I have estimated the parameters of a non-homogeneous poisson space point process using Metropolis+gibbs from some observation data. I know:
$N$: Number of points inside my observation window
$\lambda$: Intensity function
and the parameters associated with this intensity function.
If I want to generate a pattern of points using the intensity function $\lambda$. This is possible with the function rpoint from the r library spatstat: https://stackoverflow.com/questions/33874879/how-to-generate-spatial-points-with-a-pattern
My question is how in general can I generate patterns of points for any distribution function assuming that I have done inference about the parameters already. I know that rpoint assumes independence between points but how can I generate a pattern of m points from a different point process, let's say the Area interaction point process assuming that I have estimated the parameters? I have read some about the reject sampling but is not straightforward to me how to do this.
By the way, the same r package has a function that brings a pattern of points for the area-interaction process but I can not specify the $m$ number of points to be generated.