Abstract
All modern theorists use affine geometry as a basis for the vector manifold representing color sensations. Angles and vector lengths have no meaning in affine geometry, and Euclidean vector addition does not apply. All color theories and color specification systems are but transformations in affine space. Color sensations are presumed to be isomorphic to affine geometry alone but both mathematical proof and empirical demonstration show the existence of a transformation for color vectors from affine to Euclidean space. When so transformed to Euclidean space, color vector lengths and direction cosines are invariant under rotation of reference axes; the configuration is stable absolutely, and color vectors add as force vectors in mechanics. New concepts are developed for the Euclidean color space and relationships to the older concepts of affine space (as luminance) are demonstrated.
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MacAdam, D. L. Dependence of color-mixture function on choice of primaries. Journal of the Optical Society of America, 1953, 43, 533–538.
MacAdam, D. L. Orthogonal color-mixture functions. Journal of the Optical Society of America, 1954, 44, 713–724.
Maxwell, J. C. On the theory of compound colours, and the relations of the colours of the spectrum. Philosphical Transactions of the Royal Society of London, 1860, 150, 57–84.
Schrödinger, E. Grundlinien einer Theorie der Farbenmetrik im Tagessehen. Annalen der Physik, 1920, 368, 397–456, 481-520.
Stiles, W. S., & Burch, J. M. N. P.L. Colour matching investigation: final report. Optica Acta, 1955, 6, 1–26.
Thornton, W. A. Three-color visual response. Journal of the Optical Society of America, 1972, 62, 457–459.
Thurstone, L. L. The vectors of mind. Chicago: University of Chicago Press, 1935.
Weyl, H. Space-time + matter. New York: Dutton, 1920.
Weyl, H. The classical groups: Their invariants and representations. Princeton, N. J: Princeton University Press, 1938.
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We acknowledge the resolute help and superb interrogation of Constantine Trahiotis. We are profoundly beholden to Harold W. Hake.
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Cohen, J., Friden, T.P. The Euclidean nature of color space. Bull. Psychon. Soc. 5, 159–161 (1975). https://doi.org/10.3758/BF03333234
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DOI: https://doi.org/10.3758/BF03333234