Vtyjkyuk

I'm looking to describe a multivariate normal distribution in cylindrical coordinates with truncated/bound height, i.e. it has 3 axes $r$, $theta$ and $h$.

Obviously angle $theta$ is a warped normal distribution and I want to describe radius $r$ as a folded normal distribution. I also want to have the height $h$ to be bound to the range $h_1$ to $h_2$ hence a truncated normal distribution. However at the same time these axes aren't independent hence the correlations $rho_rtheta$, $rho_rh$ and $rho_htheta$ must be accounted for.

I also know that for a standard multivariate normal distribution in $x$, $y$ and $z$ coordinates this can be done as
$$
mathbfSigma =left[ beginmatrix
sigma _x^2 & rho _xysigma _xsigma _y & rho _xzsigma _xsigma _z \
rho _xysigma _xsigma _y & sigma _y^2 & rho _yzsigma _ysigma _z \
rho _xzsigma _xsigma _z & rho _yzsigma _ysigma _z & sigma _z^2 \
endmatrix right]
$$
$$
f_mathbf X(x,y,z) = fracexpleft(-frac 1 2 (mathbf x-boldsymbolmu)^mathrmTboldsymbolSigma^-1(mathbf x-boldsymbolmu)right)sqrt(2pi)^k
$$
However this works because the 3 distributions are equivalent, how can this be done for the different types of normal distribution.

Note I have also considered that I could generate random vector with a standard multivariate normal distribution in $r$, $theta$ and $h$ than, convert the values i.e. $theta = theta' mod 2pi$ and $r = |r'|$ to account for the Warpped and Folded Distributions, however I'm not sure how to apply this to the Truncated Distribution. Since My ultimate goal is the generation of the random vectors a solution to this is equally good as to one on the definition of the distribution and mapping of a uniformly distributed 3-vector with values in the range 0 to 1.