The geometrical model C([xi]) can be expressed by a linear combination of the NURBS basis functions Ri and the control points Bi, leading to :
The IGA model, on the other hand, with its element bases directly adopting the NURBS basis functions that exactly describe the geometric model, has no loss of information between the analyzed model and the original one, providing an extremely apparent advantage for curved or complicated shapes, as shown in Figure 2.
Finally, we apply NURBS manipulation [2, 18] to the rotation surface r([u.
The NURBS data is consist of the knot vector, the control points and its weights.
In this study, the rough surface has been modeled by the NURBS surface.
Una superficie NURBS esta completamente determinada por sus puntos de control [P.
After geometry recovering and mesh refinement the NURBS patches were obtained.
Este trabajo busca, explora y aporta una solucion a este problema, mediante la implementacion de un algoritmo que permite optimizar la representacion en modelos NURBS de la superficie muestreada de un objeto fisico.
NURBS surfaces can be constructed using deterministic algorithms, Piegl and Tiller  presented a method for constructing NURBS surfaces in this way, even though some method for constructing NURBS deterministically assign homogeneous weighting factors, therefore the resultant surface locally do not follow close enough the geometry described by the control points.
The product uses patent-pending N-Sided-Surfacing, a new generation of 3D surface modeling that enables fast, flexible 3D shape modeling without the hassle and grind created by NURBS and Bezier-based systems.
Some high-end CNCs have advanced options to machine NURBS surfaces directly with specially-formatted part programs.
In addition, says the company, the interface offers a stand-alone package for reverse engineering of mechanical and complex, free-form parts such as auto bodies, airplanes, boat hulls, and ergonomic consumer products; easy-to-use tools and documentation for leapfrogging to digitize large parts; powerful tools for accurately comparing digitized points to surfaces; accurate NURBS modeling features that allow users to manufacture directly from Rhino models; support for most CAD-file formats; availability in English, French, Spanish, German, Italian, Japanese, and Czech; and openGL hardware acceleration.