# 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*, *x*^{2},
*x*^{3}, which can be combined to form all polynomials up to degree 3. Function bases have
applications in least squares problems and interpolation.