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%TCIDATA{<META NAME="ViewSettings" CONTENT="31">}
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%TCIDATA{<META NAME="Title" CONTENT="The  View for 2D Plots">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 17:03:27 1997}
%TCIDATA{Language=American English}
%TCIDATA{CSTFile=MathHelp.cst}
%TCIDATA{<LINK REL="author" HREF="DM0-1.tex">}
%TCIDATA{<LINK REL="first" HREF="DM6-1.tex">}
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\input{tcilatex}
\begin{document}


\section{The\label{View intervals} View for 2D Plots}

A default has been set for bounds on coordinates for each of the choices on
the \textsf{Plot 2D} submenu. The default bounds are somewhat arbitrary, and
you will often want to change them. You can reset limits on the coordinates
and change other aspects of the view using the \textsf{Plot Properties}
tabbed dialogs as described later in this chapter.\medskip

\label{Domain Intervals}You can change the \textsf{Domain Intervals} from
the \textsf{Plot Components} page of the \textsf{Plot Properties }dialog.
The default is $-5\leq x\leq 5$ for rectangular coordinates and $-5\leq
x\leq 5$, $-5\leq y\leq 5$ for polar coordinates and implicit plots. The
default \textsf{View Intervals} are determined by the \textsf{Domain
Intervals} and the graph. To reset the \textsf{View Intervals} you first
click the \textsf{Default} box to clear it.

The following views of the plot $y=\sin x$ demonstrate the relationship
between the \textsf{Domain} and \textsf{View} intervals on the x-axis for 
\textsf{Rectangular} plots. The \textsf{Domain} intervals determine the
limits of the graph and the \textsf{View} intervals determine the limits of
the view.

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Domain: $-5<x<5$ \\ 
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49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}
\end{center}

When the \textsf{View} interval is smaller than the \textsf{Domain}
interval, the system is plotting points in the domain outside the view, and
consequently plotting fewer points inside the view than would normally be
the case. Large differences in this direction can lead to some distorted
graphs.

In the following sections, you will see examples of the default domain and
view for different types of 2D plots.

\subsection{\ Rectangular Coordinates 
\index{Plot 2D@Plot 2D!rectangular@rectangular}\label{Plot 2D} 
\index{Rectangular coordinates@Rectangular coordinates!2D plots@2D plots}%
\label{Rectangular coordinates}}

When you choose \textsf{Rectangular} from the \textsf{Plot 2D} submenu, the
view that appears is determined by inequalities of the form $a\leq x\leq b$
and $c\leq y\leq d$. The default for the view is the region bounded by $%
-5\leq x\leq 5$ and $c\leq y\leq d$, where $c$ and $d$ are chosen by the
underlying computational system and depend on the shape of the function plot.

\begin{center}
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49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}\bigskip
\end{center}

\subsection{\ Polar Coordinates\label{Polar coordinates}\label%
{Plot 2D, polar}}

When you choose \textsf{Polar} from the \textsf{Plot 2D} 
\index{Plot 2D@Plot 2D!polar@polar}submenu, the 
\index{Polar coordinates@Polar coordinates} view that appears is determined
by the inequality $-\pi \leq \theta \leq \pi $ on the angle. The view
intervals are chosen by the underlying computational system and depend on
the shape of the function plot. The following are default views.

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"normal";xis \TEXUX{x};var1name \TEXUX{$\theta $};}}
\end{center}

Changing the view for the latter graph to $-5<x<5$ and $0<y<25$ gives the
following view of the same plot.

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"25";viewset"XY";rangeset"X";phi 45;theta 45;plottype 8;numpoints
49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$\theta $};}}\bigskip

\subsection{\ Implicit Plots 
\index{Implicit plots@Implicit plots}\label{Implicit Plot 2D}}

When you choose \textsf{Implicit} from 
\index{Plot 2D@Plot 2D!implicit@implicit}the \textsf{Plot 2D} submenu, the
view is determined by inequalities of the form $a\leq x\leq b$ and $c\leq
y\leq d$. The default values for the \textsf{Domain Intervals} are $-5\leq
x\leq 5$ and $-5\leq y\leq 5$, and the default \textsf{View Intervals} are
determined by the underlying computer algebra system. Plotting with \textsf{%
Implicit} assumes rectangular coordinates. The following are default views.

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\TEXUX{$y$};}} \FRAME{itbpFU}{1.817in}{1.2047in}{0in}{\Qcb{$x^{2}+y^{2}=9$}}{%
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\TEXUX{$y$};}} \FRAME{itbpFU}{1.817in}{1.2047in}{0in}{\Qcb{$y=x^{2}$}}{}{}{%
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"red";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";ymin
"-5";ymax "5";xviewmin "-2.316";xviewmax "2.318";yviewmin "-0.1";yviewmax
"5.102";rangeset"X";phi 45;theta 45;plottype 12;num-x-gridlines
25;num-y-gridlines 25;axesstyle "normal";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}\bigskip
\end{center}

\subsection{\ Parametric Plots\label{Parametric}}

When you choose \textsf{Parametric} from 
\index{Plot 2D@Plot 2D!parametric@parametric}the \textsf{Plot 2D} submenu,
the default values 
\index{parametric equations@Parametric equations}for the \textsf{Domain
Interval} are $-5\leq t\leq 5$ and the \textsf{View Intervals} $a\leq x\leq
b $ and $c\leq y\leq d$ are determined by the underlying computer algebra
system. The following are default views.

\begin{center}
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}{}{}{\special{language "Scientific Word";type "MAPLEPLOT";width
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1;pointstyle "point";xmin "-5";xmax "5";xviewmin "-6.239";xviewmax
"6.245";yviewmin "-6.24";yviewmax "6.245";rangeset"X";phi 45;theta
45;plottype 19;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}} \FRAME{itbpFU}{1.817in}{1.2047in}{0in}{\Qcb{$\left( 3\cos
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"-3.12";xviewmax "3.122";yviewmin "-3.12";yviewmax "3.122";rangeset"X";phi
45;theta 45;plottype 19;numpoints 49;axesstyle "normal";xis
\TEXUX{x};var1name \TEXUX{$x$};}} \FRAME{itbpFU}{1.817in}{1.2047in}{0in}{%
\Qcb{$\left( x,x^{2}\right) $}}{}{}{\special{language "Scientific Word";type
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"5.204";yviewmin "-0.5";yviewmax "25.51";rangeset"X";phi 45;theta
45;plottype 19;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}}\bigskip
\end{center}

\section{\label{2D Plotting Tools}Plotting Tools for 2D Plots}

Rescaling presents interesting challenges. Several plotting tools designed
to make this process efficient and enjoyable are described in the ensuing
sections.

\begin{quote}
$\blacktriangleright $ To display plotting tools
\end{quote}

\begin{itemize}
\item  Select the view by double-clicking a plot.\medskip
\end{itemize}

Four plotting tools appear at the upper-right edge of the frame--for
translating the view, zooming in and out, and reading and storing plot
coordinates; \FRAME{dtbpF}{0.3105in}{0.8553in}{0pt}{}{}{plottool.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
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20.3125pt;original-height 59.5pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'plottool.wmf';file-properties "XNPEU";}}eight
gray handles appear on the frame; and the mouse pointer takes the shape of a
hand when it is over the view.

\strut

\subsection{\ Zooming In and Out\label{Zoom}}

The icons for the two zoom tools were designed to look like pictures of
mountains. 
\index{Zoom@Zoom!2D plots@2D plots}Click 
\index{Plot 2D@Plot 2D!zoom@zoom}the large mountain range 
\FRAME{itbpF}{0.3105in}{0.3105in}{0.0701in}{}{}{zoomin.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3105in;height 0.3105in;depth 0.0701in;original-width
20.3125pt;original-height 20.3125pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'zoomin.wmf';file-properties "XNPEU";}} to zoom
in for a closer look; click the small mountain range \FRAME{itbpF}{0.3208in}{%
0.3105in}{0.0701in}{}{}{zoomout.wmf}{\special{language "Scientific
Word";type "GRAPHIC";display "PICT";valid_file "F";width 0.3208in;height
0.3105in;depth 0.0701in;original-width 21.0625pt;original-height
20.3125pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'zoomout.wmf';file-properties "XNPEU";}} to zoom out to see additional parts
of the graph.

\begin{quote}
$\blacktriangleright $ To zoom in or out
\end{quote}

\begin{itemize}
\begin{enumerate}
\item[1.]  Click one of the two zoom tools.

\item[2.]  Move the mouse pointer over the view.

\item[3.]  Click and drag to create a small rectangle inside the
frame.\medskip
\end{enumerate}
\end{itemize}

If you zoom in (with the large mountain range), the contents of the small
rectangle expand to fill the entire frame. Parts of the plot that were
outside the small rectangle are now outside the view. If you zoom out (with
the small mountain range), the original view shrinks to fit inside the small
rectangle. Additional parts of the function plot appear in the new, expanded
view.

There are two types of behavior that occur, depending on the setting for the 
\textsf{View Intervals} in the \textsf{Axes \& View page} of the \textsf{%
Plot Properties }dialog.

\begin{itemize}
\item  To zoom in or out depending on only the $x$-coordinate, \textsf{%
Default} should be checked in the \textsf{\ Axes \& View} page of the 
\textsf{Plot Properties }dialog. (This is the default setting.)

\item  To control both the $x$- and $y$-intervals when zooming in or out,
click the \textsf{Default} box to clear it.\medskip
\end{itemize}

After zooming in or out, you can return the view to approximately where it
was previously. Click the opposite icon, and create a small rectangle with
approximately the same size and position as before, relative to the frame.

\subsection{\ Translating the View\label{Translate view}\label{Pan 2D plots}}

\begin{quote}
$\blacktriangleright $ To translate the view 
\index{Plot 2D@Plot 2D!translate view@translate view} 
\index{Pan 2D plots@Pan 2D plots}\medskip
\end{quote}

\begin{itemize}
\begin{enumerate}
\item[1.]  Select the view by double-clicking. (If the view has already been
selected, click the hand icon 
\FRAME{itbpF}{0.3105in}{0.3105in}{0.0701in}{}{}{plotpan.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
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"1";cropbottom "0";filename 'plotpan.wmf';file-properties "XNPEU";}}in the
upper-right corner of the frame.)

\item[2.]  Move the mouse pointer over the view, so that it takes on the
shape of a hand.

\item[3.]  Click and drag the frame.\medskip
\end{enumerate}
\end{itemize}

An outline of the frame moves as you drag, while the plot remains fixed.
When you release the mouse button, the frame is redrawn at its original
position with a translated view. Use this feature to ``pan'' across the
Cartesian plane in any direction to capture different portions of the plot.

\index{View@View!translate 2D plots@translate 2D plots}

\begin{quotation}
\emph{Note}\quad Zooming and translating change the view without altering
the size or position of the frame. Resizing and moving the frame change the
frame size and placement but do not change the view.
\end{quotation}

\strut \strut

\subsection{\ Plot Coordinates Dialog Bar\label{Plot coordinates dialog bar}}

Double-click a plot and click the 
\FRAME{itbpF}{0.3105in}{0.3208in}{0.0701in}{}{}{plotxy.wmf}{\special%
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"1";cropbottom "0";filename 'plotxy.wmf';file-properties "XNPEU";}} tool. A
dialog bar will appear on your screen that displays the rectangular
coordinates of the mouse cursor whenever the plot is selected and the mouse
cursor is over the plot area. Check \textsf{Polar} on the \textsf{Plot
Coordinates Dialog Bar} to see polar coordinates of points at the cursor.

\begin{quote}
$\blacktriangleright $ To record selected points
\end{quote}

\begin{enumerate}
\item  Select the \FRAME{itbpF}{0.3105in}{0.3208in}{0.0701in}{}{}{plotxy.wmf%
}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 0.3105in;height 0.3208in;depth
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"0";croptop "1";cropright "1";cropbottom "0";filename
'plotxy.wmf';file-properties "XNPEU";}} tool.

\item  Click on points in the graph.
\end{enumerate}

The rectangular coordinates of each points that you click will appear in the
box on the dialog bar.\FRAME{dtbpF}{430.4375pt}{223.75pt}{0pt}{}{}{Figure }{%
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\begin{quote}
$\blacktriangleright $ To create a matrix of coordinates
\end{quote}

\begin{enumerate}
\item  Click on the coordinate pairs you want in the matrix, to select them.

\item  Place the insertion point at the position where you want the matrix.

\item  From the \textsf{Plot Coordinates Dialog Bar}, choose \textsf{Paste}.
\end{enumerate}

\begin{quote}
$\blacktriangleright $ To plot selected points in a polygonal plot
\end{quote}

\begin{itemize}
\item  Drag the matrix to a 2D plot.

- or -

\item  Create the matrix with the plot selected, or with the insertion point
immediately to the right of the matrix (Step 2 above).
\end{itemize}

If you wish to plot only the points, first create the polygonal plot as
described above. Then select the plot, go to the \textsf{Plot Components}
page of the \textsf{Plot Properties} dialog, and change \textsf{Plot Style}
to \textsf{Point}.

\begin{quote}
$\blacktriangleright $ To remove a coordinate pair from the Plot Coordinates
Dialog Box
\end{quote}

\begin{enumerate}
\item  Click on the coordinate pairs you want to remove, to select them.

\item  From the \textsf{Plot Coordinates Dialog Bar}, choose \textsf{Remove}.
\end{enumerate}

\strut

\section{\label{Plot components}Dialogs for 2D Plots\label{Axes & View}}

You can change domain and view settings in the \textsf{Plot Components} and 
\textsf{View\ }pages of the \textsf{Plot Properties }tabbed dialog.\ 

\begin{quote}
$\blacktriangleright $ To bring up the \textsf{Plot Properties }tabbed
dialog for a plot
\end{quote}

\begin{enumerate}
\item  Select the frame or the view by clicking or double-clicking or by
placing the insertion point at the right side of the frame.

\item  Click the dialog tool in the lower-right corner of the view

- or -

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

- or -

Click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{property.wmf}{\special%
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.\medskip

\item  Click the tab for the page you want to use.\medskip
\end{enumerate}

You can make the \textsf{Plot Properties} dialog appear before a plot is
created, so that you can customize settings in advance of the plot, either
by deliberate choice for a particular plot (pressing \textsc{ctrl} as
described below) or for all plots by changing the default in \textsf{Maple
Settings}.

\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}
\item  On a on-time-only basis

\begin{enumerate}
\item  Place the insertion point to the right of an expression or function
name.

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

\item  
\begin{quote}
On a regular basis
\end{quote}

\begin{enumerate}
\item  Choose \textsf{Maple + Settings}

\item  Check \textsf{Display Plot Properties Dialog Before Plotting\bigskip }
\end{enumerate}
\end{itemize}

The \textsf{Plot Components} page is shown below.%
\FRAME{dtbpF}{300.1875pt}{376.875pt}{0pt}{}{}{Figure }{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
300.1875pt;height 376.875pt;depth 0pt;original-width
300.375pt;original-height 394.5pt;cropleft "0";croptop "0.9962";cropright
"0.9926";cropbottom "0.0459";filename 'PlotComp.wmf';file-properties
"XNPEU";}}

\strut

\subsection{\ Plot Components Page}

From the \textsf{Plot Components} page of the \textsf{Plot Properties }%
dialog you can edit, add, and delete expressions to be plotted, choose the
plot style, change the interval to be plotted and set the number of sampling
points. The item box in the upper-left corner of the dialog box shows one of
the expressions or functions you are plotting. These expressions or
functions are referred to as ``items'' and listed by \label{Item number}%
\textsf{Item Number}. You can view all current functions or expressions by
clicking the up-down arrow buttons by the item box. You can change the
curves that are plotted by editing the displayed item, by adding a new item,
or by removing an item from the list.

\begin{itemize}
\item  To change an item, edit it in the box.

\item  To add an item, click \textsf{Add Item}, and then type or paste the
item in the empty box that comes up.

\item  To delete an item from the list, click the arrow buttons until the
item is displayed in the box, and then click \textsf{Delete Item}.\label%
{Delete item}
\end{itemize}

You set the interval to be plotted by editing the numbers in the \textsf{%
Domain Intervals} boxes. The default is the interval $-5\leq x\leq 5$. This
controls the interval containing the sampling points that generate the
plot.\smallskip

You can increase the accuracy of the graph by increasing the \textsf{Sample
Size}.\label{Sample size} 
\index{Sample size} 
\index{Number of data points@Number of data points!2D plots@2D plots}\label%
{Number of data points}Because increasing the \textsf{Sample Size} slows
down the plotting process, you may want a relatively small number of data
points for real-time demonstrations and a relatively large number of data
points for printed documents.\smallskip

\label{Plot style}In a plot, the data points computed either are connected
by line segments or are displayed as points, depending on your choice\label%
{Line plot} 
\index{Line plot@Line plot}of \textsf{Plot Style} as \textsf{Line} or 
\textsf{Point}.\label{Point plot} 
\index{Point plot@Point plot}The default is \textsf{Line}, which connects
the points with lines. \smallskip

If the \textsf{Plot Style} is set to\textsf{\ Line} then you can change the
appearance of a plot by changing\label{Line style} 
\index{Line style@Line style}\textsf{Line Style}, \textsf{Thickness} 
\index{Line!thickness}\textsf{, }and\textsf{\ Line Color}.\label{Line color}%
\label{Color for Plot 2D} 
\index{Line!color}You can set

\begin{itemize}
\item  \textsf{Line Style} 
\index{Line style!dot dash}to \textsf{Solid}, \textsf{Dash}, \textsf{Dots},
or \textsf{DotDash}

\item  \textsf{Thickness} to \textsf{Thin}, \textsf{Medium}, or \textsf{Thick%
}

\item  \textsf{Line Color} to one of the 12 colors \textsf{Black}, \textsf{%
Blue}, \textsf{Brown}, \textsf{Cyan}, \textsf{Gray}, \textsf{Green}, \textsf{%
Magenta}, \textsf{Maroon}, \textsf{Navy}, \textsf{Red}, \textsf{Sienna}, or 
\textsf{Yellow}.
\end{itemize}

If several expressions appear in the same view, you can set different
parameters (such as \textsf{Plot Style}, \textsf{Line Style}, \textsf{%
Thickness}, and \textsf{Line Color}) to distinguish visually between the
different expressions. You may prefer to distinguish between expressions by
setting \textsf{Line Color} differently for each expression in screen-based
documents, and to \textsf{Black} (the default) with a variety of \textsf{%
Line Style} and/or \textsf{Thickness} for printed documents.

You can also choose \textsf{Point Plot}, which displays only the computed
points. You can choose the symbol (\textsf{Point}, \textsf{Circle}, \textsf{%
Cross}, or \textsf{Diamond}) used to plot the points 
\index{Point symbol@Point symbol}\label{Point symbol}with \textsf{Point
Symbol}.\medskip

\subsection{\ Axes Page\label{Axes page {Equal scaling for Plot 2D}}}

From the\textsf{\ Axes }page of the \textsf{Plot Properties }dialog you can
choose the type of axes displayed, the scaling for the axes, change the
appearance of the axes and add axis labels.

\begin{itemize}
\item  Click \textsf{Equal Scaling Along Each Axis} to force the $y$-axis to
use the same scale as the $x$-axis.

\item  Choose \textsf{Axis Scaling} 
\index{Scaling!log} 
\index{Scaling!log-log} 
\index{Scaling!normal} from among \textsf{Standard}, \textsf{Log}, or 
\textsf{Log-Log}.

\item  Specify the appearance of the axes by choosing an \textsf{Axes Type} 
\index{Axes type}from among \textsf{Normal, Boxed, Framed,} or \textsf{None}%
. The choices \textsf{Normal} and \textsf{None} are self-explanatory. The 
\textsf{Boxed} appearance shows the plot inside a rectangular frame, and 
\textsf{Framed} displays the left and lower edges of the box. All of these
choices (except \textsf{None}) display numerical labels on the axes or box
edges.

\item  Customize the $x$-axis and $y$-axis by setting a specified number of
tick marks for each.

\item  Add labels to the $x$-axis and $y$-axis.
\end{itemize}

The four choices for axes are shown below.

\begin{center}
\FRAME{itbpFU}{2.2589in}{1.5056in}{0in}{\Qcb{Normal axes}}{}{}{%
\special{language "Scientific Word";type "MAPLEPLOT";width 2.2589in;height
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x$};linecolor "black";linestyle 1;linethickness 1;pointstyle "point";xmin
"-5";xmax "5";xviewmin "-5";xviewmax "5";yviewmin "-1.04";yviewmax
"1.041";phi 45;theta 45;plottype 4;numpoints 49;axesstyle "normal";xis
\TEXUX{x};var1name \TEXUX{$x$};}} \FRAME{itbpFU}{2.2589in}{1.5056in}{0in}{%
\Qcb{Boxed axes}}{}{}{\special{language "Scientific Word";type
"MAPLEPLOT";width 2.2589in;height 1.5056in;depth 0in;display
"PICT";plot-snapshots TRUE;function \TEXUX{$\sin x$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax
"5";xviewmin "-5";xviewmax "5";yviewmin "-1.04";yviewmax "1.041";phi
45;theta 45;plottype 4;numpoints 49;axesstyle "boxed";xis \TEXUX{x};var1name
\TEXUX{$x$};}}

\FRAME{itbpFU}{2.2589in}{1.5056in}{0in}{\Qcb{Framed axes}}{}{}{%
\special{language "Scientific Word";type "MAPLEPLOT";width 2.2589in;height
1.5056in;depth 0in;display "PICT";plot-snapshots TRUE;function \TEXUX{$\sin
x$};linecolor "black";linestyle 1;linethickness 1;pointstyle "point";xmin
"-5";xmax "5";xviewmin "-5";xviewmax "5";yviewmin "-1.04";yviewmax
"1.041";phi 45;theta 45;plottype 4;numpoints 49;axesstyle "frame";xis
\TEXUX{x};var1name \TEXUX{$x$};}} \FRAME{itbpFU}{2.2589in}{1.5056in}{0in}{%
\Qcb{No axes}}{}{}{\special{language "Scientific Word";type
"MAPLEPLOT";width 2.2589in;height 1.5056in;depth 0in;display
"PICT";plot-snapshots TRUE;function \TEXUX{$\sin x$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax
"5";xviewmin "-5";xviewmax "5";yviewmin "-1.04";yviewmax "1.041";phi
45;theta 45;plottype 4;numpoints 49;axesstyle "none";xis \TEXUX{x};var1name
\TEXUX{$x$};}}
\end{center}

\vspace{1pt}\strut

Use the \textsc{up arrow} to locate hidden choices, should any of these fail
to appear in the dialog box. Choose \textsf{OK} to make the indicated
changes and refresh the function plot. Choose \textsf{Cancel} to leave the
tabbed dialog without taking any action.\medskip \label{View page}

\subsection{\ View Page}

From the\textsf{\ View} page of the \textsf{Plot Properties }dialog you can
set the view intervals and generate a snapshot of the plot.

To change the view, set the \textsf{View Intervals} for $x$ and $y$. The
default view intervals, described above, are determined automatically to
maximize the information contained in the plot, given the domain intervals
that are set on the \textsf{Plot Components} page. The $x$- and $y$-axes can
have radically different scales, and the curve is normally not truncated at
the top or bottom unless there are vertical asymptotes. After clicking to
remove the check mark from \textsf{Default}, you can change the \textsf{View
Intervals} by typing numbers into the boxes for the $x$- and $y$-intervals.

\label{Scaling}To make concrete the difference between the \textsf{Domain
Intervals} in the \textsf{Plot Components} page and the \textsf{View
Intervals} in the \textsf{View} page, consider the following plot of the
function $f(x)=\frac{x^{2}-1}{x^{2}+1}$. \textsf{Domain Intervals} are set
to $-5\leq x\leq 5$ and \textsf{View Intervals} are set to $-10\leq x\leq 10$
and $-2\leq y\leq 2$. The \textsf{Domain Intervals} refer to the interval or
intervals of sampling points for evaluation and the \textsf{View Intervals}
refer to the coordinates that are visible. \FRAME{dtbpF}{3in}{2.0003in}{0pt}{%
}{}{Figure }{\special{language "Scientific Word";type "MAPLEPLOT";width
3in;height 2.0003in;depth 0pt;display "PICT";function
\TEXUX{$\frac{x^{2}-1}{x^{2}+1}$};linecolor "red";linestyle 1;linethickness
1;pointstyle "point";xmin "-5";xmax "5";xviewmin "-10";xviewmax
"10";yviewmin "-2";yviewmax "2";viewset"XY";rangeset"X";phi 45;theta
45;plottype 4;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}}

\label{Axis scaling}Choose \textsf{OK} to make the indicated changes and
refresh the function plot. Choose \textsf{Cancel} to leave the tabbed dialog
without taking any action.

\subsubsection{Plot Snapshots\label{Plot snapshots}}

\emph{Plot snapshots} are computer graphics files of type *.wmf. These are
not needed for viewing or printing plots in \textsl{Scientific Notebook}.
You will need these snapshot files if you want to use a Latex compiler to
produce a dvi file of your document with another system, including with 
\textsl{Scientific Word} or \textsl{Scientific WorkPlace}. Also, you may
want these files to paste into other documents.

You can also use these snapshot files as pictures in \textsf{Scientific
Notebook}. To do this, first generate the snapshot and look on the \textsf{%
Axes} page of the \textsf{Plot Properties} dialog to see the name of the
file. With a file manager, rename the file with an appropriate descriptive
name. Then, in \textsf{Scientific Notebook}, use \textsf{File + Import
Picture} to bring the picture into a document. This will no longer be an
active plot, but will have the same appearance as one. The pictures of plots
are sometimes preferable for on-line viewing as they do not take any time to
generate. They can also be given to students as puzzles--although the plots
themselves contain all the information needed to replicate them, the
snapshot pictures contain no such information.\medskip

\subsection{\ Related topics}

\begin{itemize}
\item  \hyperref{Plotting Curves and Surfaces}{}{}{DM6-1.tex#Plotting}

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

\item  \hyperref{2D Plots of Functions and Expressions}{}{}{DM6-4.tex#Plot
expression}

\item  \hyperref{The View for 3D Plots}{}{}{DM6-5.tex#Plot 3D, view}

\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 36.875pt;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{Domain intervals}{}{}{DMIndex.tex#Domain intervals}, \hyperref{%
Implicit plots}{}{}{DMIndex.tex#Implicit}, \hyperref{Log and log log plots}{%
}{}{DMIndex.tex#Log and log log plots}, \hyperref{Parametric plots}{}{}{%
DMIndex.tex#Parametric plots}, \hyperref{Plot properties}{}{}{%
DMIndex.tex#Plot properties}, \hyperref{Plotting tools}{}{}{%
DMIndex.tex#Plotting tools}, \hyperref{Polar coordinates}{}{}{%
DMIndex.tex#Polar coordinates}, \hyperref{Rectangular coordinates}{}{}{%
DMIndex.tex#Rectangular coordinates}, \hyperref{View}{}{}{DMIndex.tex#View}, 
\hyperref{Zoom plotting tools}{}{}{DMIndex.tex#Zoom plotting tools}}

\end{document}
