The Location of Optimal Object Colors with More Than Two Transitions

The chromaticity diagram associated with the CIE 1931 color matching functions is shown to be slightly non-convex. While having no impact on practical colorimetric computations, the non-convexity does have a significant impact on the shape of some optimal object color reflectance distributions associated with the outer surface of the object color solid. Instead of the usual two-transition Schr\"odinger form, many optimal colors exhibit higher transition counts. A linear programming formulation is developed and is used to locate where these higher-transition optimal object colors reside on the object color solid surface.