# Curves and Interpolation

For our purposes, a curve is a possibly curved line showing a relationship between two factors. Corresponding to every value of the variable x we have a value y = f(x ). In programming terms, this is similar to a method that takes one Double argument and returns a Double.

Curves are also known as functions. However, because the word function is a reserved word in many languages, including Visual Basic .NET, we chose the term Curve to represent functions. In the documentation, both curve and function may be used.

Extreme Numerics.NET has a simple and intuitive object model for working with curves. You can easily create the most common types of curves, find zeros and calculate derivatives. Extreme Numerics.NET currently supports polynomials, Chebyshev series, rational curves, piecewise curves including several types of cubic splines, and a wide variety of nonlinear curves.

In addition, Extreme Numerics.NET implements the notion of a function basis. A function basis is a set of functions that can be combined to form a particular class of functions or curves. An example of a function basis is the set of monomial functions 1, x, x2, x3, which can be combined to form all polynomials up to degree 3. Function bases have applications in least squares problems and interpolation.