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"Bald Eagle" <cre### [at] netscape net> wrote:
>...
> Given that a Bezier patch can be interpreted as a Bezier spline in one dimension
> whose control points slide along Bezier splines oriented in the other dimension,
> and that this can be expressed as a parametiric equation, then
>
> It ought to be possible to define a parametric {} object in POV-Ray based on a
> set of control points and the basis functions of the Bezier splines.
>...
Yes, that is possible. Just create 3 bivariate functions with the appropriate
Bernstein polynomials and feed them to the parametric object. But you need
patience for that...
> Then, given a point <m, n> (or <u, v>) on the surface, one could place things ON
> the surface of the patch.
Yes, this image shows some white spheres and cylinders following a path in the
UV-space on the surface of a NURBS-patch:
http://dataduppedings.no/subcube/POV-Ray_Images/NURBS_Grid.jpg
See also the attached image where the I've put some sphere sweeps on a Bezier
patch. (Notice that you can read out the radii for the sphere swept curves
(0.06, 0.46 and 0.48) in the UV-mapped texture.)
>...
--
Tor Olav
http://subcube.com
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