# NURBS curve

## 1 Introduction

A *NURBS curve*, which is an acronym for *Non-Uniform Rational B-Spline curve*, is a generalization^{} of both Bézier (http://planetmath.org/BezierCurve) and BSpline (http://planetmath.org/B-splines) curves. NURBS are commonly used in computer graphics, computer-aided design (CAD), engineering (CAE), and manufacturing (CAM).

## 2 Definition

A NURBS curve is a parametric curve defined by its , a set of weighted control points, and a knot vector. It is defined as

$$c(u)=\frac{{\sum}_{i=0}^{n}{N}_{i,p}(u){w}_{i}{P}_{i}}{{\sum}_{i=0}^{n}{N}_{i,p}(u){w}_{i}}\mathit{\hspace{1em}\hspace{1em}}0\le u\le 1$$ |

where $u$ is the parameter, $p$ is the , ${N}_{i,p}$ are the B-spline basis functions, ${P}_{i}$ are the control points and ${w}_{i}$ are the weights.

Title | NURBS curve |
---|---|

Canonical name | NURBSCurve |

Date of creation | 2013-03-22 17:10:59 |

Last modified on | 2013-03-22 17:10:59 |

Owner | stitch (17269) |

Last modified by | stitch (17269) |

Numerical id | 12 |

Author | stitch (17269) |

Entry type | Definition |

Classification | msc 51N05 |

Synonym | nonuniform rational B-spline curve |

Related topic | BezierCurve |

Related topic | BSpline |

Related topic | NURBSSurface |