3.2.20 Bumpy Functions

We now consider implementing models. Each interval is given by a set of intervals. We previously defined the union of two intervals. Extending that definition results in the following method for taking the union of two intervals:

Another method, which uses to describe the result, follows:

Since each interval is a collection of intervals, the union of two intervals is simply the sum of the two collections:

. Good models of -bumpy functions may be built using the methods presented so far, using rather than , where appropriate.

Jeff Tupper

March 1996