<s>
Geometric	B-Application
modeling	I-Application
is	O
a	O
branch	O
of	O
applied	O
mathematics	O
and	O
computational	O
geometry	O
that	O
studies	O
methods	O
and	O
algorithms	O
for	O
the	O
mathematical	O
description	O
of	O
shapes	O
.	O
</s>
<s>
The	O
shapes	O
studied	O
in	O
geometric	B-Application
modeling	I-Application
are	O
mostly	O
two	O
-	O
or	O
three-dimensional	O
(	O
solid	O
figures	O
)	O
,	O
although	O
many	O
of	O
its	O
tools	O
and	O
principles	O
can	O
be	O
applied	O
to	O
sets	O
of	O
any	O
finite	O
dimension	O
.	O
</s>
<s>
Today	O
most	O
geometric	B-Application
modeling	I-Application
is	O
done	O
with	O
computers	O
and	O
for	O
computer-based	O
applications	O
.	O
</s>
<s>
Two-dimensional	O
models	O
are	O
important	O
in	O
computer	O
typography	B-Application
and	O
technical	B-Application
drawing	I-Application
.	O
</s>
<s>
Three-dimensional	O
models	O
are	O
central	O
to	O
computer-aided	B-Application
design	I-Application
and	I-Application
manufacturing	I-Application
(	O
CAD/CAM	O
)	O
,	O
and	O
widely	O
used	O
in	O
many	O
applied	O
technical	O
fields	O
such	O
as	O
civil	O
and	O
mechanical	O
engineering	O
,	O
architecture	O
,	O
geology	O
and	O
medical	B-Application
image	I-Application
processing	I-Application
.	O
</s>
<s>
Geometric	B-Application
models	I-Application
are	O
usually	O
distinguished	O
from	O
procedural	O
and	O
object-oriented	O
models	O
,	O
which	O
define	O
the	O
shape	O
implicitly	O
by	O
an	O
opaque	O
algorithm	O
that	O
generates	O
its	O
appearance	O
.	O
</s>
<s>
They	O
are	O
also	O
contrasted	O
with	O
digital	B-Algorithm
images	I-Algorithm
and	O
volumetric	B-Algorithm
models	I-Algorithm
which	O
represent	O
the	O
shape	O
as	O
a	O
subset	O
of	O
a	O
fine	O
regular	O
partition	O
of	O
space	O
;	O
and	O
with	O
fractal	B-Application
models	O
that	O
give	O
an	O
infinitely	O
recursive	O
definition	O
of	O
the	O
shape	O
.	O
</s>
<s>
However	O
,	O
these	O
distinctions	O
are	O
often	O
blurred	O
:	O
for	O
instance	O
,	O
a	O
digital	B-Algorithm
image	I-Algorithm
can	O
be	O
interpreted	O
as	O
a	O
collection	O
of	O
colored	O
squares	O
;	O
and	O
geometric	O
shapes	O
such	O
as	O
circles	O
are	O
defined	O
by	O
implicit	O
mathematical	O
equations	O
.	O
</s>
<s>
Also	O
,	O
a	O
fractal	B-Application
model	O
yields	O
a	O
parametric	O
or	O
implicit	O
model	O
when	O
its	O
recursive	O
definition	O
is	O
truncated	O
to	O
a	O
finite	O
depth	O
.	O
</s>
