If lambda is a single number,
then this algorithm generates a realisation
of the uniform Poisson process (also known as
Complete Spatial Randomness, CSR) inside the window win with
intensity lambda (points per unit area).
If lambda is a function, then this algorithm generates a realisation
of the inhomogeneous Poisson process with intensity function
lambda(x,y,…) at spatial location (x,y)
inside the window win.
The function lambda must work correctly with vectors x
and y.
If lmax is given,
it must be an upper bound on the values of lambda(x,y,…)
for all locations (x, y)
inside the window win. That is, we must have
lambda(x,y,…) <= lmax for all locations (x,y).
If this is not true then the results of
the algorithm will be incorrect.
If lmax is missing or NULL,
an approximate upper bound is computed by finding the maximum value
of lambda(x,y,…)
on a grid of locations (x,y) inside the window win,
and adding a safety margin equal to 5 percent of the range of
lambda values. This can be computationally intensive,
so it is advisable to specify lmax if possible.
If lambda is a pixel image object of class "im"
(see im.object), this algorithm generates a realisation
of the inhomogeneous Poisson process with intensity equal to the
pixel values of the image. (The value of the intensity function at an
arbitrary location is the pixel value of the nearest pixel.)
The argument win is ignored;
the window of the pixel image is used instead. It will be converted
to a rectangle if possible, using rescue.rectangle.
To generate an inhomogeneous Poisson process
the algorithm uses ``thinning'': it first generates a uniform
Poisson process of intensity lmax,
then randomly deletes or retains each point, independently of other points,
with retention probability
\(p(x,y) = \lambda(x,y)/\mbox{lmax}\).
For marked point patterns, use rmpoispp.