Why does the HSV-RGB algorithm work the way it does?

Question

I read a Wikipedia article about converting from HSV to RGB , but I do not understand. Why is each variant of the case the way it is, and why are they ordered in this way, if order matters?

Answer 1

Wikipedia describes a rather bulletproof approach to coding it, so I assume you are confused about the implementation logic. You are embarrassed by this, right?

If you look at the image next to it, you will see why:

Each channel function is a piecewise function consisting of five linear segments. The cases take into account each range of each distribution, namely the shaded areas of the above image.