1. A method for determining a set of n-dimensional colorant control signals that map to a point P in an m-dimensional color space where n>m, comprising: a) determining a forward device model that maps n-dimensional colorant control signals to m-dimensional color space signals in the m-dimensional color space; b) determining a set of n-dimensional colorant control signal simplexes that span a domain of the forward device model; c) determining a set of range space simplexes in the m-dimensional color space corresponding to the set of n-dimensional colorant control space signal simplexes by mapping the vertices of the n-dimensional colorant control signal simplexes into the m-dimensional color space using the forward device model; d) specifying a point P in the m-dimensional color space; and e) determining the set of n-dimensional colorant control signals that map to the point P in the m-dimensional color space, by performing m sequential slicing processes through the set of range space simplexes.