What is the CieLuv value of Black?

Question

The Wikipedia page about CieL*u*v* color space describes the conversion function from a color expressed in the XYZ color space.

For black, expressed as (R=0, G=0, B=0) in the RGB color space, and (X=0, Y=0, Z=0) in the XYZ color space, which values should we use to represent it in CieLuv?

The formula uses a division, 4x/(x+15y+3z), whose result is undefined for black.
Should we use (L=0, u=0, v=0), or are there more subtleties?

Answer 1

In fact black is not represented in uv. So in Luv black can be represented by L = 0 and u = v = undefined.

Answer 2

Well there's a difference between theoretical black" (all zeros) and "practical black" which is 1/1000 the lightness of white. See "Charles Poynton. Digital Video and HD. Morgan Kaufmann, second edition edition, 2012.", page 248.

So in practice it's not exactly zero. Or maybe imagine just grays: They all have u* = v* = 0, only L* is different. So when you approach black, it should be clear what it looks like.