I'm not sure what type of Luv plot I am obtaining using ColorthinkPro 3.03 on my Windows 8 machine. In reading the Colorthink documentation, I do see that they do not recommend using Luv for 3D plots:
"In general we recommend the Yxy or Luv coordinates for 2D graphing only. Lab has been found to be easier to visualize, understand, and compare when creating 3D graphs."
Bill, I downloaded the demo version of ColorthinkPro 3.03 and looked at the sRGB gamut in what they call "Luv". It must be Lu'v', because the bottom (low L) part of the gamut extends straight down from the primaries in what is in the u'v' plane, a constant sized triangle. This is not very useful, and is certainly not CIEL*u*v*. When you plot the same gamut in what they call "Lab", after some luminance, the gamut gets smaller as L goes down, culminating in a point on the bottom. That is what you'd expect for CIEL*a*b*.
Here are 2D plots of the same image as used my previous posts showing the gamut of the image in color dots and that of my printer in monochrome. The image contains some blues out of the Luv gamut (human vision). The reds and greens appear slightly out of the Luv gamut. Your plots did show that ProPhotoRGB is slightly wider in gamut than Luv in these colors.
Slightly for the green primary, wildly for the blue one. It looks like your image runs into the boundaries of the PPRGB gamut in many places, making me think that's it's been tweaked in that space.
As I understand it, 2D plots may not be optimal since they show the gamut only for one luminance value, often L* of 50, and out of gamut colors at other luminances may be missed.
Usually the 2D plots plot all the points of the 3D plots, but flatten them all onto one luminance coordinate. 2D plots thus throw away one dimension of each point. While they have their uses, 2D plots are limited, because color is inherently a three-dimensional concept.
The folks at Chromix obviously know all the color science to properly implement CIEL*u*v*. I don't know why they didn't.