Rational Curves:

The cubic spline, Bezier & B-spline curves form the core of the techniques utilized in CAD for the representation of free-form curves and data. However ,In engineering design ,standard analytic shapes such like cylinders, arcs cones, lines and planes predominate, with the consequence that models of geometry shall frequently involve both free-form and analytic geometry. Additionally, there can be a requirement to model analytic geometry by using a 'free-form' modelling technique, and this is hard, particularly for conics and other quadric forms. An ideal modelling method would permit the representation of both analytic and free-form curves in a single unified form. A unified representation would also have the advantage of decreasing the database complexity and the number of process required in a CAD system for the display and manipulation of geometric entities (that is a system can need a separate procedure to display each geometric entities or to calculate the intersection among any pair of entity types).

The class of curves that is known as rational polynomials is able of exactly representing conic and more general quadric functions, and also representing the several polynomial types that we have already met. The mathematical basis of the rational polynomials is briefly defined in the bracketed section below, and it is noted down that a number of CAD systems nowadays use rational polynomials for the representations. A very extensively used form is the non-uniform rational B-spline, or NURBS, so called because it is a rational B-spline function permitting a non-uniform knot vector.