What are NURBS? 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. Because of their...
What are NURBS?
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. Because of their flexibility and accuracy, NURBS models can be used in any process, from illustration and animation to manufacturing.
NURBS geometry has five important qualities that make it an ideal choice for computer-aided modeling.
Several industry‑standard methods are used to exchange NURBS geometry. Consequently, customers can move their valuable geometric models between the various modeling, rendering, animation, and engineering analysis programs.
NURBS have a precise and well-known definition. Most major universities teach mathematics and computer science of NURBS geometry. 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, 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 both efficiently and accurately.
Acronym for Non-Uniform Rational B-Splines. While it is generally considered to have been developed to build digital versions of the design lines used to draw the sections of the hulls of ships and aircraft bodies, it is in the fifties and in the automotive industry where it appeared the need curves represent free paths (those that do not respond to simple geometric shapes such as circle and ellipse arc). Two engineers from the automotive industry (P. de Casteljau and Bezier P.) developed independently and almost parallel the principles of what is now known generically as the spline curves. These mathematical structures allow numerically describe a curve whose geometric layout free translation enables control curve graphically in all instances. To operate, control and design algorithms that overcome the complexity of traditional equations and do it only from the “graphic” and intuitive handling of geometry (ignoring the tedious own geometric-mathematical structures that support abstractions) is a of the most important to the different design disciplines that operate on the space and complex geometries contributions. Learn more in: Folds and Refolds: Space Generation, Shapes, and Complex Components
