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nonuniform rational B-spline (NURBS)

Contributor(s): Arun Nambiar

NURBS (nonuniform rational B-splines) are mathematical representations of 2- or 3-dimensional objects, which can be standard shapes (such as a cone) or free-form shapes (such as a car). NURBS are used in computer graphics and the CAD/CAM industry and have come to be regarded as a standard way to create and represent complex objects. In addition to curves and surfaces, NURBS can also represent hypersurfaces.

Most sophisticated graphic creation tools provide an interface for using NURBS, which are flexible enough to design a wide range of shapes - anything from points to straight lines to conic sections. NURBS are compact expressions that can be evaluated and displayed quickly. NURBS work especially well in 3-D modeling, allowing the designer to easily manipulate control vertices, called ISO curves, and control curvature and the smoothness of contours. NURBS are defined by both control points and weights. It takes very little data to define a NURB.

A spline is a usually curvy pattern used to guide someone shaping something large, such as a boat hull. The B-spline is based (the B stands for basis ) on four local functions or control points that lie outside the curve itself. Nonuniform is the idea that some sections of a defined shape (between any two points) can be shortened or elongated relative to other sections in the overall shape. Rational describes the ability to give more weight to some points in the shape than to other points in considering each positions relation to another object. (This is sometimes referred to as a 4th dimensional characteristic.)

This was last updated in March 2011

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Finally! Thank you for a concise and well written definition of NURBS. I've been searching for some time for an excellent way to define this term and I've found your explanation to be one of the best.
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