11 Facts About NURBS

NURBS curves are commonly used in computer-aided design, manufacturing (CAM), and engineering (CAE).

Tools for creating and editing NURBS surfaces are found in various 3D graphics and animation software packages.

NURBS surfaces are functions of two parameters mapping to a surface in three-dimensional space.

At first NURBS were only used in the proprietary CAD packages of car companies.

Higher-level tools exist that benefit from the ability of NURBS to create and establish geometric continuity of different levels:.

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Geometric continuity mainly refers to the shape of the resulting surface; since NURBS surfaces are functions, it is possible to discuss the derivatives of the surface with respect to the parameters.

NURBS curve is defined by its order, a set of weighted control points, and a knot vector.

Order of a NURBS curve defines the number of nearby control points that influence any given point on the curve.

For example, if a NURBS describes a path through space over time, the knots control the time that the function proceeds past the control points.

B-spline basis functions used in the construction of NURBS curves are usually denoted as, in which corresponds to the control point, and corresponds with the degree of the basis function.

NURBS surface is obtained as the tensor product of two NURBS curves, thus using two independent parameters and:.