Tabulated cylinder:

Surfaces that have polynomial (implicit) forms are called as algebraic surfaces. The highest degree of all of the terms is the degree of the algebraic surface. Thus, spheres and all quadric surfaces are algebraic surfaces of degree two, whereas torus is a degree four algebraic surface.

Some algebraic surfaces contain rational parametric forms such as spheres and all of quadric surfaces. These kinds of algebraic surfaces are called as rational algebraic surfaces. Theoretically specking, given an algebraic surface in rational parametric form, this is always possible to eliminate parameters u & v so that the consequence is in an implicit form. This procedure of conversion (from parametric to implicit) is called as implicitization.

Analogous to curves, there are analytic & synthetic surfaces. Analytic surfaces are depend on wire-frame entities and include the plane surface, surface of revolution, ruled surface, and tabulated cylinder. Synthetic surfaces are composed from a given set of data points or curves and include the bi cubic, Bezier, Coons patches and B-spline,. There are few methods to produced synthetic surfaces such like rational method, tensor product method, and blending method. The rational technique develops rational surfaces that are an extension of rational curves. The blending technique approximates a surface by piecewise surfaces.

The tensor product technique is the most popular method and is extensively used in surface modelling. Its widespread utilizes is largely because of its simple separable nature involving only products of univariate basis functions, generally polynomials. It introduces no new conceptual complications because of the higher dimensionality of a surface over a curve. The properties of tensor product surfaces may easily be deduced from properties of the underlying curve schemes. The tensor product formulation is mapping of a rectangular domain described by the u and v values; for example 0 < u  < 1 and 0 < v < 1. Tensor product surfaces fit naturally onto rectangular patches. Additionally, they have an explicit unique orientation (triangulation of a surface is not unique) and special parametric or coordinate directions linked with each independent parametric variable.