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Problem Seed:

We are developing other ways to specify graphs which are to be created 'on the fly'. All of these new methods consist of adding macro packages to WeBWorK. Since they do not require the core of WeBWorK to be changed, these enhancements can be added by anyone using WeBWorK.

These two piecewise linear graphs were created by specifying the points at the nodes.
Click on the graph to view a larger image.

This graph was created using a hermite spline by specifying points at

x	-4	-3	-2	-1	0	1	2	3	4
y	0	1	2	0	1	-1	2	1	2
yp	0	1	0	-2	0	1	2	-3	1

The macro packages which allow creating graphs in this fashion are still be refined -- particularly the error messages. The numerical calculations were all written in Perl using numerical routines adapted from the Numerical Analysis book by Burden and Faires.
We are also working on a macro which will automatically identify the maximum, minimum and inflection points of an arbitary hermite cubic spline from its specifying values. This will allow automatic generation of problems in which the maximum, minimum and inflection points are to be deduced from a graph.

You can view the source for this problem. or consult the documentation for more details on the PG language.