An introduction to NURBS

A three dimensional (3D) object is composed of curves and surfaces. One must find a way to represent these to be able to model accurately an object. The two most common methods to represent a curve or a surface are the implicit and the parametric method. The implicit method is a function which depends on the axis variables and is usually equal to 0. It describes a relationship between the axis variables. For example, the function f(x, y) = x2 + y2 − 1 = 0 represents a circle of radius 1. In the parametric method each of the axis variables is a function of an independent parameter. In this form, a curve would be defined with the independent variable u as C(u) = [x(u), y(u)] a ≤ u ≤ b To represent the first quadrant of a circle in a parametric form, one can write C(u) = [cos(u), sin(u)] 0 ≤ u ≤ pi 2 or he can also write C(u) = 1 − t