A generalization of the Bézier Curve. Let a vector known as the Knot Vector be
defined

(1) |

(2) |

Define the basis functions as

(3) | |||

(4) |

Then the curve defined by

(5) |

The degree of a B-spline is independent of the number of control points, so a low order can always be maintained for purposes of numerical stability. Also, a curve is times differentiable at a point where duplicate knot values occur. The knot values determine the extent of the control of the control points.

© 1996-9

1999-05-26