Mixing LEDs to make full color lighting seems straight forward on the surface. Turn on red for red, green for green, and both for yellow. Many color fixtures work this way in fact. There is a separate DMX channel for each color under control and the fixture turns each color on in proportion to its DMX value. This method works if the application doesn’t require a particular repeatable color.
If you do need a particular color, adjusting color sliders and guessing at the output isn’t a great way to get there. What makes for better control is a color picker as is used in photo editing where you can adjust easily understandable hue, saturation and brightness values. It would also be a benefit if the color a light fixture produced with a particular value set was the same as is produced on your device or computer display with these values.
For a fixture to operate from hue, saturation and brightness it has to calculate the color target from these values then calculate the drive level for each of its sources to achieve the color target. The fixture can use information about each of the emitters efficiency and color at different operating currents and temperatures to calculate the required drive level. This method works with more than just RGB fixtures. If the fixture also has white and amber emitters the color target defined by the hue, saturation and brightness values doesn’t change. The fixture will combine its additional sources into the drive level calculations to utilize all the different color LEDs it might have.
You might want color translation in your light fixture if you want your fixture to emit a particular color, you want the color to be consistent between fixtures, and you want to set the color in a convenient way.