NURBS are usually used for 3D model, it is a technique oriented for modelling some surfaces with complex curves like organic objects, vehicles or specific objects with special curves. NURBS comes from Non-Uniform Rational B-Spline; it means NURBS uses non-uniform and rational Bézier curves. The story began in 1960s with Pierre Bézier who worked as an engineer at Renault and Paul de Casteljau who worked at Citroën; they were studying some methods to obtain a mathematical representation of freedom surfaces. After some research they published the Bezier splines, and NURBS are a generalization of those curves.
As we can see in picture below a Bezier curve is composed by next parts, the curve (C), its control points (1),(2),(3),(4) and its control polygon(P).
In rational curves, the weight defines the attraction of a point to the curve; B-splines are multiple Bezier arcs. So, we can define NURBS surface as functions of two parameters associated into a three dimensional space, surface will be defined by the control points of the Bezier curve. All the mathematical calculus is the strong point for this method of 3D modelling, because NURBS surfaces are analytically generated, they will reduce the usage of memory when we design 3D shapes and when we store them in a hard drive.
At first, NURBS were used principally for cars companies to realize their designs because cars prototypes have complex curves, all car parts are curves indeed. They became popular because you can manipulate objects easily and interactively, it was an intuitive process because you can manage all control points which are connected directly to the curve or the surface.
Therefore, NURBS curves and surfaces allow us to create objects with organic appearance as you can see in next picture.
Next, we can see how to easily create a tree with NURBS curves.
As I said before, that mechanics of designing is useful for car parts, here you can see some good examples.
Regarding to my character, I have not thought to use NURBS at first look but after that researching I need to meditate and study this option; it could be useful in order to rendering the character to a game. In theory, my character has not got any digital device which I could design with NURBS but there are some environment objects such as the cones and fences which I can model using that technique. My plan in order to this new aim is to practice again with Maya NURBS tutorials and identify what tools I will need to create a good design.