An investigation not as pattern but as warp could be interesting.
The early part to answer is: what happen outside the circle.
One answer can be: nothing, outside the circle, there is no transformation.
Or something different, as suggested in the pdf for poincarré disk.
It is "of course" to be mainly used with the image pattern, so it is
better from the very start that the reference plane be the same (to
avoid a systematic rotate), and the third coordinates is to be dropped.
So far the "perfect" illustration could be some pedestal table with such
topping, and some chess set on it...
With an outer ring, which implies some layered textures too.
About bezier bicubic patches, I do not so far understand what is the
final purpose of the request. Does it sound like gluing the mesh camera
to a bezier bicubic patch ? (mesh camera or user-function defined camera).
As a raytracing aims at generating pictures, what is a finish map in
that context ?
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