<s>
Simplicial	O
continuation	O
,	O
or	O
piecewise	B-Algorithm
linear	I-Algorithm
continuation	I-Algorithm
(	O
Allgower	O
and	O
Georg	O
)	O
,	O
is	O
a	O
one-parameter	O
continuation	B-Algorithm
method	I-Algorithm
which	O
is	O
well	O
suited	O
to	O
small	O
to	O
medium	O
embedding	O
spaces	O
.	O
</s>
<s>
The	O
value	O
of	O
at	O
the	O
corners	O
of	O
the	O
triangle	O
defines	O
a	O
unique	O
Piecewise	O
Linear	O
interpolant	B-Algorithm
to	O
over	O
each	O
triangle	O
.	O
</s>
<s>
Over	O
the	O
whole	O
mesh	O
of	O
triangles	O
,	O
this	O
piecewise	O
linear	O
interpolant	B-Algorithm
is	O
continuous	O
.	O
</s>
<s>
The	O
contour	O
of	O
the	O
interpolant	B-Algorithm
on	O
an	O
individual	O
triangle	O
is	O
a	O
line	O
segment	O
(	O
it	O
is	O
an	O
interval	O
on	O
the	O
intersection	O
of	O
two	O
planes	O
)	O
.	O
</s>
<s>
The	O
contour	O
of	O
the	O
piecewise	O
linear	O
interpolant	B-Algorithm
is	O
a	O
set	O
of	O
curves	O
made	O
up	O
of	O
these	O
line	O
segments	O
.	O
</s>
<s>
Piecewise	B-Algorithm
linear	I-Algorithm
continuation	I-Algorithm
is	O
similar	O
to	O
contour	O
plotting	O
(	O
Dobkin	O
,	O
Levy	O
,	O
Thurston	O
and	O
Wilks	O
)	O
,	O
but	O
in	O
higher	O
dimensions	O
.	O
</s>
<s>
If	O
F(x )	O
maps	O
into	O
,	O
there	O
is	O
a	O
unique	O
linear	O
interpolant	B-Algorithm
on	O
an	O
'	O
(	O
n-1	O
)	O
'	O
-dimensional	O
simplex	O
which	O
agrees	O
with	O
the	O
function	O
values	O
at	O
the	O
vertices	O
of	O
the	O
simplex	O
.	O
</s>
<s>
They	O
determine	O
the	O
value	O
of	O
the	O
unique	O
interpolant	B-Algorithm
by	O
the	O
formula	O
:	O
</s>
