\section{The Multiple Orbits Window}\label{MultOrbWin}\label{mult window}\label{window, mult}\index{Multiple Orbits window}\index{window, Multiple Orbits}
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\begin{figure}[H]
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\centerline{\psfig{figure=ps/multiple.ps,height=203pt}}
\caption{\label{multiple}
The  Multiple Orbits window.
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\end{figure}

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\begin{description}

\item[Window title:]  DsTool:  Multiple orbits 
\item[Function:]  The Multiple Orbits window allows the user to select a set of
	initial conditions from which to start trajectories.\index{trajectories, multiple}
%	In this way, multiple orbits can be computed simultaneously.  
\item[Description:]  The Multiple Orbits window is opened by 
	selecting the Multiple Orbits option from the Panels menu button located
	in the Command window.  The user selects a region of the product of the phase space and 
	parameter space centered about the point specified in the Selected Point window.
%.  The size of the region is 
%	determined by the Radius fields for the variables and parameters and
%	is centered around the point specified in the Selected Point window.
	The user may specify that points be chosen on a regular grid inside
	the region or only on the boundary.
%  When the field ``Boundary only'' is set to on, the points will form only the outline of a 
%	rectangle in two dimensions.  
	In the former case, a ``box'',
        including its interior, is selected.
        The dimension of the box depends on the number of coordinates which have Number
        of points specified greater than 1.  The total number of points will be the product
	of the values in the Number of points fields.  In the latter case, the points will 
	form only the outline of a rectangle in two dimensions.  The two dimensions
	selected will be the first two coordinates in the list with the Number of points
	specified greater than 1.  If there is only one coordinate with Number of points
	greater than 1, then the a line segment is selected.  If all the Number of points
	fields are set to 1, then only the point specified in the Selected Point window
	is selected.  
	Each edge of the set of selected points is discretized by the Number of points 
	specified for the associated coordinate, and has length twice the value of the Radius field
	for that coordinate.

%	In either case, the lengths of each coordinate
%	edge of the selected region will be twice the value in the Radius field. 
%	Each edge is discretized by the Number of points value specified
%	for that coordinate.  The result is a grid of points (or outline of a rectangle)
%	which make up a set of selected points.
%	In the case when a region is selected, then the total number of points will be the
%	product of the values in the Number of points fields.

        If a transformation other than Identity is selected, then each of these points will
        be passed through this filter.  Transformations may be defined so that these points 
        can be projected onto some submanifold of the whole space or to
        create arrays of points which are not in the form of a ``box''.

%  Transformations may
%        be user-defined, and may depend upon a parameter whose value is given by a field
%        in the Multiple Orbits window.

	Initial multiple points may also be loaded by using the mouse interface.
	Dragging the SELECT\index{mouse, select button} button while holding down CONTROL in a 2-D View 
	window will draw a rectangle
	in the viewing canvas.  Upon release of the mouse button, a notice will
	appear allowing the user two choices.  The selections are Load IC's and
	Cancel.  If the user selects Load IC's, the appropriate Radius fields on the 
	Multiple Orbits window are changed, and the new initial conditions are loaded.
	However, no orbits are computed. If the user selects Cancel, no action is taken.
%  The selections are Forwards,
%	Backwards, and Cancel.  If the user selects Forwards or Backwards, then
%	the selected point as displayed in the Selected Point window is updated
%	as if the user had selected the center point of the rectangle.  The Size
%	fields on the Multiple Orbits window of the coordinates in the 2-D View window
%	are updated to reflect the size of the user selected box.  Then a set of 
%	points are loaded and trajectories are computed, either forwards or backwards
%	as selected.  If the user had selected Cancel, then no action is taken.

%\item[Panel type:] pop-up
%\item[Panel attributes:] pinnable(in), resizable, variable template
\item[Panel items:]\mbox{}
	\begin{itemize}
	\item Images numeric field:
		Displays the number of automatic continuations to be performed.  If $n$ is
        	the value of this field, then selecting Forwards or Backwards with $n>1$ will produce 
        	the same result as selecting Forwards or Backwards with $n=1$ and then
        	selecting Continue $n-1$ times.   The default value is $1$.
        \item Transformation stack setting:
	        Allows the user to choose a transformation to apply to the selected set of points.
        	If this is set to anything but the identity, then whenever any points are loaded they will
        	automatically be mapped through the transformation.  The transformation functions
        	must be defined and installed ahead of time.  The options are Identity (the default),
		Elliptical, and Rotated. 
        \item and parameter read-write text field:
		Displays the parameter to pass to the transformation function.
        	This value will have different effects (or none at all) depending on the
        	selected function.  For the identity function, it has no effect.
        	The default value is $0$.
	\item Points on boundary only exclusive setting:
		Allows the user to choose whether the shape of the region to be selected is
		a ``box'' with interior or the outline of a rectangle (only the boundary
		of the ``box'').  The default is off, so that the shape of the region selected
		is a box.
        \item Radius read-write text fields:
		Display the radius of the box in the direction of each variable and parameter.
        	Note that the side of the box will have twice this length. 
        \item Points numeric fields:
		Display the the number of grid points to put along 
		the specified side or axis of the box.
        \item Load multiple initial conditions command button:
	        Loads the set of initial conditions using the current values
        	on the Multiple Orbits and Selected Point windows.
        \item Copy final to initial command button:
%		Copies the final values of the trajectories computed from
%        	the current multiple points into the current values of the selected points.
		Loads the final values of the trajectories computed from the 
		current initial conditions.
	\item Forwards command button:
		Starts the computation of forward trajectories  from each initial condition.
		If there are no points loaded then  points will be loaded as if the user
		had first pressed the Load multiple initial conditions command button.  
		Trajectories are computed according to the specifications on the Orbits window.
        \item Continue command button:
		Extends the trajectories computed by the Forwards or Backwards
                command buttons on the Multiple Orbits window.
	\item Backwards command button:
		Starts the computation of backward trajectories from each initial condition.
                If there are no points loaded then  points will be loaded as if the user
                had first pressed the Load multiple initial conditions command button.
                Trajectories are computed according to the specifications on the Orbits window.
	\item Dismiss command button:
		Closes the Multiple Orbits window.   
%The fields will not revert back to their default values.
	\end{itemize}
\end{description}

