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<H1><A NAME="SECTION00490000000000000000"> </A><A NAME="oneDwin"> </A><A NAME="594"> </A><A NAME="595"> </A>
<BR>
The 1-D View Window
</H1>
<BR>
<DIV ALIGN="CENTER"><A NAME="oneD"> </A><A NAME="619"> </A>
<TABLE WIDTH="50%">
<CAPTION><STRONG>Figure 2.9:</STRONG>
The 1-D View window.</CAPTION>
<TR><TD>21#21</TD></TR>
</TABLE>
</DIV>
<BR>
<DL>
<DT><STRONG>Window title:</STRONG>
<DD>DsTool: 1-D View #<I>n</I>
<DT><STRONG>Function:</STRONG>
<DD>The 1-D View window graphically displays computed data.
<DT><STRONG>Description:</STRONG>
<DD>The 1-D View window is opened by selecting the 1-D View
option from the Panels menu button located in the Command window.
The 1-D View window can only be opened when the current dynamical
system is a one-dimensional mapping,
<!-- MATH: $f:\real \to \real$ -->
22#22.
Multiple 1-D View
windows can be open simultaneously. All
1-D View windows display the same data, but they may use different scalings.
<P>
The window displays the ``cobweb diagram''<A NAME="602"> </A><A NAME="603"> </A>
for trajectories of the system.
That is, given an initial point <I>x</I><SUB>0</SUB>, we draw a vertical line from (<I>x</I><SUB>0</SUB>, 0) to
<!-- MATH: $(x_0, f(x_0))$ -->
(<I>x</I><SUB>0</SUB>, <I>f</I>(<I>x</I><SUB>0</SUB>)), and then a horizontal line to
<!-- MATH: $(f(x_0), f(x_0))$ -->
(<I>f</I>(<I>x</I><SUB>0</SUB>), <I>f</I>(<I>x</I><SUB>0</SUB>)).
We then repeat the process starting for
<!-- MATH: $x_1 = f(x_0)$ -->
<I>x</I><SUB>1</SUB> = <I>f</I>(<I>x</I><SUB>0</SUB>) drawing lines
from (<I>x</I><SUB>1</SUB>,<I>x</I><SUB>1</SUB>) to
<!-- MATH: $(x_1,f(x_1))$ -->
(<I>x</I><SUB>1</SUB>,<I>f</I>(<I>x</I><SUB>1</SUB>)) to
<!-- MATH: $(f(x_1),f(x_1))$ -->
(<I>f</I>(<I>x</I><SUB>1</SUB>),<I>f</I>(<I>x</I><SUB>1</SUB>)), and so forth.
<P>
When the window is open, data is displayed as it is computed.
When the user resizes<A NAME="604"> </A> the window, the current variable ranges are
maintained, but the scaling is adjusted accordingly.
As the user moves the mouse in the drawing canvas, the current
coordinates<A NAME="605"> </A>
of the mouse position<A NAME="606"> </A> are displayed in the window's
panel. This region is blank when the mouse does not point
into the canvas. Mouse events in the main drawing canvas have the following
effects:
<UL>
<LI>
The SELECT<A NAME="608"> </A>
button sets the direction of the iterator to ``forward.'' It
also reads the values indicated by the cursor and adjusts the value
of the variable in the Selected Point window.
<LI>
Dragging the SELECT button while holding down SHIFT creates an elastic rectangle used
to rescale<A NAME="609"> </A> the window. When the user releases SELECT, a notice
appears with the options to enlarge the
view (the default, also known as ``zoom in'')<A NAME="610"> </A>,
shrink the view (also known as ``zoom out''),
or cancel the selection. If the enlarge option is selected, the scaling is
adjusted so that the selected region fills the canvas. If the
shrink option is selected, the view is rescaled so that
the whole view is put into the selected rectangle. The
values in the horizontal and vertical min and max text fields
are updated automatically and a screen refresh is performed.
<LI>
The MENU<A NAME="611"> </A> button
sets the direction of the iterator to ``backward.'' It
also reads the values indicated by the cursor and adjusts the
value of the variable in the Selected Point window.
<LI>
Clicking the ADJUST<A NAME="612"> </A> button is equivalent to selecting
the Continue button on the Orbits window.
</UL>
<DT><STRONG>Panel items:</STRONG>
<DD>
<UL>
<LI>Horizontal message:
Identifies the three text fields to the right of this message as referring to the horizontal variable:
the phase space variable.
They are from left to right: the Horizontal min read-write text field, the Mouse abscissa position
read-only text field, and the Horizontal max read-write text field.
<LI>Horizontal min read-write text field:
Displays the current minimum value of the displayed
range of the abscissa (the variable).
<LI>Mouse abscissa position read-only text field:
Displays the current abscissa value of the mouse. If the mouse does not
point into the canvas, this region is blank.
<LI>Horizontal max read-write text field:
Displays the current maximum value of the displayed
range of the abscissa (the variable).
<LI>Vertical message:
Identifies the three text fields to the right of this message as referring to the horizontal variable:
the function value.
They are from left to right: the Vertical min read-write text field, the Mouse ordinate position
read-only text field, and the Vertical max read-write text field.
<LI>Vertical min read-write text field:
Displays the current minimum value of the displayed
range of the ordinate (the function value).
<LI>Mouse ordinate position read-only text field:
Displays the current ordinate value of the mouse. If the mouse does not
point into the canvas, this region is blank.
<LI>Vertical max read-write text field:
Displays the current maximum value of the displayed
range of the ordinate (the function value).
<LI>Refresh command button:
Clears the drawing canvas and redraws
the currently stored data as selected by the user in
the above settings.
<LI>Toggle diagonal command button:
Toggles the drawing of the diagonal (<I>y</I> = <I>x</I>) on the plotting canvas.
<LI>Toggle function command button:
Toggles the drawing of the graph of the function <I>y</I> = <I>f</I>(<I>x</I>) on the plotting canvas.
<LI>Use default ranges command button:
Sets the ordinate and abscissa to their default ranges, and then refreshes the
plotting canvas.
<LI>Clear command button:
Clears trajectory data from memory, and refreshes the canvas according
to the above settings.
<LI>Dismiss command button:
Closes the 1-D View window.
</UL></DL>
<P>
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<ADDRESS>
<I>John Lapeyre</I>
<BR><I>1998-09-04</I>
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