# Simulate a realization of Thomas-type cluster point process with complex inhomogeneities The means to simulate realizations from the Thomas-type cluster point process with complex inhomogeneities are provided. ```r rThomasInhom( kappa, alpha, omega, W, W_dil, betavec = NULL, alphavec = NULL, omegavec = NULL, z_beta = NULL, z_alpha = NULL, z_omega = NULL ) ``` ## Arguments - `kappa`: intensity or intensity function of the parent process, scalar or pixel image object of class `spatstat.geom::im()` from the `spatstat` package. - `alpha`: scalar, influences the mean number of points in individual clusters, see Details. - `omega`: scalar, influences the spread of individual clusters, see Details. - `W`: the observation window where the realization is to be generated, in the `spatstat.geom::owin()` format of the `spatstat` package. - `W_dil`: the observation window dilated by the assumed maximal cluster radius, as a binary mask with the same resolution as the covariates. - `betavec`: vector of parameters describing the dependence of the intensity function of the parent process on covariates in the list **z_beta**. - `alphavec`: vector of parameters describing the dependence of the mean number of points in a cluster on covariates in the list **z_alpha**. - `omegavec`: vector of parameters describing the dependence of the spread of the clusters on covariates in the list **z_omega**. - `z_beta`: list of covariates describing the intensity function of the parent process, each covariate being a pixel image as used in the `spatstat` package. - `z_alpha`: list of covariates describing the location-dependent mean number of points in a cluster, each covariate being a pixel image as used in the `spatstat` package. - `z_omega`: list of covariates describing the location-dependent scale of a cluster, each covariate being a pixel image as used in the `spatstat` package. ## Returns A planar point pattern, object of the type `spatstat.geom::ppp()` used in the `spatstat` package. ## Details A realization of a Thomas-type cluster point process model with possible inhomogeneity (described by covariates) are produced in any or all of the following model components: intensity function of the parent process, mean number of points in a cluster, scale of the clusters. Model parametrization is described in the documentation to the function `estintp()`. The parent process is generated in the dilated observation window **W_dil** to avoid edge-effects, the resulting point pattern is eventually truncated to the smaller observation window **W**. ## Examples ```r library(spatstat) # Unit square observation window: W <- owin() # Dilation of the observation window: W_dil <- dilation(W, 0.1) W_dil <- as.mask(W_dil) # Define covariates: f1 <- function(x, y) { x } f2 <- function(x, y) { y } f3 <- function(x, y) { 1 - (y - 0.5) ^ 2 } cov1 <- as.im(f1, W = W_dil) cov2 <- as.im(f2, W = W_dil) cov3 <- as.im(f3, W = W_dil) # Stationary Thomas process: X <- rThomasInhom(kappa = 50, alpha = log(10), omega = log(0.01), W = W, W_dil = W_dil) plot(X) # Thomas-type cluster process with inhomogeneity in all model components: X <- rThomasInhom(kappa = 10, betavec = c(1), z_beta = list(cov1), alpha = log(10), alphavec = c(1), z_alpha = list(cov2), omega = log(0.01), omegavec = c(1), z_omega = list(cov3), W = W, W_dil = W_dil) plot(X) ```

rThomasInhom function