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Transformation of Chromaticity Diagrams

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Abstract

The paper shows how, by geometric construction, it is possible to construct corresponding points on a pair of chromaticity diagrams. To do this requires only that four pairs of corresponding points be known; all other pairs of corresponding points are then uniquely determined. The method finds specific application where one of the chromaticity diagrams is arbitrary (such as one drawn in terms of the primaries of a colorimeter), and the other is the CIE diagram. It is then possible to transform the colorimeter readings directly to the CIE diagram, provided four calibrating points are known. It is shown that four corresponding lines in the two diagrams will enable complete mapping of corresponding points.

The Appendix gives a formal proof of the projective properties of chromaticity diagrams and serves as a rigorous basis for the methods developed in the body of the paper.

© 1954 Optical Society of America

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On Projective Transformations of the CIE-Chromaticity Diagram

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J. Opt. Soc. Am. 46(11) 982-986 (1956)

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Equations (20)

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