Shape elongation from optimal encasing rectangles. (English summary) Comput. Math. Appl. 60 (2010), no. 7, 2035–2042. Summary: “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 shape elongation measure defined in this way 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 th
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