NURBS surface

1 Introduction

A NURBS surface, which is an acronym for Non-Uniform Rational B-Spline surface, is a generalizationPlanetmathPlanetmath of both Bézier ( and B-splines surfaces. NURBS are commonly used in computer graphics, computer-aided design (CAD), engineering (CAE), and manufacturing (CAM).

2 Definition

A NURBS surface is parametric surface defined by its , an array of n+1 rows and m+1 columns weighted control points and a knot vector in each direction. It is defined as

c(u,v)=i=0nj=0mNi,p(u)Nj,q(v)wi,jPi,ji=0nj=0mNi,p(u)Nj,q(v)wi,j  0u1,0v1

where u and v are the parameters in each direction, p is the in the u-direction, q is the in the v-direction, Ni,p and Nj,q are the B-spline basis functions, Pi,j are the control points and wi,j are the weights.

Title NURBS surface
Canonical name NURBSSurface
Date of creation 2013-03-22 17:23:51
Last modified on 2013-03-22 17:23:51
Owner stitch (17269)
Last modified by stitch (17269)
Numerical id 6
Author stitch (17269)
Entry type Definition
Classification msc 51N05
Synonym nonuniform rational B-spline surface
Related topic NURBS