I am trying to implement a particle filter to track multiple objects. During the propagation phase I need to take N samples from a three dimensional probability distribution, which does not fit known distribution types. In a 1D distribution I would just create the cumulative distribution function, invert it and take random samples from that - can I do something similar with higher dimensional distributions?
I am implementing in Java by the way, so just giving me an R function is not going to help me too much.