Surface Modeling:

Smooth curves & surfaces should be generated in several computer graphics applications. Several real-world objects are inherently smooth, and much of computer graphics involves modelling the real world.

 Computer-aided design (CAD), high-quality character fonts, data plots, and artists' sketches all have smooth curves and surfaces. The path of any camera or object in an animation sequence is always almost smooth.

The need to represent curves and surfaces occur in two of the cases:

1. Modelling existing objects (as a face, a car, a mountain, a toy etc.);

2. Modelling "from scratch" (so-called image synthesis), whereas no physical object is existing and the same is to be modelled.

The procedure of modelling is much easier, if mathematical description of an object or at least of part of an object may be applied. Though, in the first case, a mathematical description of the object can be unavailable. One way of solution is to utilize as a model the coordinates of the infinitely several points of the object, but it is not feasible for a computer with finite storage. More frequently, the object is merely approximated with pieces (called as patches, in the particular case of surface modelling) of planes, spheres, or any other shapes that are simple to explain mathematically, and needs that points on the model be close to corresponding points on the object.