<s>
In	O
computer	O
graphics	O
,	O
a	O
nonobtuse	O
triangle	B-Algorithm
mesh	I-Algorithm
is	O
a	O
polygon	B-Algorithm
mesh	I-Algorithm
composed	O
of	O
a	O
set	O
of	O
triangles	O
in	O
which	O
no	O
angle	O
is	O
obtuse	O
,	O
i.e.	O
</s>
<s>
If	O
each	O
(	O
triangle	O
)	O
face	O
angle	O
is	O
strictly	O
less	O
than	O
90°	O
,	O
then	O
the	O
triangle	B-Algorithm
mesh	I-Algorithm
is	O
said	O
to	O
be	O
acute	O
.	O
</s>
<s>
Every	O
polygon	B-General_Concept
with	O
sides	O
has	O
a	O
nonobtuse	O
triangulation	O
with	O
triangles	O
(	O
expressed	O
in	O
big	O
O	O
notation	O
)	O
,	O
allowing	O
some	O
triangle	O
vertices	O
to	O
be	O
added	O
to	O
the	O
sides	O
and	O
interior	O
of	O
the	O
polygon	B-General_Concept
.	O
</s>
<s>
Nonobtuse	B-Algorithm
meshes	I-Algorithm
avoid	O
certain	O
problems	O
of	O
nonconvergence	O
or	O
of	O
convergence	O
to	O
the	O
wrong	O
numerical	O
solution	O
as	O
demonstrated	O
by	O
the	O
Schwarz	O
lantern	O
.	O
</s>
<s>
The	O
immediate	O
benefits	O
of	O
a	O
nonobtuse	O
or	O
acute	O
mesh	B-Algorithm
include	O
more	O
efficient	O
and	O
more	O
accurate	O
geodesic	O
computation	O
using	O
fast	B-Algorithm
marching	I-Algorithm
,	O
and	O
guaranteed	O
validity	O
for	O
planar	O
mesh	B-Algorithm
embeddings	O
via	O
discrete	O
harmonic	O
maps	O
.	O
</s>
