Understanding NURBS in Computer Graphics

NURBS stands for non uniform rational basis spline. This is a type of mathematical model that is used to create curves and surfaces in computer graphics. These are particularly useful when creating freeform shapes. Engineers first used NURBS to design car bodies, aerospace exterior panels and ship hulls, as NURBS made it possible to exactly create the needed curved surfaces. The 2 pioneers of NURBS were from the car industry and worked for Citroen and Renault. NURBS did not start to be used with computer graphics until the early 1990s. Today most computer graphic programs will use NURBS technology.


NURBS make it possible to create surfaces and curves in compact form. Basically the NURB will take 2 parameters and map them into 3D space. Control points are needed on the surface. Most of the surface editing is done through the control points. Several NURB patches can be combined together to form a construction. The boundaries of the patches are invisible, but together the hull of the ship is formed or a car panel. These curves are popular for engineering and CAD but used less frequently for computer games and films. For animation subdivision surfaces are preferred.

Control Points

The control points will be used for the shape of the curve. Each control point will be ordered or weighted depending on the parameters that set the curve. These curves can be translated into a polynomial and control points in the middle are more important than those at the ends. The control point will only affect the surrounding intervals. Therefore, it is possible to change parts of the curve. More control points will provide a better curve.

Knot Vector

There are the same amount of knots as there are control points. However the degree of the curve is also taken account in the knot vector. This vector divides the curve into intervals. Ultimately individual knots are not important. It is sequences of knots that can be activated and customized. These knots are needed to get the curve to settle in the proper space. The ability to edit knots is the sign of powerful computer graphics software. Knots are used to manipulate the objects. Knots can be inserted and knots can be removed. Many times knots are removed when manual control points have been added.


All NURBS can be seen as functions. There will be degrees (n) and control points (i). An example of a NURBS curve function is Ni,n=fi,n Ni,n – 1 + gi +1,nN i + 1,n – 1. There are many other high order functions that are used for NURBS.


There are several advantages of NURBS as they are used for defining both 2D and 3D geometry. It offers the needed precision in design and is a fast way for modeling. It is a very versatile tool that can be integrated with many programs to create high quality designs and models. With NURBS, an object needs fewer surfaces, has accurate data transfer and is much easier to edit. With fewer surfaces, this means there are fewer errors in the model. Many patches means there is a greater chance of mismatching and gaps. This can take much longer to edit. Therefore, the fewer surfaces saves plenty of time and has less chance of issues.