It is possible to increase the degree of a NURBS curve and not change its shape. Consequently, the degree is equal to (order‑1). The order of a NURBS curve is a positive whole number equal to (degree+1). You may see references to the order of a NURBS curve. Linear means degree 1, quadratic means degree 2, cubic means degree 3, and quintic means degree 5. Sometimes the terms linear, quadratic, cubic, and quintic are used. NURBS lines and polylines are usually degree 1, NURBS circles are degree 2, and most free‑form curves are degree 3 or 5. This number is usually 1, 2, 3, or 5, but can be any positive whole number. Four things define a NURBS curve: degree, control points, knots, and an evaluation rule. Since curves are the easiest to describe, we will cover them in detail. NURBS curves and surfaces behave in similar ways and share terminology. The NURBS evaluation rule, discussed below, can be implemented on a computer both efficiently and accurately.

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.

NURBS can accurately represent both standard geometric objects like lines, circles, ellipses, spheres, tori, and free‑form geometry like car bodies and human bodies.

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. Most major universities teach mathematics and computer science of NURBS geometry.

NURBS have a precise and well-known definition.

Consequently, customers can move their valuable geometric models between the various modeling, rendering, animation, and engineering analysis programs.

Several industry‑standard methods are used to exchange NURBS geometry.

NURBS geometry has five important qualities that make it an ideal choice for computer-aided modeling. Because of their flexibility and accuracy, NURBS models can be used in any process, from illustration and animation to manufacturing. NURBS, Non-Uniform Rational B-Splines, are mathematical representations of 3D geometry that can accurately describe any shape from a simple 2D line, circle, arc, or curve to the most complex 3D organic free-form surface or solid.

Subd to nurbs rhino