Computational Methods in Physics

1. Computational Methods
in Physics
PHYS 3437
Dr Rob Thacker
Dept of Astronomy & Physics (MM-301C)
thacker@ap.smu.ca

2. Today’s Lecture
 Visualization
 More on Opendx
 3d visualization methods
 Isosurfaces
 Volume rendering
 Making movies
 makempeg script & the Berkeley mpeg encoder
 References:
 Some overheads borrowed from a presentations by Tamara
Munzner, Gordon Kindlmann

3. Getting started with Opendx
 Using Import Data is perhaps
the simplest way to get started
with Opendx
 Selecting it will take you to the
Data Prompter

4. Data Prompter
 The data prompter will
create a .general file
which the import module
can read
 We’ll look at importing
gridded data
 Will take many different
types
 Let’s look at the simplest –
a regular grid

5. Datafile description
Using an engineering example in this case
Once the data is described, use “save as” in the
File menu to save the general description used by dx

6. Simplest tool
 Default viz option will allow
you to see the data
immediately
 Ensure everything loaded in OK

7. Note on Windows version
 The windows version has problems with spaces in file names
 Don’t save files with names such as
 C:Programs and somethingmyfilesand so on
 Helpful to set up an Opendx directory right at the top of the
directory tree
 e.g. C:Opendx
 Also, the default viewer in the data prompter did not work for
me
 But could just be my laptop running out of memory
 One of the drawbacks of Opendx is that it rapidly consumes memory
 A workstation dedicated to visualization usually needs ~2 GB or more of
memory
 Will exploit multiple processors though – good news!
 Everything else seems fine though, the VPE works without a problem

8. Checking data
 You can test that your loaded data is correct in a
couple of ways
 Try the test import button
 Will give information about range and so forth
 Examine the data directly with the browse data
button
 Lastly, go directly to the visualization system
described on the previous page
 Unfortunately, if something is wrong it won’t tell you
much quantitative information about the problem

9. Creating a program
 The default visualization system
is useful, but most of the time
we’ll want to create our own
programs
 When we used the data
prompter we saved a description
of the file called fan.64_ascii
in fan.general
 We can load this into our own
program
 The next few overheads walk
through a simple 3d
visualization

10. Creating the visualization program
Open the program editor and expand the ALL listing
of modules, place fileselector, import, isosurface, image
Link by left clicking
on tab and then
drawing a line to
the other box
Now double
click on fileselector

11. Fileselector
 This will bring up a control panel into which you can type the
name of the .general file saved when using the data prompter

12. Executing the program
Select Execute Once
from the execute menu

13. Image output
 Running the
program will
produce an
isosurface
output

14. Interacting with the image
 Under
options
select the
view
control:
Select rotate under mode

15. Rotate the image
 Click and drag
on the image
with the mouse
to rotate
 It isn’t that
fast though
 Note the globe
is turned on by
selecting it in
the options
menu

16. Algorithms for 3d visualization
 A bit of background to the algorithms used in
3d visualization will explain why it is such a
computationally expensive process
 Look briefly at
 Isosurface rendering
 Playing with it in Opendx using the isosurface module
 Volume rendering methods
 Volume rendering is part of the Image module

17. Voxel data
 The analogy of a pixel in 2d is the voxel in 3d
 Field values are described at the vertices rather than in
the center
 Field values along the edges and internally can be
derived by a number of interpolation functions

18. Isosurface Extraction
 Which choose a fixed iso-
value
 Then need to extract out
the contour (surface in
3d) corresponding to this
value
 The marching cubes
algorithm is the most
common method
 Patent has recently expired
on this algorithm
1 2 3 4 3
2 7 8 6 2
3 7 9 7 3
1 3 6 6 3
0 1 1 3 2
Iso-value = 5

19. First step of Marching cubes
 Classify the voxel by the values at the vertices
 Each vertex is either
- outside the surface (> isovalue)
- inside the surface (<= isovalue)
8
Iso=7
8
8
5
5
10
10
10
Iso=9
=inside
=outside

20. Marching Cubes: Triangle Example
a
b
c

21. Example Triangle configurations
 These 15 base examples can be used to derive the 28=256 total configurations

22. Surface Rendering
 2d surfaces are rendered within a
3d space & object appears “solid”
 Data must be converted into
geometrical primitives such as
triangles for rendering
 This process may lead to
information being lost or
disguised
 Makes sense for objects with a
solid surface
Volume Rendering
 Entire volume can be rendered
providing interior information
 data is not explicitly hidden
 Spatial data is mapped to a volume
of RGBA values using a transfer
function
 This volume is rendered directly
using a variety of techniques
 Makes sense for objects with
complex interior structure and no
solid boundaries
Surface vs volume rendering
compared

23. Improving on the earlier visual program
Add these new
modules
Set the opacity of
the 1st color module
to 0.3, for the second
0.7

24. New image is a combination of a
surface and a volume rendering
 Surface has
a reduced
opacity so
we can see
through it
 Interior
volume is
shown using
different
colours for
different
field values

25. Volume render alone

26. Volume Rendering Pipeline
 Data volumes are used as input to the transfer function,
which produces a sample volume of colors and
opacities as output
 Sample volume is rendered to produce a final image
transfer
function
data
volume(s)
sample
volume
rendering final
image
FRGBA(data)

27. Transfer Functions (TF’s)
 Map data value to color and opacity
Human Tooth CT
a(f)
RGB(f)
f
RGB
Shading,
Compositing…
a
Gordon Kindlmann

28. Choosing transfer functions
 This is one of the black arts of visualization
 Need to know fundamental scales of variation in your
problem (linear? Logarithmic?)
 Opacity can’t be too high otherwise we can’t see
through
 If it’s too low we don’t perceive enough information
 Colours should be chosen in sympathy with the data
 Volume rendering generally doesn’t cope well with too
much high frequency data

29. Examples
f
a
f
a
f
a
f
a
Gordon Kindlmann
Cutting out high values
has no effect
Moving to a lower value of
f doesn’t help
Sharply peaked to high opacity
effectively gives a surface render
Linear increase places too much
weight on mid range

30. Ray casting: one rendering technique
 The sample volume must now be rendered
 Vast body of literature on different techniques
 Simplest idea is ray casting
(1) Send ensemble of rays through the system corresponding to
image pixels
(2) Interpolate values along each ray from grid
(3) Local gradient is calculated to estimate amount of light
reflected back to image
(4) Values are composited together from back to front
Image source: Wikipedia

31. Trilinear Interpolation
 What is the effect of interpolation on the volume rendered image? Could
choose nearest neighbour value, or linear interpolation
 Below is a comparison of nearest neighbour to trilinear
 The additional expense of the interpolation removes a significant amount of
noise in the final image
Nearest Neighbor Trilinear Interpolation
Michael Knapp

32. Multiple layers in volume rendering
 Example using a
tool called “vfleet”
 Rendering of gas
density in one of
my simulations
 Transfer function
has been chosen to
pick out three
surfaces
 “See through”
isosurfaces
 Exactly the same
as having multiple
opaque isosurfaces

33. Making movies
 Some toolkits (e.g. AVS) will make movies from a bunch of
frames (images) for you
 Opendx unfortunately doesn’t
 First step in making a movie manually is to create a series of
frames with a fixed naming convention
 e.g. frame.00001.gif, frame.00002.gif, frame.00003.gif
 From this series of frames a number of freely available tools will
compile them into a movie for you
 Most tools rely on some kind of UNIX script to do this
 I’ll give explicit details for the “makempeg” script
 This makes MPEG-1 standard movies which are lossless
 Fairly low compression ratio, but no bad rectangular artifacts
 Ideal for scientific viz.

34. Makempeg
 I will put this Unix driver script on the class website (if
you are interested)
 Rather dated now, but it works effectively
 You need two other packages
 Berkeley MPEG encoder (will also put on website)
 This is the program that creates (encodes) the movie from your
images
 Compile this code, will create the “mpeg” executable
 netpbm image manipulation tools (can be installed in Linux)
 Need by the makempeg script to convert images into the format used
by the MPEG encoder
 Place the makempeg script and mpeg executable in the
same directory as your frames of name xxxx.yyyyy.ext

35. Running makempeg
 Example command:
 makempeg –fs 1 –fe 10 –fi 1 –base test –ext gif
 Will make a movie
 Starting at frame 1 (-fs)
 Ending at frame 10 (-fe)
 Increments between frames is 1 (-fi)
 Name of files is test.????.gif
 -base = base name
 -ext = filename extension (could be jpg, tiff…)
 Script expects 4 digit number for each frame
 i.e. test.0001.gif test.0002.gif test.0003.gif
 Script will convert to the “YUV” format and then launch the encoder
 Quite quick – may be up to 2 minutes for a larger movie, much faster for
smaller

36. Example movie made with
makempeg

37. Summary
 Use the data prompter to create the description file for
Opendx data
 Construct visual programs quickly and easily by linking
modules together in the visual program editor
 Isosurface and volume rendering techniques are both
supported by Opendx
 Selecting suitable transfer functions is non-trivial and takes
time
 Lastly, movies can be made quickly and easily from a
series of frames using a large number of freely available
tools
 I’ve provided codes for one method on the website

38. Student presentations
 No lectures March 24th, 26th, 31st
April 2nd
Mike Hiland
Ashley Campbell
Glen Hodge
Masaki Uchida
April 7th
Michael Palmer
Nick Presse
Cristina Collicott