Drawing a "tesselated" disk


I am working on a fisheye distortion, and am having an issue with the mapping. I would like to draw a disk similar to what is show here(middle of the page, ctrl+f tess):


Any ideas on how this could be done?

I would generate vertices for a cube whose faces are planes composed of a quad grid.

then, compute each vertex position from the cube center and scale the position vector to the sphere radius.

Finally draw it, at the scene center, orienting the view in the right direction and using orthographic projection. I think you should obtain the 2nd link picture.