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7. Data Probe Modules

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.

7.1 Numeric Data


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.

7.2 AUTO Solution Reconstruction Using FORT8 Files

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

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).

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

Left and Right keys

Perform rotations about the vertical axis.

Up and Down keys

Perform rotations about the horizontal axis.

Page Up and Page Down keys

Perform rotations about the axis "coming out of the screen".

Control + Left and Right keys

Translate the object horizontally.

Control + Up and Down keys

Translate the object vertically.

Control + Page Up and Page Down keys

Zoom the object.

Mouse bindings

Hold down the Middle Mouse Button

Performs rotations of the solution based upon the virtual trackball paradigm.

Release the Middle Mouse Button

The solution continues to rotate in the same direction as it was rotating when the button was release.

Click the Middle Mouse Button

The solution stops rotating.

Hold down the Right Mouse Button

Translates the solution based upon the movements of the mouse.

Hold down the Middle Mouse Button with Shift Key held down

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.

Coord and Scale

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).

Options

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.

Grid

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.

7.3 AUTO Solution Reconstruction Using An IVP Solver

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

Left and Right keys

Perform rotations about the vertical axis.

Up and Down keys

Perform rotations about the horizontal axis.

Page Up and Page Down keys

Perform rotations about the axis "coming out of the screen".

Control + Left and Right keys

Translate the object horizontally.

Control + Up and Down keys

Translate the object vertically.

Control + Page Up and Page Down keys

Zoom the object.

Mouse bindings

Hold down the Middle Mouse Button

Performs rotations of the solution based upon the virtual trackball paradigm.

Release the Middle Mouse Button

The solution continues to rotate in the same direction as it was rotating when the button was release.

Click the Middle Mouse Button

The solution stops rotating.

Hold down the Right Mouse Button

Translates the solution based upon the movements of the mouse.

Hold down the Middle Mouse Button with Shift Key held down

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.

Coord and Scale

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).

Compiler Options

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

environment variable.

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.

Options

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.

Grid

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.

7.4 General AUTO solution

This is a general module used to visualize AUTO generated solutions, either by reading them from a AUTO file (of fort.8 type), or by reconstructing them with an IVP solver.

As this module inherits the ideas both from the AUTO IVP and from the AUTO fort8 dataprobes, it also uses the same tags as these modules. The first category of tags concern the definition of the types of columns in the VBM files, which can be equation variables or parameters. Thus, the corresponding tags for the two categories are:


AUTO_EQ


AUTO_PAR

For example, if the VBM file contains the following tags:


# AUTO_EQ 0 14 
# AUTO_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.

Only the IVP option of this module needs these two tags, but they do not cause any trouble for the the fort8 option.

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.

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).

For both options, 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 /home/lcvm1/danav/VBM/demos/Troy_problem/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.

Both 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,....

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

Left and Right keys

Perform rotations about the vertical axis.

Up and Down keys

Perform rotations about the horizontal axis.

Page Up and Page Down keys

Perform rotations about the axis "coming out of the screen".

Control + Left and Right keys

Translate the object horizontally.

Control + Up and Down keys

Translate the object vertically.

Control + Page Up and Page Down keys

Zoom the object.

Mouse bindings

Hold down the Middle Mouse Button

Performs rotations of the solution based upon the virtual trackball paradigm.

Release the Middle Mouse Button

The solution continues to rotate in the same direction as it was rotating when the button was release.

Click the Middle Mouse Button

The solution stops rotating.

Hold down the Right Mouse Button

Translates the solution based upon the movements of the mouse.

Hold down the Middle Mouse Button with Shift Key held down

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

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.

Data Options

This page allows the user to choose between the two options available in this module for generating the solution, which are the IVP solver and the AUTO generated fort.8 files. 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.

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 last button on this page, labeled "Reload data", may 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 need to press the "Draw" button before seeing any change.

IVP Options

This page concerns only the IVP solver option and allows the user to compile their problem and to choose the precision of the solution reconstruction.

This form of solution reconstruction 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

environment variable.

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.

Extra Data

This page contains all the operations needed to add new columns to the solution.

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:

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:

File

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

tag. Thus, the next time the VBM file is loaded, the new columns will be automatically added, without any action needed from the user.

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.

Visual Panel

This page contains two buttons, used respectively to iconify and deiconify the visual panel.

The Visual control 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.

Coord and Scale

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).

Ribbons

This page can be used to add one or several ribbons to the solution.

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 labelled "Scale" on the center on the line, scales all the ribbons with a real value.

And 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 line at the center of the page defines each of the ribbons attached to the solution. The first three menus allow to choose 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 allows to color the ribbon according to 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). After modifying them, you must press the "Update ribbon" button at the right of the line. When the user modifies the current ribbon, the values of these coordinates change according to it. 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.

Options

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.

Grid

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.

View options

The "View options" panel allows you to set the axes options, to choose the colormap and to perform some file operations.

Axes Options

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.

Colormap

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.

Save and Load

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.

Data Panel

This page contains two buttons, used respectively to iconify and deiconify the data panel.


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