<s>
It	O
deals	O
with	O
the	O
construction	O
and	O
representation	O
of	O
free-form	O
curves	O
,	O
surfaces	O
,	O
or	O
volumes	O
and	O
is	O
closely	O
related	O
to	O
geometric	B-Application
modeling	I-Application
.	O
</s>
<s>
The	O
most	O
important	O
instruments	O
here	O
are	O
parametric	O
curves	O
and	O
parametric	O
surfaces	O
,	O
such	O
as	O
Bézier	O
curves	O
,	O
spline	B-Algorithm
curves	I-Algorithm
and	O
surfaces	O
.	O
</s>
<s>
An	O
important	O
non-parametric	O
approach	O
is	O
the	O
level-set	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Geometric	B-Application
models	I-Application
can	O
be	O
built	O
for	O
objects	B-Language
of	O
any	O
dimension	O
in	O
any	O
geometric	O
space	O
.	O
</s>
<s>
Both	O
2D	B-Algorithm
and	O
3D	O
geometric	B-Application
models	I-Application
are	O
extensively	O
used	O
in	O
computer	O
graphics	O
.	O
</s>
<s>
2D	B-Algorithm
models	I-Algorithm
are	O
important	O
in	O
computer	O
typography	B-Application
and	O
technical	B-Application
drawing	I-Application
.	O
</s>
<s>
3D	O
models	O
are	O
central	O
to	O
computer-aided	B-Application
design	I-Application
and	I-Application
manufacturing	I-Application
,	O
and	O
many	O
applied	O
technical	O
fields	O
such	O
as	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	B-Application
models	I-Application
,	O
which	O
define	O
the	O
shape	O
implicitly	O
by	O
an	O
algorithm	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
;	O
and	O
with	O
mathematical	O
models	O
such	O
as	O
the	O
zero	O
set	O
of	O
an	O
arbitrary	O
polynomial	O
.	O
</s>
<s>
However	O
,	O
the	O
distinction	O
is	O
often	O
blurred	O
:	O
for	O
instance	O
,	O
geometric	O
shapes	O
can	O
be	O
represented	O
by	O
objects	B-Language
;	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
the	O
modeling	O
of	O
fractal	B-Application
objects	B-Language
often	O
requires	O
a	O
combination	O
of	O
geometric	O
and	O
procedural	O
techniques	O
.	O
</s>
<s>
Geometric	O
problems	O
originating	O
in	O
architecture	O
can	O
lead	O
to	O
interesting	O
research	O
and	O
results	O
in	O
geometry	O
processing	O
,	O
computer-aided	B-Application
geometric	I-Application
design	I-Application
,	O
and	O
discrete	O
differential	O
geometry.	O
<	O
ref>H	O
.	O
</s>
<s>
In	O
architecture	O
,	O
geometric	O
design'''	O
is	O
associated	O
with	O
the	O
pioneering	O
explorations	O
of	O
Chuck	O
Hoberman	O
into	O
transformational	O
geometry	O
as	O
a	O
design	O
idiom	O
,	O
and	O
applications	O
of	O
this	O
design	O
idiom	O
within	O
the	O
domain	O
of	O
architectural	B-Algorithm
geometry	I-Algorithm
.	O
</s>
