<s>
In	O
computer	O
graphics	O
,	O
tessellation	B-Algorithm
is	O
the	O
dividing	O
of	O
datasets	O
of	O
polygons	B-General_Concept
(	O
sometimes	O
called	O
vertex	O
sets	O
)	O
presenting	O
objects	O
in	O
a	O
scene	O
into	O
suitable	O
structures	O
for	O
rendering	O
.	O
</s>
<s>
Especially	O
for	O
real-time	B-General_Concept
rendering	I-General_Concept
,	O
data	O
is	O
tessellated	B-Algorithm
into	I-Algorithm
triangles	I-Algorithm
,	O
for	O
example	O
in	O
OpenGL	B-Application
4.0	I-Application
and	O
Direct3D	O
11	O
.	O
</s>
<s>
A	O
key	O
advantage	O
of	O
tessellation	B-Algorithm
for	O
realtime	B-General_Concept
graphics	I-General_Concept
is	O
that	O
it	O
allows	O
detail	O
to	O
be	O
dynamically	O
added	O
and	O
subtracted	O
from	O
a	O
3D	O
polygon	B-Algorithm
mesh	I-Algorithm
and	O
its	O
silhouette	O
edges	O
based	O
on	O
control	O
parameters	O
(	O
often	O
camera	O
distance	O
)	O
.	O
</s>
<s>
In	O
Direct3D	O
11	O
pipeline	O
(	O
a	O
part	O
of	O
DirectX	O
11	O
)	O
,	O
the	O
graphics	B-Algorithm
primitive	I-Algorithm
is	O
the	O
patch	O
.	O
</s>
<s>
The	O
tessellator	O
generates	O
a	O
triangle-based	O
tessellation	B-Algorithm
of	O
the	O
patch	O
according	O
to	O
tessellation	B-Algorithm
parameters	O
such	O
as	O
the	O
TessFactor	O
,	O
which	O
controls	O
the	O
degree	O
of	O
fineness	O
of	O
the	O
mesh	B-Algorithm
.	O
</s>
<s>
The	O
tessellation	B-Algorithm
,	O
along	O
with	O
shaders	O
such	O
as	O
a	O
Phong	O
shader	O
,	O
allows	O
for	O
producing	O
smoother	O
surfaces	O
than	O
would	O
be	O
generated	O
by	O
the	O
original	O
mesh	B-Algorithm
.	O
</s>
<s>
By	O
offloading	O
the	O
tessellation	B-Algorithm
process	O
onto	O
the	O
GPU	B-Architecture
hardware	O
,	O
smoothing	O
can	O
be	O
performed	O
in	O
real	O
time	O
.	O
</s>
<s>
Tessellation	B-Algorithm
can	O
also	O
be	O
used	O
for	O
implementing	O
subdivision	O
surfaces	O
,	O
level	O
of	O
detail	O
scaling	O
and	O
fine	O
displacement	O
mapping	O
.	O
</s>
<s>
OpenGL	B-Application
4.0	I-Application
uses	O
a	O
similar	O
pipeline	O
,	O
where	O
tessellation	B-Algorithm
into	O
triangles	O
is	O
controlled	O
by	O
the	O
Tessellation	B-Algorithm
Control	O
Shader	O
and	O
a	O
set	O
of	O
four	O
tessellation	B-Algorithm
parameters	O
.	O
</s>
<s>
In	O
computer-aided	B-Application
design	I-Application
the	O
constructed	O
design	O
is	O
represented	O
by	O
a	O
boundary	B-Algorithm
representation	I-Algorithm
topological	O
model	O
,	O
where	O
analytical	O
3D	O
surfaces	O
and	O
curves	O
,	O
limited	O
to	O
faces	O
,	O
edges	O
,	O
and	O
vertices	O
,	O
constitute	O
a	O
continuous	O
boundary	O
of	O
a	O
3D	O
body	O
.	O
</s>
<s>
So	O
they	O
are	O
approximated	O
(	O
tessellated	O
)	O
with	O
a	O
mesh	B-Algorithm
of	O
small	O
,	O
easy-to-analyze	O
pieces	O
of	O
3D	O
volume	O
—	O
usually	O
either	O
irregular	O
tetrahedra	O
,	O
or	O
irregular	O
hexahedra	O
.	O
</s>
<s>
The	O
mesh	B-Algorithm
is	O
used	O
for	O
finite	B-Application
element	I-Application
analysis	I-Application
.	O
</s>
<s>
The	O
mesh	B-Algorithm
of	O
a	O
surface	O
is	O
usually	O
generated	O
per	O
individual	O
faces	O
and	O
edges	O
(	O
approximated	O
to	O
polylines	O
)	O
so	O
that	O
original	O
limit	O
vertices	O
are	O
included	O
into	O
mesh	B-Algorithm
.	O
</s>
<s>
To	O
ensure	O
that	O
approximation	O
of	O
the	O
original	O
surface	O
suits	O
the	O
needs	O
of	O
further	O
processing	O
,	O
three	O
basic	O
parameters	O
are	O
usually	O
defined	O
for	O
the	O
surface	B-Algorithm
mesh	I-Algorithm
generator	O
:	O
</s>
<s>
The	O
maximum	O
allowed	O
distance	O
between	O
the	O
planar	O
approximation	O
polygon	B-General_Concept
and	O
the	O
surface	O
(	O
known	O
as	O
"	O
sag	O
"	O
)	O
.	O
</s>
<s>
This	O
parameter	O
ensures	O
that	O
mesh	B-Algorithm
is	O
similar	O
enough	O
to	O
the	O
original	O
analytical	O
surface	O
(	O
or	O
the	O
polyline	O
is	O
similar	O
to	O
the	O
original	O
curve	O
)	O
.	O
</s>
<s>
The	O
maximum	O
allowed	O
size	O
of	O
the	O
approximation	O
polygon	B-General_Concept
(	O
for	O
triangulations	O
it	O
can	O
be	O
maximum	O
allowed	O
length	O
of	O
triangle	O
sides	O
)	O
.	O
</s>
<s>
The	O
maximum	O
allowed	O
angle	O
between	O
two	O
adjacent	O
approximation	O
polygons	B-General_Concept
(	O
on	O
the	O
same	O
face	O
)	O
.	O
</s>
<s>
This	O
parameter	O
ensures	O
that	O
even	O
very	O
small	O
humps	O
or	O
hollows	O
that	O
can	O
have	O
significant	O
effect	O
to	O
analysis	O
will	O
not	O
disappear	O
in	O
mesh	B-Algorithm
.	O
</s>
<s>
An	O
algorithm	O
generating	O
a	O
mesh	B-Algorithm
is	O
typically	O
controlled	O
by	O
the	O
above	O
three	O
and	O
other	O
parameters	O
.	O
</s>
<s>
Some	O
types	O
of	O
computer	O
analysis	O
of	O
a	O
constructed	O
design	O
require	O
an	O
adaptive	B-Algorithm
mesh	I-Algorithm
refinement	I-Algorithm
,	O
which	O
is	O
a	O
mesh	B-Algorithm
made	O
finer	O
(	O
using	O
stronger	O
parameters	O
)	O
in	O
regions	O
where	O
the	O
analysis	O
needs	O
more	O
detail	O
.	O
</s>
