# 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

 $c(u)=\frac{\sum_{i=0}^{n}N_{i,p}(u)w_{i}P_{i}}{\sum_{i=0}^{n}N_{i,p}(u)w_{i}}% \quad\quad 0\leq u\leq 1$

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 NURBSCurve 2013-03-22 17:10:59 2013-03-22 17:10:59 stitch (17269) stitch (17269) 12 stitch (17269) Definition msc 51N05 nonuniform rational B-spline curve BezierCurve BSpline NURBSSurface