> You will have to reduce the order of the NURB to cubic (may not be
> 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
> Good Luck
Not very precise what you write!!!!!!
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
bezier must be clamped -> means: the curve must correspond to the first
and last control point
to do this clamp: the first and last knots must have multiplicity
m + 1 -> number of knots
n + 1 -> number of control points
p -> degree
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" .