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> As it turns out, such a thing is no more possible than flattening an orange peel, because color perception is inherently non-Euclidean. To put it another way,
by steerablesafe 6y ago
> As it turns out, such a thing is no more possible than flattening an orange peel, because color perception is inherently non-Euclidean. To put it another way, the ratio of perceptually distinct steps around a hue circle to those directly across through gray is greater than would be expected as a circle in an ordinary Euclidean space.
What if instead of cramming the non-Euclidean space of perceived colors into an Euclidean space and interpreting straight lines there as gradients we used geodesic curves in the original non-Euclidean metric? Are there efforts to explore this area?
- banachtarski 6y agoI think the issue is you've described something qualitatively without giving the needed quantitative description of how the non euclidean space should be specified. Implicit surface with some parameterization? Family of geodesics, selecting a curve with a parameter per curve? How do artists specify where in the color space they are? How is your coordinate mapping defined?
- OscarCunningham 6y agoYou can just use the standard RGB (or any other) coordinate system, but then use data on perceptual differences to find geodesic gradients.
- steerablesafe 6y agoA parametrization and local metric at every point.
- raphlinus 6y agoThis is a good question, but it's not obvious that geodesics will lead to the most visually pleasing gradients. In particular, because of hue super-importance, a geodesic between two highly chromatic colors of different hues will bend toward gray, which might not be as representative of a "gradient" intent as linear motion through a nice space such as Oklab or IPT.
- twic 6y ago>> the ratio of perceptually distinct steps around a hue circle to those directly across through gray is greater than would be expected as a circle in an ordinary Euclidean space This is known as "the super-importance of hue", FWIW. > What if [...] we used geodesic curves in the original non-Euclidean metric? I came across a couple of examples of non-Euclidian colour spaces recently. 'Hyperbolic geometry for colour metrics': https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-22-10-12369&id=286233 https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-22-10-1... 'H2SI - A new perceptual colour space' (uses a four dimensional normalized Hilbert space, whatever that is): https://www.researchgate.net/publication/259265578_H2SI_-_A_new_perceptual_colour_space https://www.researchgate.net/publication/259265578_H2SI_-_A_...
- OscarCunningham 6y agoI was interested in doing this as a project, but I couldn't find any good data on perceptual differences to work from. MacAdam's famous paper only collected data for one brightness level. Does anyone know of good open data that could be used to generate a metric on colourspace?