> I have not been following this one closely but if all the poster
> wants to do is to go from a cubic (degree 3) Bezier curve to a
> quadratic (degree 2) Bezier curve, then there are standard
> algorithms for doing this quite simply.
The first sentence of my post to the original question:
"No doubt there are many ways to do the reduction."
The poster did not specify if he has a single cubic curve
that he wants to reduce to a single quadratic curve, or
if he has a piecewise cubic curve that he wants to reduce
to a piecewise quadratic curve. My first post to his
question suggested algorithms for each.
Quote:> Robin Forrest gave the algorithm as early as 1972.
I think "the" should have been "an". As I said, there
are many ways to do a reduction in degree.
Quote:> The technique is discussed, with a
> worked example, in the Introduction to NURBS, With Historical
> Perspective book (Section 3.13, p. 102)
I believe some time ago you also responded to one of
my posts where I suggested using a least-squares
method to minimize the L2 integral norm between the
original curve and its approximated curve, the response
being to use the "standard" algorithm by Piegl-Tiller
(as described in your book). I am curious what objections,
if any, you have to the global least-squares approach.
This approach does not force you to use any of the original
knots. You choose your "knot budget", so to speak, and
construct the approximation curve using a global measure
of error. For a single cubic curve that can be exactly
reduced to a quadratic, the least-squares method produces
exactly that quadratic.
Quote:> Note that it is not possible to degree reduce all Bezier
> curves and that the reduction process is an approximation
The original poster already acknowledged that the
reduction may be an approximation. Not sure what you
mean by "it is not possible to degree reduce all Bezier
curves". You can always choose a smaller degree
Bezier curve as an approximation to a larger degree
one. It is only a matter of how good/bad an approximation
your application is willing to tolerate.