This code was written to control the colors of LED light fixtures that use more than standard RGB colors. Though right now only an additional amber is supported, these methods could be easily extended to LEDs or other sources of any color. This is a standalone module and does not depend on any libraries, and is written to be easily translated into other languages (hence unPythonic constructs).

The HSV_to_RGBA() and HSV_to_RGBA_CIE() functions divides the hue range into four sections corresponding to red, amber, green, and blue, and crossfades between them to arrive at an approximately correct hue.

The RGBA_to_HSV_CIE() function is somewhat more complex and is naturally an approximation as we are converting from a four-dimensional space to three. The approach is to convert each light source (R, G, B, and A) into the CIE xy space, where they can be interpolated to find the color of the resulting mixture. Once this is calculated (by a simple linear mix), the xy coordinates can be converted to HSV.

In this example, the dotted line shows the colors available by mixing the amber LED with white (from an equal mix of RGB). The X is the point at R = G = B = A = 0.5.

There are two versions of the HSV to RGBA conversion, the first HSV_to_RGBA() is described here. The second approach HSV_to_RGBA_CIE() gives colors that are closer to equal angles in xy space and should thus be a perceptually smoother transition around the hue circle. The following image shows the locus in xy space of hues equally spaced in 10 degree increments given by HSV_to_RGBA() on the left and HSV_to_RGBA_CIE() on the right.

A benefit of the latter is that a round-trip conversion HSV → RGBA→ HSV will result in hues that are much closer to the original. The HSV_to_RGBA_CIE() method has an optional parameter warp that when set to true (the default) will prewarp the hue to better match the RGBA_to_HSV_CIE() results. warp uses a 6th-order polynomial fit to warp the input hue value; if round-trip hue matching is of less importance then warp mat be set to False to skip this computation.

Note on variable names^{Note 1}

colorxform.py --- Python class with methods to convert between RGB, RGBA (red, green blue, & amber), HSV, CIE XYZ and CIE xyY colorspaces with no library dependencies. For more information on the CIE colorspaces, see Wikipedia: [https://en.wikipedia.org/wiki/CIE_1931_color_space}

There are three principal methods in this class:

• HSV_to_RGBA(self, h, s, v) -- This is the orginal HSV-to-RGBA conversion routine described here: http://rotormind.com/blog/2015/Generating-RGBY-from-Hue/
• HSV_to_RGBA_CIE(self, h, s, v, warp=True) This is an improved version with better perceptual linearity in the CIE space.
• RGBA_to_HSV_CIE(self, R, G, B, A) This is the inverse function that converts a color specified in linear red, green, blue and amber value, for example as PWM brightnesses for each LED of the respective colors, into hue, value (brightness) and saturation values. This calls three additional functions:
  1. RGBA_to_xy(self, R, G, B, A) -- Converts RGBA values to CIE xy values.
  2. xy_to_hue(self, xy_vec, red_offset=None)-- Converts a CIE xy value to a hue angle by finding the angle from pure red in xy space.
  3. prewarp(self, x, coeff=None) -- A hue warping function to help correct nonlinearity in the RGBA_to_HSV_CIE() function so that the round trip RGBA_to_HSV_CIE(HSV_to_RGB()) conversion results in closer to identical hue values. This is called automatically when the default warp=True parameter is used in HSV_to_RGBA_CIE(); there is little reason not to use it.

plot_trajectories.py --- code to plot LED colors and gamut in CIE space. This uses the color_science python library https://www.colour-science.org/ and generates the plot above

linearized_RGBA_to_hue.ipynb --- A Juypyter notebook to explore and test the colorxform methods. In particular this calculates the regression coefficients for the hue warping function used in prewarp().

Note 1: color-space nomenclature is confusing! Colorspace names are in uppercase except xyY to disambiguate X, Y from x, y from CIE xyY space. Four-color space is RGBA with A for Amber. (Though Y is often used for for amber/Yellow to disambiguate from alpha channel "A", we use A here to disambiguate from Y in xyY and XYZ color spaces.)