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•
(
Region I
) region between the half-lines
L
1
P
and
L
2
P
. Shortest path:
SL
;
•
(
Region I'
) region between the two arc circles
C
1
P
and
C
2
P
. Shortest path:
SL
;
•
(
Region II
) region between the circle arc
C
2
P
(bound of
Region I'
) and the spiral
T
2
P
(bound of
Region V
), symmetric to
Region II'
. Shortest path:
T
2
−
SL
;
•
(
Region III
) region between the half-line
L
1
P
(bound of
Region I
) and the spiral
T
1
P
(bound of
Region V
), symmetric to
Region III'
. Shortest path:
SL
−
T
1
P
;
T2
P
IV
Q
Q
III'
L2
P
C1
P
T1
P
Q
Q
II'
II
Q
I'
P
I
Q
T2
P
C2
P
L1
P
III
Q
T1
P
V
Q
(a)
Q
Q
Q
Q
Q
Q
Q
III'
VI
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
IV
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
II'
Q
Q
Q
Q
Q
Q
Q
I'
II
P
P
P
P
P
P
P
I
Q
Q
Q
Q
Q
Q
Q
V
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
VII
III
Q
Q
Q
Q
Q
Q
Q
(b)
Fig. 18.8
Shortest paths: (a) according to [2]; and (b) according to [30]
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