Optimal color primaries for three- and multiprimary wide gamut displays

Geometry of Multiprimary Display Colors I: Gamut and Color Control

“…Now we note that because the parallelepipeds in the righthand-side of (73) are essentially disjoint, the intersection of two parallelepipeds is contained within the boundary of both parallelepipeds. Combining this with the continuity and uniqueness of the CCF defined in (87) we can see that for any two parallelepipeds in (24) that have a non-empty intersection, the intersection is a proper face of both parallelepipeds, which completes the induction step for Clause 8 for Theorem 1.…”

“…Once these parameters have been computed, all the facets, edges, and vertices can be uniquely and exhaustively enumerated using ( 28), (31), and (32), respectively, to obtain the complete representation of the gamut boundary. We note that although Algorithm 1 obtains these gamut and CCF representations for a K primary gamut directly, without iterating on the number of primaries K, the sequence of the primaries in the primary matrix P does determine the parallelepiped tiling in (24), its associated CCF in (33), and the parallelepiped chains in Clause 9 associated with the pairs of opposing gamut facets in (28) for each J ∈ C 2 ( K ). We therefore refer to the representation in ( 24) as a progressiveby-primary gamut tiling and the associated CCF C (•) in ( 33) as the corresponding progressive-by-primary tiling CCF.…”

“…is then the representation of reproducible colors in the perceptual color space. Since F t1 (•) is a continuous one-to-one mapping, using (24), G F can alternatively be expressed as the essentially-disjoint union…”

“…The representation of the tristimulus gamut G and the perceptual gamut G F in (24) and (36), respectively, partition the gamut into essentially-disjoint sets: G is tiled by a set of parallelepipeds P(•), whose perceptual representations F t1 (P(•)) yield an essentially disjoint partition of G F . This geometrical representation can be conveniently exploited for the computation of the gamut volume in both tristimulus and perceptual color spaces.…”