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No, it’s not possible to have uniform color differences at all scales and in all directions in a 3-dimensional Euclidean space. If you go around a hue circle in
by jacobolus 9y ago
No, it’s not possible to have uniform color differences at all scales and in all directions in a 3-dimensional Euclidean space. If you go around a hue circle in little steps and then sum up all the perceived color differences you end up with more than π times the sum of differences you get if you go across the circle through gray.
- zokier 9y agoIs that implying that you could have uniform model in higher-dimensional space? Afaik there isn't really any particular reason why we should be limited to three dimensions.
- jacobolus 9y agoSure, you could make your 3-dimensional color space a manifold with negative curvature embedded in a higher-dimensional Euclidean space. A quick google scholar search turned up https://www.osapublishing.org/oe/abstract.cfm?uri=oe-22-10-12369 https://www.osapublishing.org/oe/abstract.cfm?uri=oe-22-10-1... but there are plenty of other sources discussing similar topics.
- kccqzy 9y agoMy math is a bit rusty but isn’t a manifold locally Euclidean? The GP is talking about how we can’t have Euclidean difference.
- jacobolus 9y agoA sphere and a hyperboloid are both locally Euclidean (as is color space). The interesting stuff starts to happen as you move around a bit further in the space.