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(
Succ
(
BF
1(
r
))) is not link-2 visible from
Succ
(
r
). If the vertex
BB
1(
r
)(
BF
1(
r
))
exists, we define the backward (forward) link-2 ray-shooting of
r
, denoted by
BB
2(
r
)(
BF
2(
r
)), to be the smallest (largest) boundary point such that no point
of
P
(
BB
2(
r
)
,BB
1(
r
)) (
P
(
BF
1(
r
)
,BF
2(
r
))) is link-2 visible from
Succ
(
r
). The
backward (forward) link-2 component of
r
is then defined as the boundary chain
P
[
BB
1(
r
)
,BB
2(
r
)] (
P
[
BF
2(
r
)
,BF
1(
r
)]). See Fig.
2
(a). Note that
P
[
r, B
(
r
)] is
always contained in the backward or forward link-2 component of
r
. Also, if
the forward component of
r
is non-redundant, we analogously define its back-
ward/forward link-2 ray-shooting and the backward/forward link-2 component
P
[
FB
1(
r
)
,FB
2(
r
)]/
P
[
FF
2(
r
)
,FF
1(
r
)]. See Fig.
2
(a). (In the above notion, the
first letter “B” (or “F”) stands for the original backward (or forward) component
of
r
.) Note that it is possible that only one of the backward and forward link-2
ray-shootings from
r
is defined. See Fig.
2
(b). (Since
P
is not
LR
-visible, at least
one of the backward and forward link-2 ray-shootings from
r
is defined.)
BF2(a)
BF1(a)
FB2(b)
c
FB1(b)
b
a
b
a
FF1(b)
BB1(c)
BF2(b
)
F
F1(a)
FF2(b)
BB1(a)
BB2(c)
FF2(a)
BF1(b)
BB2(a)
(b)
(a)
Fig. 2.
Link-2 ray-shootings and link-2 components.
We call the link-2 components, which are derived from the non-redundant
backward and forward components, the link-2
ʱ
-components and
ʲ
-components,
respectively. A link-2
ʱ
-component is
non-redundant
if it does not contain any
other link-2
ʱ
-component, no matter which is the forward or backward
ʱ
-component. For instance, the
ʱ
-component
P
[
BB
1(
c
)
,BB
2(
c
)] in Fig.
2
(b)
contains the
ʱ
-component
P
[
BF
2(
b
)
,BF
1(
b
)] and is thus redundant. (Since
P
is
not
LR
-visible, both the forward and backward link-2
ʱ
-components of a vertex
r
cannot be non-redundant simultaneously.) We make the analogous definition
for the non-redundant
ʲ
-components.
From the definition of link-2
ʱ
-components, the following observation can
simply be made. (The observation on the link-2
ʲ
-components can be made
analogously.)
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