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Best Relative Placement: a New Ability for Spatial Processing

MALEK, M.R.^{1} and HAHN, M.^{2}

^{1} University of Tehran, Iran

^{2} University of Applied Sciences - Stuttgart, Germany

Email: malek@ncc.neda.net.ir
Key words: Nonlinear Model, Spatial Analysis, Least-Squares Method

The placement is not a new problem. The placement of some subjects with
respect to given constraints frequently takes place in urban planning,
agriculture, network design in geodesy, and so on. If relative relations
between subjects are given, we call it relative placement. Consequently,
we define "best relative placement" (BRP) as: Non-precise relative relations,
like near, far, etc., are given for n subjects. There are n(n+1)/2 independent
relations in addition to requested some spatial constraints. BRP is a procedure
to find the best location of each subject with respect to a given region
such that all constraints and relations are fulfilled.

In this paper, a new spatial function called "best relative placement"
is developed. Two different approaches for solving a BRP problem are discussed
which are based on the least-squares method and interval mathematics. It
will be shown that interval mathematics behaves well even for nonlinear
programming tasks. The least-squares and interval methods are examined
using real data.