These are used in many engineering design systems to allow convenient design and adjustment of curved surfaces, in applications such as aircraft or automobile body design. In contrast to semi-algebraic models, which are implicit equations, NURBS and other splines are parametric equations. This makes computations such as rendering easier; however, others, such as collision detection, become more difficult. These models may be defined in any dimension. A brief 2D formulation is given here.

A curve can be expressed as

(3.18) |

in which are

(3.19) |

The basis of the recursion is if , and otherwise. A

Steven M LaValle 2012-04-20