Design of Quadratic B-Spline Curves

We restrict the discussion below to the one dimensional case below. It easily generalizes. Here's an example for a two segment quadratic:

Design of Cubic B-Spline Curves

Now let's extend this to cubic curves Here's an example for a 4 segment cubic:

We want to generalize this construction

Knots, Domain Knots and Intervals

Greville Abscissas and de Boor Ordinates

Knot Insertion

The de Boor Algorithm

To evaluate an $n$th degree B-spline curve (given its de Boor polygon and knot sequence) at parameter $u$, insert $u$ into the knot sequence until it has multiplicity $n$. The corresponding polygon vertex is the point on the curve.

The Bezier Case

Problems



William Shoaff
1999-03-04