Rational Curves:

The Bezier, cubic spline and B-spline curves make the core of the techniques utilized in CAD for the representation of free-form data and curves. However In engineering design, , standard analytic shapes such like, cylinders, arcs ,cones, lines and planes predominate, along the consequence that models of geometry shall frequently involve both free-form and analytic geometry. Additionally, there might be a requirement to model analytic geometry utilizing a 'free-form' modeling technique, and it is difficult, specifically for conics and other quadric forms. An ideal modeling technique would allow the representation of analytic and free-form both curves in a single unified form. A unified representation would also contain the advantage of decreasing the database complexity and the number of process needed in a CAD system for the manipulation and display of geometric entities (that is a system might require a separate process to display each of the geometric entities, or to compute the intersection among any pair of entity kinds).

The class of curves that is called as rational polynomials is able of exactly representing conic and more common quadric functions, & also showing the several polynomial types that already we have met. The mathematical fundamental of the rational polynomials is shortly described in the bracketed section below, and it is noted down that a number of CAD systems currently use rational polynomials for the representations. A very broadly utilized form is the non-uniform rational B-spline, or NURBS, so known as because it is a rational B-spline function permitting a non-uniform knot vector.