The following sections describe the usage of modules which may be utilized to visualize specific solutions contained within a bifurcation diagram. These modules communicate with VBM through an interface described in Section.
An example of the Numeric Data module.
This Data Probe is quite simple but has been found to be very useful. On the left it lists all of the names that have been defined in the VBM file and on the right it shows the values of all of the columns at the marked point. The bar at the top of the window is the same color as the marker sphere to which the Data Probe is attached.
This module is used to visualize solutions computed using AUTO (by Doedel, et. al.). To function, this module requires that points given to it have the
AUTOFort8_file
tag. This tag tells the module where it can find the full solutions, as produced by AUTO, so that it can produce graphical representations of the solution. An example of the usage of this tag follows.
# AUTOFort8_file /home/lcvm1/redrod/bvp.fort8 1
0.0 0.0 -1.5364222362e-31 0.0 0.0 0.0 1.0 0.0 0.0
In the previous example the
AUTOFort8_file
fort.8
files and we refer to the AUTO documentation for
further information on the structure of such files.
The final entry in the tag is an integer which
gives the label of the solution within
the AUTO data file to visualize (AUTO fort.8
may contain more then one solution).
This module is based on DataViewer, and uses the following keyboard and mouse binding to manipulate the visualization. Note, this information is repeated in several sections since it is the same for all DataViewer based modules. We include it to make each section as self-contained as possible.
Keyboard bindings
Perform rotations about the vertical axis.
Perform rotations about the horizontal axis.
Perform rotations about the axis "coming out of the screen".
Translate the object horizontally.
Translate the object vertically.
Zoom the object.
Mouse bindings
Performs rotations of the solution based upon the virtual trackball paradigm.
The solution continues to rotate in the same direction as it was rotating when the button was release.
The solution stops rotating.
Translates the solution based upon the movements of the mouse.
As the mouse is moved up the solution is moved closer to the eye-point, and as the mouse is moved down the solution is moved further away from the eye-point.
The control panel for this module is shown in Figure. Note, some of the control panels are common to several modules. We have chosen to describe them multiple times to make the documentation for each module self contained.
The control panel for the
AUTO FORT8 based Data Probe module.
This page allows the user to select what columns of data from the fort.8 file to plot in the Data Probe viewer. The X coordinate,Y coordinate, and Z coordinate rows allow manipulation of the spatial coordinates which are plotted, while the Color coordinate row controls the use of a column of data as a color (more detail on the coloring feature can be found in Section).
An example row of the "Coord and Scale"
option page.
Each row begins with a label which shows the minimum value for the selected column and ends with a label which shows the maximum value (as denoted by "a" and "e" in Figure). These minimums and maximums are taken over the entire solution. The selection widget (denoted by "b" in Figure) allows the user to select which column of the data they wish to visualize. The first type-in widget (denoted by "c" in Figure) allows the user to select a scaling value for the column. Each value in the column is multiplied by the scaling value before being plotted. A useful trick is to scale some value by 0 to get a "plan view" of the other two columns. The second type-in widget (denoted by "e" in Figure) allows the user to translate each column of data separately. The translation value is added to each value in the column. For example, the "Center" button at the bottom of this paged may be used to set the translation value for X, Y, and Z so that the solution appears in the center of the window. Note that the color row does not have scale or translation since they do not make sense for the color coordinate (more on the color coordinate is in Section).
This page allows the setting of general visualization options. At the top of this page are two toggle buttons. If the top button (marker "Lines") is selected then the solution will be rendered as lines (i.e. unshaded). If the bottom button (marker "Cylinders") is selected then the solution will be rendered as tubes (i.e. shaded). The next widget is marked "Width" and is used to set the width with which the solution is drawn.
WARNING: The width has different interpretations depending on whether "Lines" or "Cylinders" is chosen. For "Lines" it is number of pixels, and for "Cylinders" it is the radius of the cylinder. The graphics may look quite strange if the drawing method is changed without making the appropriate change to the width. For example a value of "3" may be perfectly reasonable for the number of pixels in a line, but far too large for the width of the cylinder.
The next two controls on this page are two sliders with which the user can control the lighting complexity and the geometry complexity. The exact definition of these values is beyond the scope of this manual, but the idea is that these allow the user to trade image quality for rendering speed. Low values of these sliders make the image render faster, but be lowering image quality (e.g. smaller number of triangles per sphere, turning off shading), while high values render more slowly but are of higher quality. "7" is the default value and the user is encouraged to experiment to find values which are good balance between speed and quality.
Finally, there are two toggle buttons "Write points off" and "Write points on" which controls the production of additional debugging output. For general usage the "Write points off" should be selected.
The "Grid" pages controls the appearance of the grid in the Data Probe window. The toggle buttons "Grid on" and "Grid off" control whether the grid appears or not. The slider labeled "Grid lines" allows the user to set the number of lines to be used in the creation of the grid. Higher numbers make the grid "denser". The "First Start", "Second Start", "First End", and "Second End" type-ins allow the use to define the coordinates of two opposite corners of the grid so that it may be moved around. The "R","G", and "B" type-ins control the color of the grid, while the "Cylinder on" and "Cylinder off" toggles whether the grid is drawn as lines (i.e. no shading) or as cylinders (i.e. shading). The "Width" type-in in interpreted as number of pixels when the grid is drawn without shading and as the radius of the cylinder when it is drawn with shading. Finally, the three toggle buttons labeled "YZ Plane", "XY Plane", and "XZ Plane" control the orientation of the grid.
This module is used to visualize solutions of a discretized ODE by using an IVP solver. To function, this module requires that points given to it have the
AUTO_EQ
AUTO_PAR
tags. An example of the usage of these two tags follows.
# AUTO_EQ 0 14
# AUTO_PAR 15 34
Normally, both of these tags will appear in the
global tag section of the VBM file, though
they may be used as pointwise tags as well.
These tag tells the module which columns
of data it should give to the IVP solver.
The AUTO_EQ
should be followed
by two integers which defines
those columns of the data needed
by the IVP solver. The first integer denotes
the starting column, and the second integer denotes
the ending column (note: these are inclusive
and the first column is 0). These columns
are used, in order, as the initial conditions
for the system of ODEs.
Similarly,
the AUTO_PAR
should be followed
by two integers which defines
those columns of the data that represent
parameters in the ODE.
As the name of these tags suggest, this module is designed to work with AUTO. The difference between this module and the Data Probe described in Section is that this module reconstructs the solution using an IVP solver, while the module in Section reads a file produced by the original computation.
This module also uses an environment variables to define
how it should compile the IVP solver.
VBM_1D_AUTO_FORTRAN_COMPILER
must be
set to a command line which can be used to compile the
Fortran IVP solver. It allows
you give any additional flags needed for your problem and compiler.
The default value is f77 -O
.
If this is inappropriate for your system this module will fail.
The advantage of this module is that the data storage in much smaller, since the original fort.8 file may be discarded. The disadvantage is that if the ODE is stiff then the solution reconstruction may not be possible. The user must decide which mode of operation is more appropriate for their problem.
This module is based on DataViewer, and uses the following keyboard and mouse binding to manipulate the visualization. Note, this information is repeated in several sections since it is the same for all DataViewer based modules. We include it to make each section as self-contained as possible.
Keyboard bindings
Perform rotations about the vertical axis.
Perform rotations about the horizontal axis.
Perform rotations about the axis "coming out of the screen".
Translate the object horizontally.
Translate the object vertically.
Zoom the object.
Mouse bindings
Performs rotations of the solution based upon the virtual trackball paradigm.
The solution continues to rotate in the same direction as it was rotating when the button was release.
The solution stops rotating.
Translates the solution based upon the movements of the mouse.
As the mouse is moved up the solution is moved closer to the eye-point, and as the mouse is moved down the solution is moved further away from the eye-point.
The control panel for this module is shown in Figure. Note, some of the control panels are common to several modules. We have chosen to describe them multiple times to make the documentation for each module self contained.
The control panel for the
AUTO IVP based Data Probe module.
This page allows the user to select what columns of data from the fort.8 file to plot in the Data Probe viewer. The X coordinate,Y coordinate, and Z coordinate rows allow manipulation of the spatial coordinates which are plotted, while the Color coordinate row controls the use of a column of data as a color (more detail on the coloring feature can be found in Section).
An example row of the "Coord and Scale"
option page.
Each row begins with a label which shows the minimum value for the selected column and ends with a label which shows the maximum value (as denoted by "a" and "e" in Figure). These minimums and maximums are taken over the entire solution. The selection widget (denoted by "b" in Figure) allows the user to select which column of the data they wish to visualize. The first type-in widget (denoted by "c" in Figure) allows the user to select a scaling value for the column. Each value in the column is multiplied by the scaling value before being plotted. A useful trick is to scale some value by 0 to get a "plan view" of the other two columns. The second type-in widget (denoted by "e" in Figure) allows the user to translate each column of data separately. The translation value is added to each value in the column. For example, the "Center" button at the bottom of this paged may be used to set the translation value for X, Y, and Z so that the solution appears in the center of the window. Note that the color row does not have scale or translation since they do not make sense for the color coordinate (more on the color coordinate is in Section).
This module functions by compiling a AUTO "right hand side" file, written in Fortran, with an IVP solver (also written is Fortran). This module then communicates with the AUTO program using standard interprocess communication protocols. This page is used to control the compilation of the Fortran program.
Note: The Fortran program must be compiled, using this interface, before this module will perform any visualizations.
The top type-in allows the use to enter a
directory in which the Fortran program may
write temporary files. If this directory
is set to "NULL" (which is the default)
the this module will create a temporary
directory itself (normally in /usr/tmp
).
The second type-in allows the user to
enter where the AUTO right hand side
file may be found.
This module uses the same AUTO Fortran
file as described in
Section,
and the main point to remember is that the
STPNT
function must be commented out.
This Data Probe
attempts to be intelligent about choosing a
good default to put here by looking at
any compute engine blocks in the VBM file,
but this value should always be checked
before the Fortran program is
compiled.
Finally, if the "Compile" button is pressed the Fortran program will be compiled and the communication will be initiated.
Note: the default prefix for the compile command used to create the Fortran program is "f77 -O". If this is not appropriate for your system you may override this default by setting the
VBM_VIEW_AUTO_IVP_FORTRAN_COMPILER
This page allows the setting of general visualization options. At the top of this page are two toggle buttons. If the top button (marker "Lines") is selected then the solution will be rendered as lines (i.e. unshaded). If the bottom button (marker "Cylinders") is selected then the solution will be rendered as tubes (i.e. shaded). The next widget is marked "Width" and is used to set the width with which the solution is drawn.
WARNING: The width has different interpretations depending on whether "Lines" or "Cylinders" is chosen. For "Lines" it is number of pixels, and for "Cylinders" it is the radius of the cylinder. The graphics may look quite strange if the drawing method is changed without making the appropriate change to the width. For example a value of "3" may be perfectly reasonable for the number of pixels in a line, but far too large for the width of the cylinder.
The next two controls on this page are two sliders with which the user can control the lighting complexity and the geometry complexity. The exact definition of these values is beyond the scope of this manual, but the idea is that these allow the user to trade image quality for rendering speed. Low values of these sliders make the image render faster, but be lowering image quality (e.g. smaller number of triangles per sphere, turning off shading), while high values render more slowly but are of higher quality. "7" is the default value and the user is encouraged to experiment to find values which are good balance between speed and quality.
Finally, there are two toggle buttons "Write points off" and "Write points on" which controls the production of additional debugging output. For general usage the "Write points off" should be selected.
The "Grid" pages controls the appearance of the grid in the Data Probe window. The toggle buttons "Grid on" and "Grid off" control whether the grid appears or not. The slider labeled "Grid lines" allows the user to set the number of lines to be used in the creation of the grid. Higher numbers make the grid "denser". The "First Start", "Second Start", "First End", and "Second End" type-ins allow the use to define the coordinates of two opposite corners of the grid so that it may be moved around. The "R","G", and "B" type-ins control the color of the grid, while the "Cylinder on" and "Cylinder off" toggles whether the grid is drawn as lines (i.e. no shading) or as cylinders (i.e. shading). The "Width" type-in in interpreted as number of pixels when the grid is drawn without shading and as the radius of the cylinder when it is drawn with shading. Finally, the three toggle buttons labeled "YZ Plane", "XY Plane", and "XZ Plane" control the orientation of the grid.