NURBS geometry has five important qualities that make it an ideal choice for computer-aided modeling.

• There are several industry standard ways to exchange NURBS geometry. This means that customers can and should expect to be able to move their valuable geometric models between various modeling, rendering, animation, and engineering analysis programs. They can store geometric information in a way that will be usable 20 years from now.
• NURBS have a precise and well-known definition. The mathematics and computer science of NURBS geometry is taught in most major universities. This means that specialty software vendors, engineering teams, industrial design firms, and animation houses that need to create custom software applications, can find trained programmers who are able to work with NURBS geometry.
• NURBS can accurately represent both standard geometric objects like lines, circles, ellipses, spheres, and tori, and free-form geometry like car bodies and human bodies.
• The amount of information required for a NURBS representation of a piece of geometry is much smaller than the amount of information required by common faceted approximations.
• The NURBS evaluation rule, discussed below, can be implemented on a computer in a way that is both efficient and accurate.

Evaluation Rule

A curve evaluation rule is a mathematical formula that takes a number and assigns a point. The NURBS evaluation rule is a formula that involves the degree, control points, and knots. In the formula there are some things called B-spline basis functions. The B and S in NURBS stand for “basis spline.” The number the evaluation rule starts with is called a parameter. You can think of the evaluation rule as a black box that eats a parameter and produces a point location. The degree, knots, and control points determine how the black box works.