However, similar to curves, many implicit surfaces do not have any parametric form. Therefore, in terms of expressive power, implicit surfaces are more powerful than parametric surfaces. Here are a few technical terms. The highest degree of all terms is the degree of the algebraic surface. Therefore, spheres and all quadric surfaces are algebraic surfaces of degree two, while torus is a degree four algebraic surface.
Some algebraic surfaces have rational parametric forms such as spheres and all quadric surfaces.
This type of algebraic surfaces are called rational algebraic surfaces. Theoretically, given an algebraic surface in rational parametric form, it is always possible to eliminate parameters u and v so that the result is in an implicit form. However, not all algebraic surfaces are rational. Unfortunately, determining if an algebraic surface is rational is very difficult, although algebraic geometry has provided such characterization theorems. Computationally, it is infeasible.