We go on to develop further analytic theory for the half-Gilbert model using stopping-set ideas once again, with some novel features. In this paper we explore this coincidence, mindful of the fact that, for one model, our results are from a simulation (with inherent sampling error).
Translation tessellation rectangle of flounder full#
We demonstrate the remarkable fact that plots of the two distributions appear to be identical when the intensity of seeds in the half model is twice that in the full model. For the half rectangular tessellation, we compute analytically, via recursion, a series expansion for the ray-length distribution, whilst, for the full rectangular version, we develop an accurate simulation technique, based in part on the stopping-set theory for Poisson processes (see Zuyev (1999)), to accomplish the same. In the half rectangular version, east- and south-growing rays do not interact with west and north rays. In the full rectangular version, lines extend either horizontally (east- and west-growing rays) or vertically (north- and south-growing rays) from seed points which form a Poisson point process, each ray stopping when another ray is met. We investigate the ray-length distributions for two different rectangular versions of Gilbert's tessellation (see Gilbert (1967)).
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