How to/Help create a CIELAB color space wheel in Adobe illustrator?

Question

I am trying to create an RGB approximation of the CIELAB color space wheel for a* and b*. I know that effectively the there needs to be an angular/conical gradient from a central point with Yellow (top Y-axis), Red (right X-axis), Blue (bottom Y-axis), and green (left X-axis), and neutral gray at the origin.

I have struggled a lot trying to get make this.

I have gotten close using the free-form gradient tool in Illustrator, however, the main issue here is that my gradients, especially obvious with the central neutral gray one seem square shaped, rather than radial. While it looks close, it isn't entirely accurate

What I want is a wheel with a conical gradient from a neutral gray point at the origin. The points closest to the origin are more gray-hued of the corresponding red, yellow, blue, and green of the corresponding axes. On the ends of 4 main axis end points the highest chroma color point is located. (i.e. Yellow (255,255,0) at the top point of the Y-axis, Red (255,0,0) on right X-axis, Blue (0,0,255) on the bottom Y-axis, Green (0,255,0) on the left X-axis), and Gray (128,128,128) in the center.

There should be an outward conical gradient of those colors. Starting from gray at the origin. Surrounding the origin are gray hues of the above colors, and as you progressively move outwards towards the edge of the circle the color becomes "purer", with the absolute RGBY on the ends of the corresponding axes. Image 2 kind of gives the idea.

My .ai file attempt can be found here: https://file.io/s0QXHygG5O3q

and I would really appreciate if someone could help.

Thank you!

[

Answer 1

Not sure if it's a question about coding, though...