Tr3:
3-D surface triangulationTr3:
3-D surface triangulationTable of contents
Tr3 is a home-grown programme for triangulating 3-D surfaces
between serial-section contours. It takes a .tr3
plain-text model-definition file (as produced by Fie) as input and produces a VRML model file
(.wrl, for use by
Thrup’ny, for example);
a finite-element model file (.sap) for use by SAP IV and our other
modelling software;
and JSON files for use by Thrwp’ny
(example).
Tr3 is implemented in Fortran. It was originally developed under VMS, and later under Unix for Alpha, and is currently being developed under Debian GNU/Linux and (alas) Microsoft Windows; the binaries are available for downloading below. It can be used for any purpose as long as I am informed of its use. So far there is no documentation beyond what you’re looking at.
Either download the Tr3 executable for 32-bit Windows (about 1.6 Mbytes) or (if your computer is part of the McGill BME network) create a shortcut to the executable on probeShare. Follow the general instructions for installation of Dip software.
If you are using a copy of Tr3 installed on your local hard disk,
then you must also provide the Glib library and two
associated libraries. Download the following DLL files into the same
directory that tr3.exe is in:
Tr3 also uses a statically linked copy of the GLE Tubing and Extrusion Library by Linas Vepstas.
If your computer is part of the McGill BME network, create a
symbolic link (ln -s) to the executable on
probeShare. Otherwise download the Tr3 executable from here:
To make Tr3 executable, open a terminal window
(in some versions of Linux, by doing
),
and do
cd Downloads
chmod u+x tr3
Alternatively, you can right-click on the file in a
file-browsing window, select and
then the tab, and check
the box .
You can run Tr3 by opening a terminal window and giving the command
./Downloads/tr3 or, if you have already cd’d
into the Downloads directory, just ./tr3.
Tr3 uses version 6.2 of the Independent JPEG Group’s JPEG library
so you may need to install it (Debian package libjpeg62)
if you don’t have it (which may happen if you only have a later
version installed).
You may need to look at the general instructions for installation of Dip software.
By default, Tr3’s graphics are displayed on the screen. If you run
Tr3 from the command line, you can optionally specify that Tr3 should
plot its graphics to a file in one of a few formats. The command can
take the following forms:
tr3 /plot
(you will be asked to provide filename/dev=type)
tr3 /plot=filename
(you will be asked to provide type)
tr3 /plot=filename/dev=type
The plotting device types are described in the Dip documentation
under Specifying the output type.
When you first run Tr3 you are asked to select a .tr3 file. The menu usage is the same as for Fie’s .
Once the .tr3 file has been read in, you will be asked to select which subset you wish to process, if any subsets have been defined in the .tr3 file. The first item in the subset menu will be , which is equivalent to not having defined any subset at all.
The next step is to select options, if desired.
The option allows you to monitor and guide the triangulation process. This is done when you suspect that artefacts in the 3-D model (e.g., jaggedness) are caused by a poor triangulation. See below for details.
The option
is used to tell Tr3 to combine all triangles that have the same descriptive
text into a single object, regardless of which line, join or cap they
are derived from in Fie. This means that most viewers will render the
entire object smoothly, rather than showing abrupt transitions between
triangles derived from different lines, joins and caps. If this option
is not selected, the default file name will include the text string
_dbg (for ‘debug’).
The
option tells Tr3 whether to attempt to generate surfaces indicating where
x and y clipping have been enabled as a subset
attribute in Fie. If the automatically generated surfaces are not
successful, you may want to disable them here and create such
surfaces manually.
The option tells
Tr3 to create distinctive edges in the model where the clipping occurs.
The option controls how Tr3 triangulates caps. It is unlikely that you’ll need to worry about this.
The option can enable Taubin iterative surface smoothing. You will be asked for the number of iterations to use. More iterations results in a smoother surface but the shape may be unacceptably deformed. This smoothing works best if the surfaces are already reasonably smooth, and in principle it is probably better to do your smoothing within Fie.
The option controls whether Fie’s marked voxels are displayed in the 3-D model. This is seldom desired.
The option does not currently work with either Thrup’ny or Thrwp’ny.
The option controls whether the 3-D model is output in JSON format (as well as in VRML and SAP format). There are three possible settings:
.jsonList
file; and a set of .json files, one for each object.
The files are written into a subdirectory named json, which must already
have been created within the directory where the .tr3 file lives.
To view the resulting model using Thrwp’ny, open the HTML file
in your Web browser
(example).
Once you have selected the desired options, click the bottom button to
continue.
A default output file name will be suggested, based on the name of the .tr3 file
and the name of the selected subset. The name may also contain _dbg,
depending on the options chosen (see above).
Normally you should just accept the default name by hitting the Enter or Return key. The actual triangulation will then start. If your model is small, Tr3’s graphical output may flash past so quickly that you hardly see it. Tr3 should end with a message saying and an button.
While Tr3 is running, it may produce warning messages. Make note of such messages and then click on (or press any key) to continue.
One such warning, at the end, may say No real elements, no .sap file created.
This happens if no thicknesses or material properties are specified. This is normal for
models that are used only for visualization and not for simulation.
If the option is selected (see above) then Tr3 stops after triangulating each line pair, join and cap and allows you to accept or modify the result.
The image on the right shows a typical Tr3 verification screen. The upper left panel shows a line in two slices (black and red) and the triangles (green) that Tr3 has used to connect them. Below and on the right are side views of the two lines and the triangles. At the bottom are three lines of text:
| Skip triangulation of this pair |
| Toggle alignment of centres |
| Change cost function |
| Accept triangulation of this pair |
| Accept triangulation of rest of Line |
| Accept Every remaining line triangulation |
| Quit |
The function is seldom if ever required.
The function controls
whether Tr3 does a preliminary alignment of the two lines before trying to determine
the optimal triangulation. The current state is displayed as either
(aligned) or (unaligned) in the third line of text,
and clicking the button reverses the state. Sometimes one or the other will
give a better triangulation.
| Area |
| Narrowness = (1/(1-COSmax))**p |
| Edge length |
| Narrowness 2 = (1/THmin)**p |
| Narrowness 3 = COSmax**p |
| - Partial-volume |
| Mixed: - Partial-volume + p*Narrowness |
The button is another way of affecting how the triangulation is done. Tr3 determines an optimal triangulation by minimizing a ‘cost’ (Funnell, 1984). For example, Tr3 may minimize the total surface area formed by the triangles between two lines.
There are several different cost functions available. Sometimes the triangulation can be improved by choosing one or the other. Some of the cost functions have adjustable parameters:
Tr3 creates a log file called tr3_log.tmp in your home
directory. As Tr3 is running, certain information is recorded in that file.
It may be useful for debugging.
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