The Geometry of Colour - Softcover

Centore, Paul

Softcover

ISBN 10: 099902910X ISBN 13: 9780999029107

Publisher: Paul Centore, 2017

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The Geometry Of Colour is intended for specialist and non-specialists alike, who are curious about a surprising application of the easily understood, but little known, geometric objects called zonohedra. A zonohedron is a special case of the Minkowski sum (also called the vector sum), which "adds" two shapes to produce a new shape. For instance, adding a square and a much smaller circle produces a slightly larger square, but with rounded corners. To add two line segments, sweep the end of one segment over the length of the other, resulting in a parallelogram. A zonohedron results from adding multiple line segments, but in three dimensions rather than two. Zonohedra are convex and rotationally symmetric, and typically have two pointed vertices, at an originating and terminating point. They are of interest because their geometric structure encodes combinatorial relations among their generating line segments. The Geometry Of Colour applies the mathematical theory of zonohedra in an unexpected setting: colour science. More specifically, color matching (quantifying when two isolated coloured lights appear identical) and its implications are presented through a series of geometric constructions. Three seemingly unrelated areas (human colour vision, colour correction for cameras, and electronic display gamuts) are shown to share a common zonohedral foundation. The zonohedral structure is then used to demonstrate some important known results, as well as to shed some light on current areas of research. Manipulation of appropriate models in three dimensions motivates most of the constructions and demonstrations, makes them easy to visualize, and highlights issues for algorithm development. To appeal to as wide an audience as possible, the book emphasizes the naturalness of the geometric constructions, and gives many concrete examples. Though it is mathematically rigorous, and assumes a knowledge of basic linear algebra, the spatio-visual presentation should make it accessible and understandable even to readers without such knowledge. Colour itself of course is universally understood, and the science of colour rests on a solid empirical and theoretical basis. The Geometry Of Colour portrays colour science through a new lens, offering the reader a surprising presentation of a familiar topic.

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