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Question about conversion from cartesian dkl coordinates to spherical dkl coord

Thank you for the useful helper functions for converting from dkl to rgb!

Similar to this code, is there a function to convert from Cartesian DKL coordinates to spherical DKL coord.?

My goal is to start with an rgb set of values and end with spherical DKL coordinates (unless colors can be set in either version of DKL colorspace).

Alternatively, is there a way to go directly from rgb values to spherical DKL coordinates?

Thanks in advance for your help!