Technical Note—An Algorithm for Determining Whether m Given Demand Points Are on a Hemisphere or Not

Wen-Hsien Tsai, Maw-Sheng Chern and Tsong-Ming Lin
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Wen-Hsien Tsai: National Central University, Chung-Li, Taiwan, Republic of China
Maw-Sheng Chern: National Tsing Hua University, Hsin-Chu, Taiwan, Republic of China
Tsong-Ming Lin: National Taiwan Institute of Technology, Taipei, Taiwan, Republic of China

Transportation Science, 1991, vol. 25, issue 1, 91-97

Abstract: Location problems on a sphere can be solved easily by mathematical programming or geometrical methods if it is known that all the demand points are located on a hemisphere. This paper presents an algorithm for determining whether m given demand points are on a hemisphere or not. In this algorithm, the great circle is rotated successively until the hemisphere which contains the m given demand points is found or it becomes known using our criteria that the m given demand points are not on a hemisphere. The convergence of this algorithm is proved, and two illustrative examples are presented.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:25:y:1991:i:1:p:91-97

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