Quote:> You will have to reduce the order of the NURB to cubic (may not be

possible

> for all curves) and then increase the multiplicity of each knot to 4 by

> inserting duplicate knot values.

> The NURBS Book by Les Piegl and Wayne Tiller has excellent pseudo-c

> examples.

> Good Luck

> Icabod

Not very precise what you write!!!!!!

you say:

1- reduce the order of the NURB to cubic

2- "increase multiplicity to 4 ..."

both points are not "very" True:

1- bezier can have any degree you want -> but: with higher degree it become

difficult to control the curve.

1- a bezier curve doesn't have interior knots

2- so: the number of control points is equal the Order

since:

bezier must be clamped -> means: the curve must correspond to the first

and last control point

and:

to do this clamp: the first and last knots must have multiplicity

order.

m + 1 -> number of knots

n + 1 -> number of control points

p -> degree

p +1->order

m +1 = (n+1) + (p+1);

so to convert a nurbs to a bezier:

1- each knot-span [a, b) must be transformed to [a...a, b..b] -> a and b

each with multiplicity equal order.

2- so you get a sequence of Bezier-curves

- each with a knot-vector without interior knots

- each with number of control points equal the order of the curve

N.B. if you need a degree-Reduction-Algo, i wrote a very good one with 80%

better Results than

the one present in the "Nurbs-Book" .