NURBS curve

1 Introduction

A NURBS curve, which is an acronym for Non-Uniform Rational B-Spline curve, is a generalizationPlanetmathPlanetmath of both Bézier ( and BSpline ( 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)=i=0nNi,p(u)wiPii=0nNi,p(u)wi  0u1

where u is the parameter, p is the , Ni,p are the B-spline basis functions, Pi are the control points and wi 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