1. A method for determining colorant control values for a color imaging device having four or more colorants, comprising: a) defining a color mapping for a set of paths through a three-channel color space relating the three-channel color space values along that path to corresponding colorant control values for the four or more colorants of the color imaging device; b) defining a color mapping function for the three-channel color space relating the three-channel color space values to colorant control values for the four or more colorants of the color imaging device by interpolating between the color mapping defined for the set of paths, including: i) for each input three-channel color space value, slicing through the three-channel color space with a plane that includes the input three-channel color space value; ii) identifying slice vertices corresponding to the intersections between the set of paths and the plane; iii) using the color mapping for the set of paths to determine vertex colorant control values corresponding to the three-channel color space value at the slice vertices; and iv) interpolating between the vertex colorant control values to determine colorant control values corresponding to the input three-channel color space value; c) forming a forward three-channel color model relating the three-channel color space values to device-independent color values by using the color mapping function to relate the three-channel color space values to colorant control values for the four or more colorants of the color imaging device, and then further relating the colorant control values for the four or more colorants of the color imaging device to corresponding device-independent color values; d) inverting the forward three-channel color model to determine an inverse three-channel color model relating the device-independent color values to the three-channel color space values; and e) combining the inverse three-channel color model and the color mapping function to determine an inverse device color model relating device-independent color values to colorant control values for the four or more colorants of the color imaging device.