
,	O
these	O
cartograms	B-Application
are	O
usually	O
homomorphic	O
and	O
at	O
least	O
partially	O
contiguous	O
.	O
</s>
<s>
Several	O
examples	O
of	O
block	O
cartograms	B-Application
were	O
published	O
during	O
the	O
2016	O
U.S.	O
presidential	O
election	O
season	O
by	O
The	O
Washington	O
Post	O
,	O
the	O
FiveThirtyEight	O
blog	O
,	O
and	O
the	O
Wall	O
Street	O
Journal	O
,	O
among	O
others	O
.	O
</s>
<s>
The	O
major	O
disadvantage	O
of	O
this	O
type	O
of	O
cartogram	B-Application
has	O
traditionally	O
been	O
that	O
they	O
had	O
to	O
be	O
constructed	O
manually	O
,	O
but	O
recently	O
algorithms	O
have	O
been	O
developed	O
to	O
automatically	O
generate	O
both	O
square	O
and	O
hexagonal	O
mosaic	O
cartograms	B-Application
.	O
</s>
<s>
While	O
an	O
area	O
cartogram	B-Application
manipulates	O
the	O
area	O
of	O
a	O
polygon	O
feature	O
,	O
a	O
linear	O
cartogram	B-Application
manipulates	O
linear	O
distance	O
on	O
a	O
line	O
feature	O
.	O
</s>
<s>
Distance	O
cartograms	B-Application
are	O
also	O
useful	O
for	O
comparing	O
such	O
concepts	O
among	O
different	O
geographic	O
features	O
.	O
</s>
<s>
A	O
distance	O
cartogram	B-Application
may	O
also	O
be	O
called	O
a	O
central-point	O
cartogram	B-Application
.	O
</s>
<s>
A	O
common	O
use	O
of	O
distance	O
cartograms	B-Application
is	O
to	O
show	O
the	O
relative	O
travel	O
times	O
and	O
directions	O
from	O
vertices	O
in	O
a	O
network	O
.	O
</s>
<s>
For	O
example	O
,	O
on	O
a	O
distance	O
cartogram	B-Application
showing	O
travel	O
time	O
between	O
cities	O
,	O
the	O
less	O
time	O
required	O
to	O
get	O
from	O
one	O
city	O
to	O
another	O
,	O
the	O
shorter	O
the	O
distance	O
on	O
the	O
cartogram	B-Application
will	O
be	O
.	O
</s>
<s>
When	O
it	O
takes	O
a	O
longer	O
time	O
to	O
travel	O
between	O
two	O
cities	O
,	O
they	O
will	O
be	O
shown	O
as	O
further	O
apart	O
in	O
the	O
cartogram	B-Application
,	O
even	O
if	O
they	O
are	O
physically	O
close	O
together	O
.	O
</s>
<s>
Distance	O
cartograms	B-Application
are	O
also	O
used	O
to	O
show	O
connectivity	O
.	O
</s>
<s>
Though	O
the	O
exact	O
time	O
and	O
distance	O
from	O
one	O
location	O
to	O
another	O
is	O
distorted	O
,	O
these	O
cartograms	B-Application
are	O
still	O
useful	O
for	O
travel	O
and	O
analysis	O
.	O
</s>
<s>
Both	O
area	O
and	O
linear	O
cartograms	B-Application
adjust	O
the	O
base	O
geometry	O
of	O
the	O
map	O
,	O
but	O
neither	O
has	O
any	O
requirements	O
for	O
how	O
each	O
feature	O
is	O
symbolized	O
.	O
</s>
<s>
For	O
linear	O
cartograms	B-Application
,	O
line	O
width	O
can	O
be	O
scaled	O
as	O
a	O
flow	B-Application
map	I-Application
to	O
represent	O
a	O
variable	O
such	O
as	O
traffic	O
volume	O
.	O
</s>
<s>
For	O
area	O
cartograms	B-Application
,	O
it	O
is	O
very	O
common	O
to	O
fill	O
each	O
district	O
with	O
a	O
color	O
as	O
a	O
choropleth	O
map	O
.	O
</s>
<s>
For	O
example	O
,	O
has	O
used	O
this	O
technique	O
to	O
map	O
topics	O
relating	O
to	O
global	O
social	O
issues	O
,	O
such	O
as	O
poverty	O
or	O
malnutrition	O
;	O
a	O
cartogram	B-Application
based	O
on	O
total	O
population	O
is	O
combined	O
with	O
a	O
choropleth	O
of	O
a	O
socioeconomic	O
variable	O
,	O
giving	O
readers	O
a	O
clear	O
visualization	O
of	O
the	O
number	O
of	O
people	O
living	O
in	O
underprivileged	O
conditions	O
.	O
</s>
<s>
Another	O
option	O
for	O
diagrammatic	O
cartograms	B-Application
is	O
to	O
subdivide	O
the	O
shapes	O
as	O
charts	O
(	O
commonly	O
a	O
pie	B-Application
chart	I-Application
)	O
,	O
in	O
the	O
same	O
fashion	O
often	O
done	O
with	O
proportional	O
symbol	O
maps	O
.	O
</s>
<s>
One	O
of	O
the	O
first	O
cartographers	O
to	O
generate	O
cartograms	B-Application
with	O
the	O
aid	O
of	O
computer	O
visualization	O
was	O
Waldo	O
Tobler	O
of	O
UC	O
Santa	O
Barbara	O
in	O
the	O
1960s	O
.	O
</s>
<s>
Prior	O
to	O
Tobler	O
's	O
work	O
,	O
cartograms	B-Application
were	O
created	O
by	O
hand	O
(	O
as	O
they	O
occasionally	O
still	O
are	O
)	O
.	O
</s>
<s>
The	O
National	O
Center	O
for	O
Geographic	O
Information	O
and	O
Analysis	O
located	O
on	O
the	O
UCSB	O
campus	O
maintains	O
an	O
online	O
with	O
resources	O
regarding	O
cartograms	B-Application
.	O
</s>
<s>
A	O
number	O
of	O
software	O
packages	O
generate	O
cartograms	B-Application
.	O
</s>
<s>
Most	O
of	O
the	O
available	O
cartogram	B-Application
generation	O
tools	O
work	O
in	O
conjunction	O
with	O
other	O
GIS	B-Application
software	I-Application
tools	O
as	O
add-ons	O
or	O
independently	O
produce	O
cartographic	O
outputs	O
from	O
GIS	O
data	O
formatted	O
to	O
work	O
with	O
commonly	O
used	O
GIS	O
products	O
.	O
</s>
<s>
Examples	O
of	O
cartogram	B-Application
software	O
include	O
ScapeToad	O
,	O
Cart	O
,	O
and	O
the	O
Cartogram	B-Application
Processing	O
Tool	O
(	O
an	O
ArcScript	O
for	O
ESRI	O
's	O
ArcGIS	B-Application
)	O
,	O
which	O
all	O
use	O
the	O
Gastner-Newman	O
algorithm	O
.	O
</s>
<s>
The	O
CRAN	O
package	O
provides	O
an	O
implementation	O
of	O
a	O
rectangular	O
cartogram	B-Application
algorithm	O
.	O
</s>
<s>
Year	O
Author	O
Algorithm	O
Type	O
Shape	O
preservation	O
Topology	O
preservation	O
1973ToblerRubber	O
map	O
method	O
area	O
contiguouswith	O
distortion	O
Yes	O
,	O
but	O
not	O
guaranteed	O
1976OlsonProjector	O
method	O
area	O
noncontiguousyes	O
No	O
1978Kadmon	O
,	O
ShlomiPolyfocal	O
projection	B-Application
distance	O
radial	O
Unknown	O
Unknown	O
1984Selvin	O
et	O
al.DEMP	O
(	O
Radial	O
Expansion	O
)	O
methodarea	O
contiguouswith	O
distortion	O
Unknown	O
1985Dougenik	O
et	O
al.Rubber	O
Sheet	O
Distortion	O
method	O
area	O
contiguouswith	O
distortion	O
Yes	O
,	O
but	O
not	O
guaranteed	O
1986ToblerPseudo-Cartogram	O
methodarea	O
contiguouswith	O
distortion	O
Yes	O
1987SnyderMagnifying	O
glass	O
azimuthal	O
map	B-Application
projections	I-Application
distance	O
radial	O
Unknown	O
Unknown	O
1989	O
et	O
al.Piezopleth	O
mapsarea	O
contiguouswith	O
distortion	O
Unknown	O
1990TorgusonInteractive	O
polygon	O
zipping	O
methodarea	O
contiguouswith	O
distortion	O
Unknown	O
1990DorlingCellular	O
Automata	O
Machine	O
methodarea	O
contiguouswith	O
distortionYes	O
1993Gusein-Zade	O
,	O
TikunovLine	O
Integral	O
methodarea	O
contiguouswith	O
distortion	O
Yes	O
1996DorlingCircular	O
cartogramarea	O
noncontiguousno	O
(	O
circles	O
)	O
No	O
1997Sarkar	O
,	O
BrownGraphical	O
fisheye	O
views	O
distance	O
radial	O
Unknown	O
Unknown	O
1997Edelsbrunner	O
,	O
WaupotitschCombinatorial-based	O
approacharea	O
contiguouswith	O
distortion	O
Unknown	O
1998Kocmoud	O
,	O
HouseConstraint-based	O
approacharea	O
contiguouswith	O
distortion	O
Yes	O
2001Keim	O
,	O
North	O
,	O
PanseCartoDrawarea	O
contiguouswith	O
distortion	O
Yes	O
,	O
algorithmically	O
guaranteed	O
2004Gastner	O
,	O
NewmanDiffusion-based	O
methodGastner	O
,	O
Michael	O
T	O
.	O
and	O
Mark	O
E	O
.	O
J	O
.	O
Newman	O
,	O
"	O
Diffusion-based	O
method	O
for	O
producing	O
density-equalizing	O
maps.	O
"	O
</s>
