The shortest path computation is important in industrial automation, especially for robot and autonomous vehicle navigation. However, most of the computations concentrate on computing the shortest path between two points within a polygon. The common approach for handling a bounded domain with free form boundary is to convert the domain into a polygon by boundary approximation so that the conventional computing algorithms can be used. Such an approximation affects the accuracy of the path. This article presents an approach to compute the shortest path between two given points in a free form boundary domain without any boundary approximation. This is addressed geometrically by imaginably placing a source at one of the points which radiates the shortest paths to various points of the domain. Some shortest paths are deflected by the geometry of the boundary so that they are no longer straight lines. Based on the deflections of the shortest paths, the bounded domain is partitioned into a set of subdomains. A tree is then constructed to show the relationships among these subdomains. The shortest path between two points is obtained from this tree.

Issue Section:
Research Papers
Keywords:
shortest path, free form boundary domain, partition
Topics:
Algorithms, Computation, Geometry

References

1.
Rohnert
,
H.
,
1986
, “
Shortest Paths in the Plane With Convex Polygonal Obstacles
,”
Inf. Process. Lett.
,
23
(
2
), pp.
71
–
76
.10.1016/0020-0190(86)90045-1
Google Scholar
Crossref
Search ADS
 
2.
Toussaint
,
G. T.
,
1986
, “
Shortest Path Solves Edge-to-Edge Visibility in a Polygon
,”
Pattern Recogn. Lett.
4
(
3
), pp.
165
–
170
.10.1016/0167-8655(86)90015-2
Google Scholar
Crossref
Search ADS
 
3.
Ghosh
,
S. K.
, and
Mount
,
D. M.
,
1987
, “
An Output Sensitive Algorithm for Computing Visibility Graphs
,”
Proceeding SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
, pp.
11
–
19
.
4.
Hershberger
,
J.
, and
Suri
,
S.
,
1999
, “
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
,”
SIAM J. Sci. Comput.
,
28
(
6
), pp.
2215
–
2256
.10.1137/S0097539795289604
Google Scholar
Crossref
Search ADS
 
5.
Kapoor
,
S.
,
Maheshwari
,
S. N.
, and
Mitchell
,
J. S. B.
,
1997
, “
An Efficient Algorithm for Euclidean Shortest Paths Among Polygonal Obstacles in the Plane
,”
Discrete Comput. Geom.
,
18
(
4
), pp.
377
–
383
.10.1007/PL00009323
Google Scholar
Crossref
Search ADS
 
6.
Ling
,
H.
, and
Jacobs
,
D. W.
,
2007
, “
Shape Classification Using the Inner-Distance
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
29
(
2
), pp.
289
–
299
.
Google Scholar
Crossref
Search ADS
 
7.
Lee
,
D. T.
, and
Preparata
,
F. P.
,
1984
, “
Euclidean Shortest Paths in the Presence of Rectilinear Barriers
,”
Networks
,
14
(
3
), pp.
393
–
410
.10.1002/net.3230140304
Google Scholar
Crossref
Search ADS
 
8.
Melissaratos
,
E. A.
, and
Souvaine
,
D. L.
,
1992
, “
Shortest Paths Help Solve Geometric Optimization Problems in Planar Regions
,”
SIAM J. Sci. Comput.
,
21
(
4
), pp.
601
–
638
.10.1137/0221038
Google Scholar
Crossref
Search ADS
 
9.
Bourgin
,
R. D.
, and
Howe
S. E.
,
1993
, “
Shortest Curves in Planar Regions With Curved Boundary
,”
Theor. Comput. Sci.
,
112
(
2
), pp.
215
–
53
.10.1016/0304-3975(93)90019-P
Google Scholar
Crossref
Search ADS
 
10.
Fabel
,
P.
,
1999
, “
Shortest Arcs in Closed Planar Disks Vary Continuously With the Boundary
,”
Topol. Appl.
,
95
(
9
), pp.
75
–
83
.10.1016/S0166-8641(97)00275-7
Google Scholar
Crossref
Search ADS
 
11.
Ram
,
S. B.
, and
Ramanathan
,
M.
,
2012
, “
The Shortest Path in a Simply-Connected Domain Having a Curved Boundary
,”
Comput.-Aided Des.
,
43
(
8
), pp.
923
–
933
.
12.
Li
,
F.
, and
Klette
,
R.
2006
, “
Finding the Shortest Path Between Two Points in a Simple Polygon by Applying a Rubberband Algorithm
,” The Pacific-Rim Symposium on Image and Video technology, pp.
280
–
291
.10.1007/11949534
15.
Boissonnat
,
J. D.
, and
Teillaud
,
M.
,
2006
,
Effective Computational Geometry for Curves and Surfaces
,
Springer
.
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