Animated Plots

<BODY LANG="EN"> <HR><center> <table border=1> <td><A NAME="tex2html81" HREF="node6.html"><img height=36 width=36 alt="PREVIOUS" src="http://www.cs.utah.edu/icons/latex2html/previous.gif"></A></td> <td><A NAME="tex2html87" HREF="uces-5.html"><img height=36 width=36 alt="UP" src="http://www.cs.utah.edu/icons/latex2html/up.gif"></A></td> <td><A NAME="tex2html89" HREF="node8.html"><img height=36 width=36 alt="NEXT" src="http://www.cs.utah.edu/icons/latex2html/next.gif"></A></td> <td><a href="contents-node7.html"><img height=36 width=36 alt="CONTENTS" src="http://www.cs.utah.edu/icons/latex2html/toc.gif"></a></td> <td><a href="reset.hamlet"><img height=36 width=36 alt="RESET" src="http://www.cs.utah.edu/icons/latex2html/stop.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="http://www.cs.utah.edu/icons/latex2html/copyright.gif"></a></td> <td><a href="mailto:hamlet@cs.utah.edu"><img height=36 width=36 alt="FEEDBACK" src="http://www.cs.utah.edu/icons/latex2html/feedback.gif"></a></td> <td><a href="http://www.cs.utah.edu/%7Ehamlet/icons.html"><img height=36 width=36 alt="ABOUT" src="http://www.cs.utah.edu/icons/latex2html/about.gif"></a></td> </table> </center> <HR><H1><A NAME="SECTION00050000000000000000">Animated Plots</A></H1> <P> <A NAME="animations"> </A> Maple's animation capability affords you yet another way to put three dimensions on a two-dimensional plot. Suppose that we'd like to understand the height reached by the ball as a function of time <EM>and</EM> initial angle. We originally approached this problem by putting three different curves on the same plot. With animation, we can put an arbitrary number of curves on successive plots. <P> The functions that do animation are contained in the <TT>plots</TT> library. You will be able to use them only if you first do this: <P> <table><td valign=top><a href="send6.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><code>with(plots);</code></td></table> <P> Now let's animate the problem described above: <P> <table><td valign=top><a href="sende11.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><PRE>animate(height(50, theta, `time (sec)`), `time (sec)`=0..10, theta=0..Pi/2);</PRE></td></table> <P> Notice that we are specifying two ranges. The first range gives the range of the horizontal axis, and the second range gives the range of the animation. <P> An animation window should appear. By clicking on the various buttons, you can ``play'' the animation. (Click on the question mark button to get started.) What you will see is height as a function of time as the initial angle varies from 0 to 90 degrees. <P> Every ``frame'' in the animation gives a plot of height as a function of time for some angle. When you play the animation, the angle varies in discrete steps between 0 and <IMG WIDTH=24 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline138" SRC="img5.gif" > . You can control the number of steps, or frames, by setting the <TT>frame</TT> parameter. For example, to obtain 15 frames: <P> <table><td valign=top><a href="sende12.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><PRE>animate(height(50, theta, `time (sec)`), `time (sec)`=0..10, theta=0..Pi/2, frames=15);</PRE></td></table> <P> Parametric plots can also be animated. Let's animate the trajectory of the ball for different angles: <P> <table><td valign=top><a href="sende13.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><PRE>animate([distance(50, theta, t), height(50, theta, t), t=0..10], theta=0..Pi/2);</PRE></td></table> <P> Here, each frame shows a complete trajectory for a specific angle. <P> <HR><center> <table border=1> <td><A NAME="tex2html81" HREF="node6.html"><img height=36 width=36 alt="PREVIOUS" src="http://www.cs.utah.edu/icons/latex2html/previous.gif"></A></td> <td><A NAME="tex2html87" HREF="uces-5.html"><img height=36 width=36 alt="UP" src="http://www.cs.utah.edu/icons/latex2html/up.gif"></A></td> <td><A NAME="tex2html89" HREF="node8.html"><img height=36 width=36 alt="NEXT" src="http://www.cs.utah.edu/icons/latex2html/next.gif"></A></td> <td><a href="contents-node7.html"><img height=36 width=36 alt="CONTENTS" src="http://www.cs.utah.edu/icons/latex2html/toc.gif"></a></td> <td><a href="reset.hamlet"><img height=36 width=36 alt="RESET" src="http://www.cs.utah.edu/icons/latex2html/stop.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="http://www.cs.utah.edu/icons/latex2html/copyright.gif"></a></td> <td><a href="mailto:hamlet@cs.utah.edu"><img height=36 width=36 alt="FEEDBACK" src="http://www.cs.utah.edu/icons/latex2html/feedback.gif"></a></td> <td><a href="http://www.cs.utah.edu/%7Ehamlet/icons.html"><img height=36 width=36 alt="ABOUT" src="http://www.cs.utah.edu/icons/latex2html/about.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I><A NAME="tex2html1" HREF="http://www.cs.utah.edu/~zachary">Joseph L. Zachary</A> <BR> <A NAME="tex2html2" HREF="http://www.cs.utah.edu/~hamlet">Hamlet Project</A> <BR> <A NAME="tex2html3" HREF="http://www.cs.utah.edu/">Department of Computer Science</A> <BR> <A NAME="tex2html4" HREF="http://www.utah.edu/ HTML_Docs/UofUHome.html">University of Utah</A></I> </ADDRESS> </BODY>