The isotropic correlation function of plane figures: the triangle case

Details The isotropic correlation function of plane figures: the triangle case The isotropic correlation function of plane figures: the triangle case

2010-06-08

arxiv.org/abs/1006.1496v1

Physics

Mathematical Physics

11 pages, 2 figures

Scientific paper

The knowledge of the isotropic correlation function of a plane figure is useful to determine the correlation function of the cylinders having the plane figure as right-section and a given height as well as to analyze the out of plane intensity collected in grazing incidence small-angle scattering from a film formed by a particulate collection of these cylinders. The correlation function of plane polygons can always be determined in closed algebraic form. Here we report its analytic expression for the case of a triangle. The expressions take four different forms that depend on the relative order among the sides and the heights of the triangle.

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