Example: a circle

Non-rational splines or Bézier curves may almost a circle, but they cannot represent it exactly. Rational splines can represent any cone-shaped section, including the circle, exactly. This representation is not unique, but one achievability appears below:

x y z weight

1 0 0 1

1 1 0

0 1 0 1

−1 1 0

−1 0 0 1

−1 −1 0

0 −1 0 1

1 −1 0

1 0 0 1

The adjustment is three, back a amphitheater is a boxlike ambit and the spline's adjustment is one added than the amount of its piecewise polynomial segments. The bond agent is . The amphitheater is composed of four division circles, angry calm with bifold knots. Although bifold knots in a third adjustment NURBS ambit would commonly aftereffect in accident of chain in the aboriginal derivative, the ascendancy credibility are positioned in such a way that the aboriginal acquired is continuous. In fact, the ambit is always differentiable everywhere, as it have to be if it absolutely represents a circle.

The ambit represents a amphitheater exactly, but it is not absolutely parametrized in the circle's arc length. This means, for example, that the point at does not lie at (except for the start, average and end point of anniversary division circle, back the representation is symmetrical). This is obvious; the x alike of the amphitheater would contrarily accommodate an exact rational polynomial announcement for , which is impossible. The amphitheater does accomplish one abounding anarchy as its constant goes from 0 to , but this is alone because the bond agent was arbitrarily called as multiples of .