Line segment picking is the process of picking line segments at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random line segment is one such that the position of each endpoint has a uniform distribution within the shape. In the case of convex shapes, any line segment so picked lies entirely inside the shape. It is possible to compute the mean line segment length in closed form for some simple shapes. In some cases, a closed form can also be obtained for the full probability density function of line segment lengths.
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