NURBS

NURBS curves are defined as rational polinomyals, and are more general, strictly speaching, than conventional B-Splines and Beziér curves. They have a large set of variables, which allow you to create mathematically pure forms. However working with them requires a little more intuition:

• Knots. Nurbs curves have a knot vector, a row of numbers that specify the parametric definition of the curve. Two pre-sets are important for this. "Uniform" produces a uniform division, for closed curves, but for open one you will end with "free" ends, difficult to locate precisely. "Endpoint" sets the knots in such a way that the first and last vertexes are always part of the curve, hence much easier to place;

• Order. The order is the 'depth' of the curve calculation. Order '1' is a point, order '2' is linear, order '3' is quadratic, etc. Always use order '5' for Curve paths; this behaves fluidly under all circumstances, without irritating discontinuities in the movement. Mathematically speaking this is the order of both the Numerator and the Denominator of the rational polynomial defining the NURBS;

• Weight. Nurbs curves have a 'weight' per vertex - the extent to which a vertex participates in the "pulling" of the curve.

Figure 3 Shows the Knot vector settings as well as the effect of varying a single knot weight. Just as with Beziers, the resolution can be set per curve.