"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> "Bald Eagle" <cre### [at] netscapenet> wrote:
> >...
>...
> If you calculate the two partial derivatives (d/dU and d/dV) for each of the
> bivariate functions for a Bezier patch you can use these to reorient objects to
> align with the U-, V- and normal directions of the surface.
>
> This article contains some useful information about that:
>
>
https://www.scratchapixel.com/lessons/advanced-rendering/bezier-curve-rendering-utah-teapot/bezier-patch-normal
>
> The attached image shows cubes that are reoriented to align with the directions
> I mentioned above. It also shows a lot of splines that creates a grid on the
> surface of the patch.


Here's another image where the cubes have been scaled in the U/V-directions by
the lengths of the vectors used for reorienting them. (These vectors were
created with the partial derivatives of the bivariate functions for the Bezier
patch.)

--
Tor Olav
http://subcube.com

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