Limitations of Two-Dimensional Plotting

Although the plots that we have been producing are nice, they are not quite powerful enough to visualize the ballistic trajectory problem. Here are two representative problems:

• Although we can look at how the height reached or the distance traveled by the ball varies with respect to time, we can't look at both at the same time. In other words, we can't directly visualize the trajectory followed by the ball.
• It would be interesting to look at height (or distance) as a function of both time and initial angle. Unfortunately, on our two-dimensional plots we have only two variables.

The fundamental problem here is that we have too many variables and not enough space on a simple two-dimensional plot. Fortunately, Maple provides a variety of ways to address this problem. In each of the sections that follows, we will consider a visualization problem and explore the Maple solution.

Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah