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.
The Extreme Optimization Mathematics Library for .NET has a simple and intuitive object model for working
with curves. You can easily create the most common types of curves, find zeroes and calculate derivatives. The
Extreme Optimization Mathematics Library for .NET currently supports constants, lines, quadratic curves,
polynomials and Chebyshev approximations.
In addition, the Extreme Optimization Mathematics Library for .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.