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Research Papers

# Computation of the Shortest Path in a Bounded Domain With Free Form Boundary by Domain Partitioning

[+] Author and Article Information
ChiKit Au

Faculty of Engineering,
University of Waikato,
Private Bag 3105
Hamilton 3260, New Zealand
e-mail: ckau@waikato.ac.nz

Youngsheng Ma

Department of Mechanical Engineering,
University of Alberta,
Edmonton T6G 2G8, Canada
e-mail: yongsheng.ma@ualberta.ca

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF Computing AND INFORMATION Science IN ENGINEERING. Manuscript received November 25, 2013; final manuscript received November 27, 2013; published online February 26, 2014. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 14(2), 021004 (Feb 26, 2014) (11 pages) Paper No: JCISE-13-1263; doi: 10.1115/1.4026183 History: Received November 25, 2013; Revised November 27, 2013

## Abstract

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.

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## Figures

Fig. 1

The shortest path between two points

Fig. 3

The shortest path between two points in a bounded domain with curved boundary

Fig. 4

The shortest paths from various points in a bounded domain to a point P

Fig. 5

Tangents computations

Fig. 6

The detail views of the curve sources

Fig. 7

Domain partitioning

Fig. 8

A tree structure to show the source relationships

Fig. 9

The shortest path generation

Fig. 10

The shortest path computation between two points in an bounded domain with palm shape

Fig. 11

The shortest path between point P and various positions of point Q

Fig. 12

The shortest path computation between two relocated points P and Q

Fig. 13

The regeneration of the shortest path due to the boundary variation

Fig. 14

The shortest path from point Q to point P

Fig. 15

The different domain partitioning with respect to two points

Fig. 16

Generation of the shortest path for an object with dimension

Fig. 17

Tangent computation in brute force approach

Fig. 18

The worst situation of the algorithm for partitioning a domain with 4 concave segments

Fig. 19

An example generated by the algorithm

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