In computer graphics, a procedural surface is a representation of a surface as a mathematical implicit equation, rather than an explicit representation.

It is an approximation of the implicit Colebrook-White equation.

However, it may occur that the tangent line exists and may be computed from an implicit equation of the curve.

Given a curve given by such an implicit equation, the first problems that occur is to determine the shape of the curve and to draw it.

If the ellipse is given by the implicit equation , then the area is .

Implicitization consists in computing the implicit equations of such a curve.

The implicit equation is the following resultant:

Eliminate the from to get a Gröbner basis of the ideal (of the implicit equations) of the variety.

In 1770, Joseph Louis Lagrange (1736-1813) published his power series solution of the implicit equation for v mentioned above.

Adams used Newton's method to solve the implicit equation .