🚀 go-pugleaf

Hi reader,

For a 2-dimensional homogenous Poisson distribution, 
p(i,A) = exp(-A*d)*(A*d)^i/i! where p(i,A) is the probability
of i occurrences in an area A, d is the spatial density
(number of occurrences per unit area). Similar to the
one-dimensional Poisson distribution, 2-dimensional one
also has the memoryless property. 

To simulate a 2-dimensional Poisson environemnt, one can
divide an area A into many small areas with equal size B.
If B is small enough, p(0,B) + p(1,B) is very close to 1
and hence, p(i,B), for i > 1, can be discarded. For each
small area B, the probability of occurrence is p(1,B) and
the probability of no occurrence is p(0,B), and this is
a binominal process. If B is very small, one can assume
that the location of the occurrence is the center of the 
area B If this process repeats for each area B, the 
distribution of of any area in A is a 2-dimensional
Poisson. However, such a simulation takes long time, does
anyone has better suggestion for a faster simulation of
a 2-dimensional Poisson environment? If you have any
suggestion, please email to me (email address victorw@ee.ubc.ca).
Your help will be very much appreciated.

Victor