1. A method for mapping spectral colors in an Interim Connection Space of a full spectral space based on a colorimetric gamut map in a color space, the method comprising: accessing a spectral color value in the Interim Connection Space; transforming the spectral color value into a colorimetric color value in the color space; mapping, by using a processor, the colorimetric color value into mapped colorimetric color value in a first subspace of the Interim Connection Space, wherein mapping the colorimetric color value comprises gamut-mapping the colorimetric color value using the colorimetric gamut map, followed by identifying the color space with the first subspace; determining an intersection of a spectral gamut in the Interim Connection Space and an affine subspace characterized by the mapped colorimetric color value; and projecting the spectral color value onto the intersection, wherein the first subspace is an orthogonal complement of a null space of a transformation from the Interim Connection Space to the color space.