unfoldr (version 0.2)

simSpheroidSystem: Simulation of spheroid system

Description

Simulation of Poisson spheroid system

Usage

simSpheroidSystem(theta, size, shape = "const", orientation = "rbetaiso",
  stype = c("prolate", "oblate"), rjoint = NULL, box = list(c(0, 1)),
  pl = 0)

Arguments

theta

simulation parameters

size

name of random generating function for size distribution

shape

scalar shape parameter

orientation

name of random generating function for orientation distribution

stype

spheroid type

rjoint

name of joint random generating function

box

simulation box

pl

print level

Value

• list of spheroids either of class prolate or oblate

Details

The function simulates a Poisson spheroid system according to the supplied simulation parameter theta in a predefined simulation box. For demonstration purposes there are three types of major-axis length distributions available which are set by the size argument.

Further the function simulates either stype="prolate" or stype='oblate' spheroids. For the directional orientation of the spheroid's major-axis one has the choice of a uniform (runifdir), isotropic random planar (rbetaiso, see reference) or von Mises-Fisher (rvMisesFisher) distribution. The simulation box is a list containing of vector arguments which correspond to the lower and upper points in each direction. If the argument box has only one element, i.e. list(c(0,1), the same extent is used for the other dimensions. If rjoint names a joint random generating function then argument size is ignored.

The argument pl denotes the print level of output information during simulation. Currently, only pl=0 for no output and pl>100 for some additional info is implemented.

References

Ohser, J. and Schladitz, K. 3D images of materials structures Wiley-VCH, 2009

Examples

# directional distribution
rbetaiso <- function(kappa) {
   phi <- runif(1,0,1)*2*pi
   q <- runif(1,0,1)
   theta=acos((1-2*q)/sqrt(kappa*kappa-(1-2*q)*(1-2*q)*(kappa*kappa-1)))
   list("u"=c(sin(theta)*cos(phi),sin(theta)*sin(phi),cos(theta)),
		   "theta"=theta,"phi"=phi)					
}
   
# multivariate size distribution and orientation distribution 
rmulti <- function(m,s,kappa) {	
   dir <- rbetaiso(kappa)
   M <- chol(s, pivot = TRUE)
   M <- M[, order(attr(M, "pivot"))]
   x <- exp(matrix(m,nrow=1) +
          matrix(rnorm(ncol(s)), nrow = 1, byrow = TRUE) %*%M)
   a <- min(x)
   b <- max(x)
   
   list("a"=a,"b"=b,"u"=dir$u,"shape"=a/b,
        "theta"=dir$theta, "phi"=dir$phi)

}

set.seed(1234)
sigma <- matrix(c(0.1,0.1,0.1,0.25), ncol=2)
theta <- list("lam"=500,"rmulti"=list("m"=c(-3.0,-2.0),"s"=sigma,"kappa"=0.5))
S <- simSpheroidSystem(theta,rjoint="rmulti",box=list(c(0,5)),pl=101)

# Spheroids with lognormal distributed length of major axis
theta <- list("lam"=1000,"size"=list("meanlog"=-2.5,"sdlog"=0.5),
              "shape"=list("s"=0.5),
              "orientation"=list("kappa"=1.5))
S <- simSpheroidSystem(theta,size="rlnorm",orientation="rbetaiso",
                       box=list(c(0,5)),pl=101)

# Spheroids of constant sizes
theta <- list("lam"=1000,"size"=list(0.25),"shape"=list("s"=0.5),
              "orientation"=list("kappa"=1))
S <- simSpheroidSystem(theta,size="const",orientation="rbetaiso",
                       box=list(c(0,5)),pl=101)