Forma, Vol. 24 (No. 3), pp. 111-116, 2009
Original Paper

Rectilinear Distance in Rotated Regular Point Patterns

Masashi Miyagawa

Department of Ecosocial System Engineering, University of Yamanashi, 4-3-11 Takeda, Kofu, Yamanashi 400-8511, Japan E-mail address:

(Received November 2, 2009; Accepted February 3, 2010)

Abstract. This paper examines the relationship between road directions and the rectilinear distance in regular point patterns. We derive the distributions of the rectilinear distances to the nearest and the second nearest points in rotated regular point patterns. These distributions demonstrate that road directions significantly affect the rectilinear distances. As an application of the nearest and the second nearest distances, we consider a facility location problem in which customers are serviced by either the nearest or the second nearest facility.

Keywords: Road Direction, Distance Distribution, Average Distance, Maximum Distance

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