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A zonohedral approach to optimal colours
Author(s) -
Centore Paul
Publication year - 2013
Publication title -
color research and application
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.393
H-Index - 62
eISSN - 1520-6378
pISSN - 0361-2317
DOI - 10.1002/col.20713
Subject(s) - chromaticity , constructive , computation , mathematics , simple (philosophy) , set (abstract data type) , confusion , space (punctuation) , computer science , algorithm , optics , artificial intelligence , process (computing) , physics , psychology , philosophy , epistemology , psychoanalysis , programming language , operating system
This article demonstrates that the CIE XYZ colour solid is a zonoid. An approximating zonohedral colour solid is constructed explicitly from a set of generating vectors, which are integrals of colour‐matching functions over narrow intervals of the visible spectrum. The zonohedral approach yields an intuitive, constructive proof of the Optimal Colour Theorem: the reflectance function of an optimal colour takes on only the values 0 or 1, with at most two transition wavelengths. In addition, zonohedral techniques can simplify computations: for example, optimal colours can be found without calculating transition wavelengths. Finally, zonohedra provide a simple, unified approach to colour space and eliminate much of the confusion arising from chromaticity diagrams. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2013