Patent ID: 8451521

Claim:
A method for determining a locus of colorant formulations that produce a desired color on a four colorant marking device, the method comprising: retrieving a LUT comprising a plurality of sub-cubes arrayed on a structured grid in a four dimensional colorant space of a color marking device, each vertex of each sub-cube being associated with a colorant formulation and a corresponding output color of said color marking device; tesselating said sub-cubes into a plurality of pentahedrons; approximating a relationship between colorant formulation and color in each pentahedron by a linear function; identifying a pentahedron that encompasses a desired color; determining colorant formulation values at two locations where a locus penetrates the faces of said identified pentahedron; and repeating until a boundary of a gamut of said color marking device has been reached: continuing said locus into pentahedrons which are adjacent to the faces of the pentahedron penetrated by said locus; determining colorant formulation values at two locations where said locus penetrates said faces of each adjacent pentahedron; and seeding a next iteration with each of said adjacent pentahedrons.