Halbert <hha### [at] capitalnet> wrote in message
news:399877d1$1@news.povray.org...
> > 2. The bezier patch has control points outside the mesh, so how is it
> > not qualified as a NURBS? Just because it's a surface?
>
> Correct me if I am wrong( and I very well could be.) I think that a bezier
> patch is a uniform rational surface in that the contol points all have the
> same weight. In a NURBS surface the control points can have different
> weights and one point may affect the shape of the curve more than others.
Of
> coarse, I am not the expert. I'll bet Warp would know.
>

A bezier patch is very similar to a NURBS surface. In fact, if you have a
NURBS
surface with the minimum number of points in it, it is exactly the same
thing as
a bezier surface.

The problem with beziers is that they only naturally form a single small
piece
of surface with only a limited number of points in it - NURBS surfaces are
what
are called "piecewise", which means that they are actually a bunch of small
surfaces that are glued together to make one large one.

NURBS is basically a mechanism for stringing together a whole bunch of
beziers such that all the beziers are guaranteed to be smooth to one another
and
are easier to manipulate.

If you just use individual beziers, it becomes very difficult to get a high
degree of
smoothness between them. You can get 2 adjacent curves to share tangents ok
(which is how Adobe Illustrator works), but it is difficult to get them to
share curvatures also.

The thing that makes NURBS good isn't just that they have control points
outside of
the mesh - it's that you can have any number of control points that you want
to make
a large surface that is one very smooth piece.

It is possible for a bezier to have different weights on every control
point - that's what
"rational" means.

The confusing part about NURBS is that there are 2 totally different
mechanisms that
change the way that a control point can affect the curve - one is the weight
of the
control point, and one is the knot sequence for the curve. Beziers can have
weights,
but they don't have knots.


      - Michael

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