Abstract
Displays that render colors using combinations of more than three lights
are referred to as multiprimary displays. For multiprimary displays, the
gamut, i.e., the range of colors that can be rendered using additive
combinations of an arbitrary number of light sources (primaries) with
modulated intensities, is known to be a zonotope, which is a specific
type of convex polytope. Under the specific three-dimensional setting
relevant for color representation and the constraint of physically
meaningful nonnegative primaries, we develop a complete, cohesive, and
directly usable mathematical characterization of the geometry of the
multiprimary gamut zonotope that immediately identifies the surface
facets, edges, and vertices and provides a parallelepiped tiling of the
gamut. We relate the parallelepiped tilings of the gamut, that arise
naturally in our characterization, to the flexibility in color control
afforded by displays with more than four primaries, a relation that is
further analyzed and completed in a Part II companion paper. We
demonstrate several applications of the geometric representations we
develop and highlight how the paper advances theory required for
multiprimary display modeling, design, and color management and provides
an integrated view of past work on on these topics. Additionally, we
highlight how our work on gamut representations connects with and
furthers the study of three-dimensional zonotopes in geometry.