Simulating spatial point patterns that have spatial structure similar to that of given spatial point pattern

Dear list,

I have some spatial point pattern *X* distributed in polygon *wind* and I
wonder how can I simulate different point patterns that by their spatial
properties (for example, number of points, spatial autocorrelation of
intensity function and etc.) would resemble *X* spatial point pattern? I am
very new in spatial point pattern analysis, so I am not exactly sure what
parameters should I want to replicate in my simulations, nor do I know the
best methods to do so.

So far, I have tried a number of different methods, but none of these gave
me a satisfactory result.

I will share what I have tried:

   1. *rpoispp* function from *spatstat* with parameter ex=*X*. Number of
   points were different and simulated patterns of points seemed to have much
   more homogeneous distribution than *X*
   2. Estimate intensity of *X* with *density.ppp* and *nndensity*.
   Calculate variogram of intensity functions and feed sill and range
   parameters into *gstat* function to simulate random field *R*. Than I
   scaled *R* values so that the sum of them would be the same as sum of
   intensity values of *X* and minimum value of *R* would be 0. Then I used
   *rpoissp(R,wind)* to generate points. The problem was that the number of
   points was slightly different than that of *X* and distribution of
   points seemed not respectful of *R* image. Finally, intensities of
   generated point patterns exhibited different variograms.
   3. I also tried to scale *R* values from .1 to .9 and use them as
   probabilities in generating values of binary variable with many trials.
   Then I filtered the same number of most successful cases as there are
   points in *X* to get the locations of points. However, the resulting
   distribution of points was too respectful of *R* and autocorrelation of
   intensities of these points were different from that of *X*.
   4. Finally, with the help of *spsann* I tried simulated spatial
   annealing algorithm to optimize Kinhom function of random point pattern, so
   that this function would converge to that of *X*. It worked - functions
   looked very similar, but the problem is that I do not think that this is
   the right parameter to optimize, since visually point patterns were very
   different. Also, the calculation time was too long for me, as I will need
   to simulate many point patterns. But maybe this was due to poor choice of
   parameter values, as my understanding of how to use *spsann* is
   extremely limited. If that's the case and calculation time can be
   decreased, this method seems to be the most promising - all I need is to
   choose more suitable parameter to optimize for.

Thank you for your advice.

---
Ma student
Liudas Daumantas
Vilnius University