However, not every set of coordinates in XYZ space corresponds to a color that the average human can see. Theoretically, the XYZ axes go off to infinity in both the positive and negative direction. X and Z carry additional information about how the cones in the human eye respond to light waves of varying frequencies. In the XYZ color space, Y corresponds to relative luminance Y also carries color information related to the eye's "M" (yellow-green) cone response. To visualize XYZ, think of a three-dimensional cartesian coordinate system (high school algebra) with axes labelled X, Y, and Z. In 1931 color scientists used the results of the Wright and Guild experiments to create the 1931 CIEXYZ color space ("XYZ" for short). In the late 1920s William David Wright and John Guild independently conducted a series of color matching experiments that mapped out all the colors the average human (meaning the average of the humans in the experiments) can see. XYZ Color mapping experiments: what the average human sees The naming of colors carries one out of the narrow realm of color perception, and into the larger realm of cultural and linguistic interpretation and classification of color, and thence into even larger philosophical, aesthetic, theological, and metaphysical considerations. So our perception of color is composed of both intensity information and chromaticity information. Light varies in wavelengths, which our eyes and brain interpret as varying colors, and also in intensity. Light enters the eyes, is processed by light receptors ( cones and rods), and sent via the optic nerves to the brain for further processing and interpretation. Rather color is part of how we sense the world around us. On the other hand, color isn't out there in the world in the same tangible way that light is. On the one hand, light comes from the sun or other radiant sources, and is refracted by mediums (water, the atmosphere, glass) and diffusely or specularly reflected by surfaces. Nominal ranges are often extended in practice. RGB numbers have the nominal range 0 to 1, as does Y from XYZ and xyY. Summary plus a short historical perspective on linear gamma image editingĪll RGB, XYZ, and yxY numbers in this tutorial are floating point numbers.xyY - enough colors, all the colors, and imaginary colors.RGB - locate black, white, red, green, and blue in XYZ space.# I'm fairly sure there's a more efficient way of doing this. But if it is, you can avoid having to interpolate: def method_3(): In general, with sampled data, this will not be true. For every possible unique (x,y) pair, there is a corresponding (x,y,z) in your data.įrom this, it follows that the number of (x,y,z) pairs must be equal to the square of the number of unique x points (where the number of unique x positions equals the number of unique y positions).The number of different x sample positions equals the number of different y sample positions.There's a third option, depending on how your (x,y,z) is set up. Method 3: No Interpolation (constraints on sampled data) This method produces the following graphs: Z = iddata((mat, mat), mat, (X,Y), method='nearest') # Depending on your "error", you may be able to use other methods # Interpolate (x,y,z) points over a normal (x,y) grid # This works if you have (x,y,z) tuples that you're *not* generating, and (x,y) points Method 2: Interpolating given z points over a regular grid # Method 2: Here, the returned matrix looks like: mat = , Y_err = (np.random.rand(*y.shape) - 0.5) * xy_max_error X_err = (np.random.rand(*x.shape) - 0.5) * xy_max_error # Half of this will be in the + direction, half will be in the - dir. # First we generate the (x,y,z) tuples to imitate "real" data First, I define a function that generates fake data: def gen_fake_data(): If you don't have that ability, and are given a fixed (x,y,z). This is relatively easy, since you can generate z at whatever points you want. # This works if you are generating z, given (x,y) # dim_? is the granularity in that direction If you just have just a list of ( x, y, z) tuples, it's harder (see method_2() below, and maybe method_3()).Ĭonstants # min_? is minimum bound, max_? is maximum bound, you know the formula for it) it's very easy (see method_1() below). Depending on whether you're generating z or not, you have at least two different options.
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