Random Distances Associated with Arbitrary Triangles: A Recursive Approach with an Arbitrary Reference Point




Ahmadi, Maryam
Pan, Jianping

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In this work, we propose a decomposition and recursion approach in order to obtain the distance distributions associated with arbitrary triangles. The focus of this work is to derive the distance dis- tributions from an arbitrary reference point to a random point within the triangle, where the reference point can be inside or outside of the triangle. Our approach is based on the distance distributions from a vertex of an arbitrary triangle to a random point inside. By decomposing the original triangle, using the probabilistic sum, and using the distance distributions from the vertex of the decomposed triangles, we obtain the desired distance distributions. We compare our analytical results with those of simulation, where a close match can be seen between them. Since any polygon can be decomposed into triangles, this approach also applies to the random distances from an arbitrary reference point to an arbitrary polygon, regardless convex or concave.



Random distances with a reference point, Distance distribution functions, Arbitrary triangles, Arbitrary polygons