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Old 05-28-2019, 05:30 PM   #19
Agemegos
 
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Join Date: May 2005
Location: Oz
Default Re: [Space] Mapping Large Flat Areas

Quote:
Originally Posted by Rupert View Post
Reading that box, and seeing where the formula came from, I think that the 2D equivalent would be based off the area of a circle, etc. rather than volume, and would thus come out at about: 0.8 x (A/N)^0.5

I could be utterly wrong, though.
The p.d.f. for nearest neighbour at distance x, for a uniform random distribution (i.e a Poisson process) is given here as 1-e^-(density * volume). For the case of a Poisson process on a 2-D plane that ends up implying that the average nearest-neighbour distance is 0.5/sqrt(number/area).
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