Authors: Dražić, Slobodan
Ralević, Nebojša
Žunić, Joviša 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Shape elongation from optimal encasing rectangles
Journal: Computers and Mathematics with Applications
Volume: 60
Issue: 7
First page: 2035
Last page: 2042
Issue Date: 1-Oct-2010
Rank: M21
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2010.07.043
Abstract: 
Let S be a shape with a polygonal boundary. We show that the boundary of the maximally elongated rectangle R(S) which encases the shape S contains at least one edge of the convex hull of S. Such a nice property enables a computationally efficient construction of R(S). In addition, we define the elongation of a given shape S as the ratio of the length of R(S) (determined by the longer edge of R(S)) and the width of R(S) (determined by the shorter edge of R(S)) and show that a so defined shape elongation measure has several desirable properties. Several examples are given in order to illustrate the behavior of the new elongation measure. As a by-product, of the method developed here, we obtain a new method for the computation of the shape orientation, where the orientation of a given shape S is defined by the direction of the longer edge of R(S).
Keywords: Computational geometry | Elongation | Encasing rectangle | Image processing | Shape
Publisher: Elsevier
Project: Serbian Ministry of Science and Technology, grant ON144018

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