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Comparing Curves and RealFunction Delegates
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Comparing Curve classes and RealFunction delegates
The classes that inherit from Curve on the one hand, and the
RealFunction delegate on the other, both represent mathematical
functions of one real parameter that return a real number. You can create a RealFunction from a Curve by encapsulating the curve's ValueAt method. You can create a Curve from a RealFunction using the GeneralCurve class, which takes a RealFunction delegate in its constructor. They are different in nature,
however.
A Curve object represents a function in the mathematical
sense. Very often, a specific type of function has special properties that enable many calculations to be performed
more efficiently. For example: polynomials are easy to integrate and differentiate. To use a numerical integration
algorithm for polynomials would be inefficient.
A RealFunction delegate encapsulates only the calculation of
the value of the function. This is sufficient for most applications. The equation solver classes, as well as the classes that implement
numerical integration and differentiation algorithms, all use a
RealFunction delegate. These operations can be controlled to a
great degree. Note that the Curve class has methods
corresponding to these applications, but the degree of control is much more limited.
In other words: a Curve object focuses on the mathematical
function as a mathematical object, and the specific mathematical properties and relationships of a particular type of
curve. A RealFunction delegate isolates the primary purpose of a
mathematical function - to calculate a return value for a given argument - into a simple data type. This allows it to
fit easily into any of a number of more complex procedures for solving numerical problems.
In summary:
- If you work with a mathematical function for which a specialized Curve type exists, it is usually better to use
the Curve type.
- In other situations it is more of a trade-off between the simplicity of the direct abstraction of a
mathematical function versus the degree of control you have over the calculation of derivatives, integrals and
zeroes.
Up: Curves Next: Curve Fitting Previous: Piecewise Curves and Cubic Splines Contents
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