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%TCIDATA{<META NAME="Title" CONTENT="Plotting Curves and Surfaces">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 17:02:37 1997}
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\section{Plotting\label{Plotting} Curves and Surfaces}

The plotting capabilities of symbolic algebra systems are among their most
powerful features. With \textsl{Scientific Notebook} you can carry out
operations interactively. You can plot functions and expressions; examine
the results; revise the plot and examine the results of the revision; add
multiple functions to the plot; and carry out a variety of other plotting
procedures. This adds an experimental dimension to problem solving that was
not easily accessible in the past. In the preceding chapter, several plots
were provided to illustrate properties of functions. You will find yourself
creating plots in many situations to help answer questions about the
behavior of different functions or families of functions.

\strut

\subsection{\ General Information}

In the following, we describe techniques for creating plots with \textsl{%
Scientific Notebook}, showing how to plot lines and curves in the Euclidean
plane, and lines, curves, and surfaces in three-dimensional Euclidean space.
We describe the basic routines \textsf{Rectangular, Polar}, and\textsf{\
Implicit }from the \textsf{Plot 2D} submenu, and \textsf{Rectangular}, 
\textsf{Cylindrical},\textsf{\ Spherical}, and \textsf{Tube }from the 
\textsf{Plot 3D} submenu.\textsf{\ } The submenus of \textsf{Plot 2D}, 
\textsf{Plot 3D}, and \textsf{Calculus} also contain a variety of
specialized plotting routines for advanced topics in calculus, vector
calculus, and differential equations. Those \textsl{Scientific Notebook}
plotting options are introduced and discussed in later chapters, along with
the related mathematics.

\strut

You can tell \textsl{Scientific Notebook} to plot an expression or function
in several ways, as described in the ensuing sections. Most of these are
variations on the following basic procedure.

\begin{quote}
$\blacktriangleright $ To plot an expression involving one variable
\end{quote}

\begin{enumerate}
\item[1.]  Place the insertion point in the expression.

\item[2.]  Click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{2dplot.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename '2dplot.wmf';file-properties "XNPEU";}}; or from
the \textsf{Plot 2D} submenu, choose \textsf{Rectangular}.\medskip
\end{enumerate}

A frame containing a plot of the expression appears in line after the
expression, with the lower edge resting on the text baseline and the
insertion point at the right of the plot. In the next section of this
chapter---The Frame, The View, and The Plot Properties Tabbed Dialog---you
will find information on repositioning and resizing the frame. Following
that is information on revising plots.

The first attempt at a plot uses the default parameters that are set on the
Plot Intervals page of the Maple Settings dialog. There are many settings
you can adjust to obtain the view you prefer.

The following plot shows the function $y=x\sin x$ with the default domain
interval $-5<x<5$ and the default view intervals on $x$ and $y$. To make
this plot, leave the insertion point in the expression $x\sin x$, and click 
\FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{2dplot.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename '2dplot.wmf';file-properties "XNPEU";}}or from
the \textsf{Plot 2D} submenu, choose \textsf{Rectangular}.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular }or click \FRAME{itbpF}{%
0.3001in}{0.3001in}{0.0701in}{}{}{2dplot.wmf}{\special{language "Scientific
Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file
"F";width 0.3001in;height 0.3001in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename '2dplot.wmf';file-properties "XNPEU";}}
\end{quote}

\begin{quotation}
$x\sin x$
\end{quotation}

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";function \TEXUX{$x\sin x$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";xviewmin
"-5";xviewmax "5";yviewmin "-4.947";yviewmax "1.955";phi 45;theta
45;plottype 4;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}}

There are other ways to enter plot information, to change both the
appearance and the position of the plot, and to plot multiple items on the
same axes. These points are explained one at a time in the following
sections. First, we will discuss terminology and general properties
pertaining to all \textsl{Scientific Notebook} plots.

\strut

\subsection{Default Options For Plots}

The first attempt at a plot uses the default parameters that are set on the 
\textsf{Plot Options}, \textsf{Plot Intervals}, and \textsf{Plot Frame}
pages of the \textsf{Maple Settings} dialog.

\begin{quote}
$\blacktriangleright $ To set defaults for \textsf{Plot Options} settings%
\label{Maple settings, plot options}
\end{quote}

\begin{enumerate}
\item  From the \textsf{Maple} menu, choose \textsf{Settings}.

\item  Click the \textsf{Plot Options} tab.

\begin{itemize}
\item  Change \textsf{2D Plot Attributes} for \textsf{Axes Type}, \textsf{%
Thickness}, \textsf{Line Color}, or \textsf{Plot Style} by checking the
appropriate box or making an appropriate selection from a list.

\item  Change \textsf{3D Plot Attributes} for \textsf{Axes Type, Plot Style,}
or \textsf{Shading} by making appropriate selections from lists.

\item  Check \textsf{Display Plot Properties Dialog Before Plotting} if you
wish to set plotting options each time you make a plot, rather than using
default settings.
\end{itemize}

\item  Choose \textsf{OK}.
\end{enumerate}

\begin{quote}
$\blacktriangleright $ To set defaults for \textsf{Plot Intervals}
\end{quote}

\begin{enumerate}
\item  From the \textsf{Maple} menu, choose \textsf{Settings}.

\item  Click the \textsf{Plot Intervals} tab.

\item  Check \textsf{2D} or \textsf{3D}, and then choose a \textsf{Plot Type}%
.

\item  For that plot type, set default \textsf{Coordinates} and \textsf{%
Sample Size}.

\item  Choose \textsf{OK}.
\end{enumerate}

\begin{quote}
$\blacktriangleright $ To set defaults for \textsf{Plot Frame} settings\label%
{Maple settings, plot frame}
\end{quote}

\begin{enumerate}
\item  From the \textsf{Maple} menu, choose \textsf{Settings}.

\item  Click the \textsf{Plot Frame} tab.

\begin{itemize}
\item  Change \textsf{Model Screen Attributes} by checking the appropriate
box.

\item  Change \textsf{Miscellaneous, Placement,} and \textsf{Baseline
Default Settings for New Plots} by checking appropriate boxes.

\item  Change \textsf{Size Default Settings for New Plots} by setting
appropriate dimensions.
\end{itemize}

\item  Choose \textsf{OK}.
\end{enumerate}

\strut

\subsection{\ The Frame,\label{Frame} 
\index{View@View!2D plots@2D plots}\label{View}the View, and the Plot
Properties Tabbed Dialog}

Whenever you choose any of the options from either the \textsf{Plot 2D} or 
\textsf{Plot 3D} submenu to create a plot, a rectangular \textsl{frame} 
\index{Frame@Frame!select@select}appears on the screen. The region of
Euclidean space shown inside the frame is referred to as the \textsl{view}.
\ 

\begin{itemize}
\item  To make changes to the size of the plot and to its placement in your
document with the mouse, you must select the frame.

\item  To make changes to a plot with the mouse, including changes to the $x$
interval, or $y$ interval, or any other attributes, you must select the
view.\medskip
\end{itemize}

To make these changes using the \textsf{Plot Properties} dialog, you may
select either the frame or the view.

\begin{quote}
$\blacktriangleright $ To select the frame\label{Frame select}
\end{quote}

\begin{itemize}
\item  Click the frame.\medskip

You can click anywhere within the rectangle, including in any part of the
plot that is showing in the frame.

Eight black \textsl{handles} (solid boxes) appear around the edges of the
frame and one tool appears in the lower-right corner, indicating that the
frame is selected. You select the frame to make changes to the size, shape,
and placement of the plot.%
\FRAME{dtbpF}{2.2796in}{1.7677in}{0pt}{}{}{frame1.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
2.2796in;height 1.7677in;depth 0pt;original-width 226.5pt;original-height
152.9375pt;cropleft "0";croptop "1";cropright "1";cropbottom
"-0.0131";filename 'frame1.wmf';file-properties "XNPEU";}}
\end{itemize}

\begin{quote}
$\blacktriangleright $ To select the view 
\index{View@View!select@select}\label{View select}
\end{quote}

\begin{itemize}
\item  Double-click the frame.

You can double-click anywhere within the rectangle, including in any part of
the plot that is showing in the frame.%
\FRAME{dtbpF}{158.8125pt}{110.375pt}{0pt}{}{}{Figure }{\special{language
"Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display
"PICT";valid_file "F";width 158.8125pt;height 110.375pt;depth
0pt;original-width 224.625pt;original-height 155.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'frame2.wmf';file-properties
"XNPEU";}}
\end{itemize}

Eight gray handles appear around the edges of the frame, and four tools
appear along the right edge of the frame. When the mouse pointer is over the
frame, it has the shape of a hand. In this state, the view is selected. You
select the view to make changes to the functions that are being plotted, to
the view intervals, and to many other attributes of the actual picture that
appears in the frame.

\begin{quote}
$\blacktriangleright $ To bring up the \textsf{Plot Properties} tabbed dialog%
\label{Plot properties} 
\index{View@View!select@select}
\end{quote}

\begin{enumerate}
\item[1.]  Click to select the frame, or double click to select the view.

\item[2.]  Click the dialog tool in the lower-right corner of the frame or
view\textsf{\medskip }

- or -\textsf{\medskip }

From the \textsf{Edit} menu, choose \textsf{Properties\medskip }

- or -

Click 
\FRAME{itbpF}{0.3001in}{0.3001in}{0.0701in}{}{}{property.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 0.3001in;height 0.3001in;depth
0.0701in;original-width 17.8125pt;original-height 16.9375pt;cropleft
"0";croptop "1";cropright "1";cropbottom "0";filename
'Property.wmf';file-properties "XNPEU";}} .\medskip
\end{enumerate}

This brings up the \textsf{Plot Properties} dialog with tabbed pages \textsf{%
Frame}, \textsf{Labeling}, \textsf{Plot Components}, \textsf{Axes}, and 
\textsf{View}.\FRAME{dtbpF}{301.875pt}{124.5625pt}{0pt}{}{}{Figure }{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 301.875pt;height 124.5625pt;depth 0pt;original-width
300.375pt;original-height 121.9375pt;cropleft "0.0071";croptop "1";cropright
"1";cropbottom "0";filename 'PlotPrp2.wmf';file-properties "XNPEU";}}

The defaults for the frame settings can be changed on the \textsf{Plot Frame}
page of the \textsf{Maple Settings }dialog.

\begin{quote}
$\blacktriangleright $ To bring up the \textsf{Plot Properties} tabbed
dialog 
\index{View@View!select@select}in advance of creating the plot
\end{quote}

\begin{itemize}
\begin{enumerate}
\item  Place the insertion point to the right of an expression

\item  Press \textsc{ctrl} while choosing the plot menu item.
\end{enumerate}
\end{itemize}

\strut

\subsection{\ Related topics}

\begin{itemize}
\item  
\hyperref{Frame Properties}{}{}{DM6-2.tex#Frame Properties}

\item  \hyperref{The View for Two Dimensional Plots}{}{}{DM6-3.tex#View
intervals}

\item  \hyperref{Exercises and Solutions}{}{}{DM6-7.tex#Exercises}
\end{itemize}

\rule{0.67in}{0.01in}

\hyperref{\FRAME{itbpF}{38.875pt}{24.5pt}{6pt}{}{}{index.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid-file "F";width 38.875pt;height 24.5pt;depth
6pt;original-width 36.125pt;original-height 22.5625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'index.wmf';file-properties
"XNPEU";}}}{}{}{DMIndex.tex#Math Index}\quad {\small Index entries: 
\hyperref{Frame}{}{}{DMIndex.tex#Frame}, \hyperref{Plot properties}{}{}{%
DMIndex.tex#Plot properties}, \hyperref{View}{}{}{DMIndex.tex#View}}

\end{document}
