<s>
In	O
computational	O
geometry	O
,	O
a	O
constrained	B-Algorithm
Delaunay	I-Algorithm
triangulation	I-Algorithm
is	O
a	O
generalization	O
of	O
the	O
Delaunay	B-Algorithm
triangulation	I-Algorithm
that	O
forces	O
certain	O
required	O
segments	O
into	O
the	O
triangulation	O
as	O
edges	O
,	O
unlike	O
the	O
Delaunay	B-Algorithm
triangulation	I-Algorithm
itself	O
which	O
is	O
based	O
purely	O
on	O
the	O
position	O
of	O
a	O
given	O
set	O
of	O
vertices	O
without	O
regard	O
to	O
how	O
they	O
should	O
be	O
connected	O
by	O
edges	O
.	O
</s>
<s>
It	O
can	O
be	O
computed	O
efficiently	O
and	O
has	O
applications	O
in	O
geographic	O
information	O
systems	O
and	O
in	O
mesh	B-Architecture
generation	I-Architecture
.	O
</s>
<s>
The	O
input	O
to	O
the	O
constrained	B-Algorithm
Delaunay	I-Algorithm
triangulation	I-Algorithm
problem	O
is	O
a	O
planar	O
straight-line	O
graph	O
,	O
a	O
set	O
of	O
points	O
and	O
non-crossing	O
line	O
segments	O
in	O
the	O
plane	O
.	O
</s>
<s>
The	O
constrained	B-Algorithm
Delaunay	I-Algorithm
triangulation	I-Algorithm
of	O
this	O
input	O
is	O
a	O
triangulation	O
of	O
its	O
convex	O
hull	O
,	O
including	O
all	O
of	O
the	O
input	O
segments	O
as	O
edges	O
,	O
and	O
using	O
only	O
the	O
vertices	O
of	O
the	O
input	O
.	O
</s>
<s>
This	O
generalizes	O
the	O
defining	O
property	O
of	O
two-dimensional	O
Delaunay	B-Algorithm
triangulations	I-Algorithm
of	O
points	O
,	O
that	O
each	O
edge	O
have	O
a	O
circle	O
through	O
its	O
two	O
endpoints	O
containing	O
no	O
other	O
vertices	O
.	O
</s>
<s>
Jonathan	O
Shewchuk	O
has	O
generalized	O
this	O
definition	O
to	O
constrained	B-Algorithm
Delaunay	I-Algorithm
triangulations	I-Algorithm
of	O
three-dimensional	O
inputs	O
,	O
systems	O
of	O
points	O
and	O
non-crossing	O
segments	O
and	O
triangles	O
in	O
three-dimensional	O
space	O
;	O
however	O
,	O
not	O
every	O
input	O
of	O
this	O
type	O
has	O
a	O
constrained	B-Algorithm
Delaunay	I-Algorithm
triangulation	I-Algorithm
according	O
to	O
his	O
generalized	O
definition	O
.	O
</s>
<s>
Several	O
algorithms	O
for	O
computing	O
constrained	B-Algorithm
Delaunay	I-Algorithm
triangulations	I-Algorithm
of	O
planar	O
straight-line	O
graphs	O
in	O
time	O
are	O
known	O
.	O
</s>
<s>
The	O
constrained	B-Algorithm
Delaunay	I-Algorithm
triangulation	I-Algorithm
of	O
a	O
simple	O
polygon	O
can	O
be	O
constructed	O
in	O
linear	O
time	O
.	O
</s>
<s>
Constrained	B-Algorithm
Delaunay	I-Algorithm
triangulation	I-Algorithm
can	O
also	O
be	O
used	O
in	O
Delaunay	B-Algorithm
refinement	I-Algorithm
methods	O
for	O
mesh	B-Architecture
generation	I-Architecture
,	O
as	O
a	O
way	O
to	O
force	O
the	O
mesh	O
to	O
conform	O
with	O
the	O
domain	O
boundaries	O
as	O
it	O
is	O
being	O
refined	O
.	O
</s>
