Geometry of Multiprimary Display Colors II: Metameric Control Sets and Gamut Tiling Color Control Functions

Abstract

Multiprimary displays reproduce colors by using combinations of four or more lights that are referred to as primaries. A display control vector defines the relative intensities of the primaries and determines the rendered color. For multiprimary displays, a color may be reproduced using multiple alternative control vectors. We provide a complete characterization of the Metameric Control Set (MCS), i.e., the set of control vectors that reproduce a given color on the display. Specifically, we show that MCS is a convex polytope whose vertices are control vectors obtained from (parallelepiped) tilings of the gamut, i.e., the range of colors that the display can produce. The mathematical framework that we develop: (a) characterizes gamut tilings in terms of fundamental building blocks called facet spans that we identify and define, (b) establishes that the vertices of the MCS are fully characterized by the tilings of the gamut, and (c) introduces a methodology for the efficient enumeration of gamut tilings. The framework reveals the fundamental inter-relations between the geometry of the MCS and the geometry of the gamut developed in a companion Part I paper, and provides insight into alternative strategies for color control. Our characterization of tilings and the strategy for their enumeration also advance knowledge in geometry, providing new approaches and computational results for the enumeration of tilings for a broad class of zonotopes in R 3 . INDEX TERMS multiprimary displays, metameric control sets, color gamut, color control, color control function, zonotope tiling, polar zonohedra