A terminating algorithm is developed for the problem of finding the point of smallest Euclidean norm in the convex hull of a given finite point set in Euclidean n-space, or equivalently for finding an "optimal" hyperplane separating a given point from a given finite point set. Its efficiency and accuracy are investigated, and its extension to the separation of two sets and other convex programm...

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 s...

1 I n t r o d u c t i o n This paper investigates the problem of realizing a given graph G as a "nearest neighbour graph" of a set P of points in the plane. Roughly speaking, a "nearest neighbour graph" is a geometric graph formed from a set of points in the plane by joining two points if one is the nearest neighbour of the other. Fig. 1. A mutual nearest neighbour graph One specific kind of ne...

Several types of nearest neighbor (NN) search have been proposed and studied in the context of spatial databases. The most common type is the point NN query, which retrieves the nearest neighbors of an input point. Such a query, however, is usually meaningless in highly dynamic environments where the query point or the database objects move/change over time. In this paper we study alternative f...

for assessment and comparison of measuring density methods of festuca ovina, bromus tomentellus and prangos ferulacea, three plants communities are selected. in all of plant community, reference area was defined and samples 7000 (70*100) square meter was selected. whole the area, sampling was accumplished as systematic-random. in each area, 5 transect 100 meter are established. then in areas 70...

We show that a Poisson cluster point process is a nearest-neighbour Markov point process 2] if the clusters have uniformly bounded diameter. It is typically not a nite-range Markov point process in the sense of Ripley and Kelly 12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighb...