Simple 2D Graphs

<BODY LANG="EN"> <HR><center> <table border=1> <td><A NAME="tex2html33" HREF="node1.html"><img height=36 width=36 alt="PREVIOUS" src="http://www.cs.utah.edu/icons/latex2html/previous.gif"></A></td> <td><A NAME="tex2html39" 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="tex2html41" HREF="node3.html"><img height=36 width=36 alt="NEXT" src="http://www.cs.utah.edu/icons/latex2html/next.gif"></A></td> <td><a href="contents-node2.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="SECTION00020000000000000000">Simple 2D Graphs</A></H1> <P> <A NAME="twodplots"> </A> Let's try to visualize the height of the ball, for given values of <I>V</I> and <IMG WIDTH=6 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline136" SRC="img4.gif" > , as a function of time. The standard way to do this is to plot the independent variable (time, in this case) on the horizontal axis vs. the dependent variable (height, in this case) on the vertical axis. <P> Producing such a two-dimensional graph in Maple is quite easy. To do this, you must give Maple, at a minimum, <P> <UL> <LI> a symbolic expression containing the independent variable as the only unbound variable and <LI> the range over which the independent variable will vary. <P> </UL> <P> For example, the Maple command <P> <table><td valign=top><a href="send3.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><code>plot(height(50, Pi/4, t), t=0..10);</code></td></table> <P> will plot the height of a ball thrown with initial velocity 50 meters/sec at an angle of 45 degrees as a function of time, as time ranges from 0 to 10 seconds. Maple will do this by bringing up a separate window. When you are done with the window you can dispose of it by pulling down its <B>File</B> menu and choosing <B>Exit</B>. <P> The <TT>plot</TT> command will accept a number of optional arguments. Often, you will want to specify the range of the y-axis as well as of the x-axis. For example, perhaps we'd like to fix our graph so that the ball doesn't continue through the ground: <P> <table><td valign=top><a href="send4.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><code>plot(height(50, Pi/4, t), t=0..10, 0..100);</code></td></table> <P> We might also want to label the axes and give the graph a title: <P> <table><td valign=top><a href="sende1.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><PRE>plot(height(50, Pi/4, `time (secs)`), `time (secs)`=0..10, `height (meters)`=0..100, title=`Height attained in ballistic trajectory`);</PRE></td></table> <P> If we are going to produce a number of such plots, it is handy to have a function that takes the initial velocity and initial angle and then produces the plot for us: <P> <table><td valign=top><a href="sende2.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><PRE>plotHeight := (velocity, theta) -> plot(height(velocity, theta, `time (secs)`), `time (secs)`=0..10, `height (meters)`=0..100, title=`Height attained in ballistic trajectory`);</PRE></td></table> <P> Now we can produce our plot with the simple command: <P> <table><td valign=top><a href="send5.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><code>plotHeight(50, Pi/4);</code></td></table> <P> This is a good illustration of the power of user-defined functions. <P> <HR><center> <table border=1> <td><A NAME="tex2html33" HREF="node1.html"><img height=36 width=36 alt="PREVIOUS" src="http://www.cs.utah.edu/icons/latex2html/previous.gif"></A></td> <td><A NAME="tex2html39" 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="tex2html41" HREF="node3.html"><img height=36 width=36 alt="NEXT" src="http://www.cs.utah.edu/icons/latex2html/next.gif"></A></td> <td><a href="contents-node2.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>