The poles (sometimes known as control points) of a surface define its shape. The order of a polynomial is one greater than the degree, and gives the number of coefficients rather than the greatest exponent. Some CAD systems use the term order instead of degree. A surface with degree 2 would be curved in one direction, while a degree 3 surface could (but does not necessarily) change once from concave to convex curvature. For example, a surface with a degree of 1 would be a flat cross section surface. The degree of a surface determines its mathematical properties, and can be seen as representing the shape by a polynomial with variables to the power of the degree value.

The forms of freeform surfaces (and curves) are not stored or defined in CAD software in terms of polynomial equations, but by their poles, degree, and number of patches (segments with spline curves). Most systems today use nonuniform rational B-spline (NURBS) mathematics to describe the surface forms however, there are other methods such as Gordon surfaces or Coons surfaces. Initially developed for the automotive and aerospace industries, freeform surfacing is now widely used in all engineering design disciplines from consumer goods products to ships. They are used to describe forms such as turbine blades, car bodies and boat hulls. Freeform surfaces do not have rigid radial dimensions, unlike regular surfaces such as planes, cylinders and conic surfaces.

Freeform surface, or freeform surfacing, is used in CAD and other computer graphics software to describe the skin of a 3D geometric element.

Creo surface modeling