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 is 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.
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
Finally, the precision of this solver can be set within the "Number of steps" typein. The default step of the solver is 0.005 corresponding to 200 generated points. Note that the solution will contain 201 points, corresponding to the initial point plus the generated ones.
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 is a general module used to visualize AUTO generated solutions, either by reading them from an AUTO file (of fort.8 type), either by reconstructing them with an IVP solver, or by combining the two methods.
To function, this module needs two tags specifying the way it should use the list of variable names and the initial data coming from the bifurcation diagram. They concern the definition of the types of columns in the VBM files, which can be equation variables or parameters.
Reconstruct_EQ
Reconstruct_PAR
For example, if the VBM file contains the following tags:
# Reconstruct_EQ 0 14
# Reconstruct_PAR 15 34
then the 15 first columns of the VBM files are the initial values of the equation variables (i.e. for s=0.0), while columns from the 16th to the 35th are the parameters in these equations. This means that the 15 first names in the list will be used to display the solution, while the 20 next names can eventually be used during the reconstruction.
If these tags are absent, then the module can use the following tags instead:
AUTO_EQ
AUTO_PAR
If the solution is reconstructed both by using a fort8 file and then by calling an IVP solver, then the module needs both Reconstruct and AUTO tags. The AUTO tags will design the columns in the fort8 file, while the Reconstruct tags denote the columns built by the IVP solver.
These tags are used to set the names of the columns in the solution, but also to generate the initial data and the parameter values for reconstruction with the IVP solver, so they should be present in any case.
This module also uses an environment variables to define how it should
compile the IVP solver. VBM_VIEW_AUTO_IVP_FORTRAN_COMPILER
must be set to a command line which can be used to compile the Fortran
IVP solver. It allows the you to 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.
For the AUTO generated fort.8 files, this module also uses the
AUTOFort8_file
tag. The use of this tag is the same as for the AUTO fort8 dataprobe. 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
tag is followed by
the full path to the desired AUTO data file. Such files are known as
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).
Independently of the data option, this module uses the
VBM_extra_data_file
tag to provide the name of the file containing the definition of extra columns in the solution.
For example, if the VBM file contains
# VBM_extra_data_file ./fq.sav
then the extra column defined in the file named as the argument of this tag will be automatically loaded as the VBM file is read.
All the options of this module use the variable names defined in the
VBM file. If these variables are not defined, and the fort8 option is
chosen, then the variables get assigned the names x0,x1,...
.
Finally, this module uses a compute engine block specially designed for it. Its name is "Reconstruct" and the information it should provide to the module is the names of the working directory and of the problem file. See the IVP Options subsection for more details.
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.
Note that this module uses two control panels. The first one, called "Data panel", is used for all the choices and actions concerning the numerical data in the module. The second one, called "Visual panel", is used for all the choices and actions concerning the graphical part of this dataprobe.
These control panels can be simultaneously activated from the main window of the module, by pressing the button called "Deiconify panels". The opposite button on this window, labeled "Iconify panels", will iconify them both.
While working with each of the two panels, the other panel can be deiconified using their last page, which is labeled as the other panel ("Visual panel" if inside the data panel, and "Data panel" if inside the visual panel). These pages only contain two buttons, which can iconify and deiconify the other panel.
The data control panel 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 numerical control panel for the
General AUTO Data Probe module.
This page allows the user to choose between the three options available in this module for generating the solution, which are the IVP solver,the AUTO generated fort.8 files and a combination of both of them. In the first case, the solution is reconstructed with the IVP solver starting from its first point (for s=0.0) stored in the VBM file. In the second case, the solution is read from the fort.8 file. In the third case, the solution is read from the fort8 file, and then new columns are added to it by calling an IVP solver.
The advantage of the IVP solver is that the data storage is 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.
The 2 first data options use the Reconstruct tags, and if these tags are not specified, the AUTO tags (see beginning of the section for more details). The last data option uses both categories of tags the following way: the AUTO tags denote the columns in the fort8 file, while the Reconstruct tags the columns added afterwards by solving an IVP problem.
The last button on this page, labeled "Reload data", should be pressed in the following situations:
Pressing this button will have the effect of regenerating the solution considering all the options and actions associated to it. The user still needs to press the "Draw" button before seeing any change.
This page is shown in Figure and concerns the data options using an IVP solver. It allows the user to manage the executable linking their problem to the IVP solver and to choose the precision of the solution reconstruction.
The IVP solver page for the
General AUTO Data Probe module.
The IVP solution reconstruction functions by compiling an AUTO "right hand side" file, written in Fortran, with an IVP solver (also written is Fortran). This page is used to control the compilation of the Fortran program.
The top group of widgets displays the name of the current working
directory and allows the user to set it. The "Set working directory"
button calls a file dialog inside which this directory can be
selected, and then modifies the preceding text according to the
choice. This directory is used by the executable of the user problem
to write temporary files. If this directory is set to "NULL" (which
is the default), then the module will create a temporary directory
itself (normally in /usr/tmp
).
The second group of widgets displays the name of the problem file, and
allows the user to set it. If the problem name is an executable (ended by a
".exe"), then it is copied into the working directory, unless it is
identified as the "problem.exe" in this directory. 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.
The two previously described parameters (the working directory and the problem file) are NULL by default. Their value can also be automatically set for each VBM file by including a special compute engine block in it. The compute engine block must have the following structure:
##Begin VBM_Compute_Module
NULL
NULL
./work/problem.exe
./work
Reconstruct
Example of reconstruction block
##End
The first two lines, containing "NULL", are not used by this module, but must be present for reasons of block formatting. The next line contains the name of the user problem file for reconstruction. As mentioned before, if this name ends by ".exe", it will be copied into the working directory. If the path to the problem is not absolute, be sure to run VBM from the right directory.
The fourth line contains the name of the working directory. The next line contains the name of the block. The last line contains a comment that is not used by this module.
If this compute engine block is not present in the VBM file, then this module will search for compute engines with the name "VBM_1D_AUTO". If several such compute engines exist, then the module will use the last one it encounters.
Note: even if the VBM_1D_AUTO compute engine specifies a working directory, this module will not use it, in order to avoid conflicts with any running compute engine. Thus, the name of the problem file is the only information the module takes from the compute engine. We recommend to check the default information in this case before the Fortran program is compiled.
The next typein shows the compiler command line, which should contain the name of the fortran compiler and all the options needed for the problem. The default value for it 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
If the "Compile" button is pressed the Fortran program will be compiled and the communication will be initiated.
Finally, the precision of this solver can be set within the "Number of steps" typein. The default step of the solver is 0.005 corresponding to 200 generated points. Note that the solution will contain 201 points, corresponding to the initial point plus the generated ones.
This page is shown in Figure and contains all the operations needed to add new columns to the solution.
The Extra Data page for the
General AUTO Data Probe module.
Importing modules
The first operation that can be performed is importing a module. As the new columns are computed, they could need to call a function defined in a Python module outside VBM.
To import a module, you must type its name in the typein at the top of the page, labeled "Module name". Then you must press the "Import" button. Then any function defined inside it can be called by its name.
For Python programmers, the described actions have the following effect:
from 'module_name' import *
Call functions
The next operation that can be performed on this page is adding a new column by calling a function. For this, you must do the following:
s, f, q, r
and you use "q" as parameter in the function call, then this parameter
will have the integer value 2. You can also pass the whole data matrix
to the function, by using the name "solution".
Note: If you define your function in a module, then you must import
the module for the computation of the new column to work. Typein functions
The last action on this page is adding a new column as a typein expression. The main difference between this operation and the previous one is that for the call functions, the new column is computed in one function call. In the present case, the new column is computed point by point, and any function used inside its expression is called for each point of the solution. Thus, this type of computation can take longer. it is recommended to use it only for simple expressions.
To add a new column by a typein expression, you must do the following:
This page groups all the operations linked to saving and reading the extra columns added in the previous page to and from a file.
The first button, labeled "Save extra variables" activates a save file dialog. If a file name is entered in this dialog, then a file with this name will be created, and all the extra columns will be saved in it. This file will contain:
When the file has been created, the filename can be used in the VBM file as an argument for the
VBM_extra_data_file
If more columns are added after an extra data file has been saved, they can be saved in the same file as before. By this action, both the previous columns and the new ones will be in the same file. If the name of this file has been added to the VBM file as a tag, then all the extra columns will also be loaded at start.
The second button in this page, named "Read variables file", activates a read file dialog which can be used to read in a file created by pressing the first button on this page. If the file has been created in another manner, hazardous effects may result.
A file created in one VBM file can be read inside another VBM file, as long as the variable names used by the new columns are consistent. Though, this operation can be dangerous, so we do not recommend it.
This page contains two buttons, used respectively to iconify and deiconify the visual panel.
The visual control panel 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 visual control panel for the
General AUTO Data Probe module.
This page allows the user to select what columns of the data 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, shown in Figure, can be used to add one or several ribbons to the solution.
The Ribbons page for the
General AUTO Data Probe module.
All the ribbons can be turned on and off by using the "Ribbon on/off" buttons on the top center of this page. In the beginning, these buttons will only activate one ribbon. If several ribbons are defined afterwards, they will turn on and off all the ribbons attached to the solution.
The line below the "Ribbon on/off" buttons contains general properties that apply to all the ribbons at once.
The first one, linked to the left buttons on this line, allows the user to choose between a mirrored ribbon (symmetrical towards the centerline of the solution) and a one-sided ribbon. The default option is mirrored.
The second one, linked to the typein labeled "Scale" on the center on the line, scales all the ribbons with a real value.
The last one, linked to the top right buttons on this line, allows the user to choose between a ribbon drawn as a surface (plain) and as a vector field. By default the ribbons are drawn as surfaces.
The four menus at the center of the page define each of the ribbons attached to the solution. The first three menus set the columns of the data used for the x, y, and z coordinates of the ribbon. The values in these columns are used relatively to the centerline. Thus, in each point of the solution, the ribbon will be defined by a vector with the origin on the centerline and with offset defined by the 3 coordinates.
A fourth coordinate sets the color the ribbon in relation with a column of the data. The ribbon also uses the colormap defined on the View Options page (see below).
These four coordinates are specific to each ribbon, and their values concern the current ribbon (see Ribbon selection below). By default they all have the 0 value, which usually designs the variable "s".
The bottom line on this page allow the user to work with several ribbons attached to the same solution. The first button on this line, labeled "Add ribbon", adds a new ribbon to the solution, as its name states its. The particularity of this operation is that if the ribbons are off, they will be turned on, without adding a new ribbon. A consequent message will also be printed on the standard output.
The next widget on this line, labeled "Ribbon selection", allow to choose the current ribbon. This selection will have the effect of setting all the values on the middle line as being the ones of the selected ribbon. It also designates the ribbon number to be deleted by the "Delete ribbon" operation. When adding a new ribbon, this value will automatically be updated to the last ribbon number, so the new ribbon can be set right away.
The next button, labeled "Delete ribbon", will delete the current ribbon. If the ribbon is the last added, then the current ribbon becomes the previous one. Otherwise, the current ribbon conserves its number, but of course, its identity is different, because the remaining ribbons are shifted. The coordinates of the ribbon are also updated according to the current ribbon selection. The particularity of this button is that if there is only one ribbon left, it will not be deleted, but turned off instead. A consequent message is also printed on the standard output.
Note. Any of the described actions on this page will not have any visual effect until the "Draw" button is pressed.
This page, shown in Figure, controls 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.
The Options page for the
General AUTO Data Probe module.
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 are 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 control the production of additional debugging output. If the "Write points on" button is selected, then the centerline of the solution will be printed on the standard input. This feature can be useful to see the actual values in the solution. For general usage the "Write points off" should be selected.
The "Grid" page, shown in Figure, controls the appearance of the grid in the Data Probe window.
The Grid page for the
General AUTO Data Probe module.
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.
The "View options" page, shown in Figure , allows you to set the axes options, to choose the colormap and to perform some file operations.
The View Opions page for the
General AUTO Data Probe module.
The "Axes Option" section of this page controls the appearance of the coordinate axes in the bifurcation diagram window. The "Axes length" type-in controls the length of the axes, while the "Axes width" type-in allows the user to enter the width of the axes in pixels. Finally, the "Axes on" and "Axes off" toggle switch may be used to control whether the axes appear in the window or not.
Note, the axes always appear at the center of the coordinate system for the bifurcation diagram (after any translations have been applied). Accordingly, the bifurcation diagram always spins around the origin of the axes.
DataViewer provides several different color maps which may be used to translate floating point values into colors (i.e. RGB values). In DataViewer a color map is a function defined over some range of floating point numbers (defined by a minimum and maximum value) which returns an RGB triple. An example of such a function might assign black to the minimum value, white to the maximum value, and interpolate values in between as some shade of grey. Another example might assign blue to the minimum value, red to the maximum value, and the interpolate values in between to create a "rainbow" (we note that while the idea of a "rainbow" which smoothly varies from blue to red may be quite intuitive, the actual implementation of such a colormap can be somewhat subtle).
Normally VBM will compute the minimum and maximum values for the color map by using the appropriate column of data over the entire bifurcation diagram.
The "Colormap" section of the "View options" page allows the user to choose from three different colormaps for the visualization of their data. The "Linear Color Map" sets the minimum value to blue, the maximum value to red, and uses a "rainbow" in between. The "Gray-Scale" color map sets the minimum value to black, the maximum value to which, and uses shades of grey in between. The "Discrete Color Map" color map is different from the previous two in that it only returns colors at integer values and white everywhere else. It is a special purpose color map and it probably not useful for general visualization problems.
One color map which is somewhat specialized is the "11 discrete colors" colormap. In this colormap points of the bifurcation diagram are divided into eleven groups, and two points are placed in the same group if the values in their columns defined by "COLOR Coordinate" are sufficiently close. The eleven colors in this colormap have been chosen to have the highest color separation possible (i.e. they are easy to tell apart from each other). If there are more than eleven groups of values then the twelfth and higher groups are all assigned the color white.
The "Save and Load" section of this page contains buttons for saving and reading information about the bifurcation diagram, including saving it in other formats.
Save View
There are many parameters which make up how a specific bifurcation diagram appears, e.g. its current rotation, width, what columns have been selected, etc. The file chooser activated by this button may be used to save a file which contains all of the parameter for the current visualization so that it may be read in later to recover the same view.
Read View
The file chooser activated by this button may be used to read in a view file which was previously saved with the "Save View" operation. Note, the contents of the view file depends on the VBM file which was being visualized at the time the view file was created. If you attempt to read in a view file which was created for a different VBM file then you are currently visualizing the behavior is undefined (it may work, but will probably not do what you expect!).
Save VRML
This button will soon be used to save a VRML version of the current bifurcation diagram. This functionality is under construction and this module does not use it yet.
This page contains two buttons, used respectively to iconify and deiconify the data panel.