Biomedical Engineering Reference
In-Depth Information
Figure 5.
Basic types of intersections between a plane and a simplex in 3D.
Unlike marching methods, continuation algorithms attempt to trace the sur-
face into neighboring simplices [13]. Thus, given a transverse simplex, the algo-
rithm searches its neighbors to continue surface reconstruction. The key idea is
to generate the combinatorial manifold (set of transverse simplices) that holds the
isosurface.
The following definition will be useful. Suppose that two simplices
σ
0
and
∈
σ
0
and
v
∈
σ
1
, which have a common face and vertices
v
σ
1
both opposite to
the common face. The process of obtaining
v
from
v
is called
pivoting
.Wenow
present the basic continuation algorithm [13].
Algorithm 1
PL Generation Algorithm
Find a transverse triangle
σ
0
=
{
;
V
(
σ
0
)=set of vertices of
σ
0
while
V
(
σ
)
=
∅
σ
0
}
∈
do
for some
σ
∈
such that
V
(
σ
)
=
∅
get
σ
;
get
v
V
(
σ
)
obtain
σ
from
σ
by pivoting
v
into
v
if
σ
is not transverse
then
drop
v
from
V
(
σ
)
else
if
σ
∈
then
drop
v
from
V
(
σ
),
v
∈
from
V
(
σ
)
else
⇐
=
+
σ
V
(
σ
)
⇐
= set of vertices of
σ
drop
v
from
V
(
σ
),
v
from
V
(
σ
)
end if
end if
end while
