Keep the grey cells working

Now that I've graduated, well... everything seems to bore me.

But fret not. A friend sent this to me: https://www.coursera.org/

Yay! Loads of fun.

Fluid Dynamics - Smoke

As I'm doing my survey for the dissertation, I've come across some newer papers on this subject that improves the complexity / limitation of some of the popular methods.

Here they are. I will need them when I start my project.



Starting out with Fluid Dynamics

http://www.efluids.com/



PAPERS

Energy-Preserving Integrators for Fluid Animation

http://www.cs.caltech.edu/~keenan/project_epifa.html


Washington Uni: http://grail.cs.washington.edu/projects/



TUTORIALS

http://software.intel.com/en-us/articles/fluid-simulation-for-video-games-part-1/

http://ta.twi.tudelft.nl/isnas/report94-24/isrep2.html



WIKIS

CFD : http://www.cfd-online.com/Wiki/Main_Page



FLUID PEOPLE

Bridson - http://www.cs.ubc.ca/~rbridson/
Treuille - http://www.cs.cmu.edu/~treuille/
Stam - http://www.dgp.toronto.edu/~stam/reality/Research/pub.html
Fedkiw - http://physbam.stanford.edu/~fedkiw/
Selle - http://physbam.stanford.edu/~aselle/

Nielsen - http://www.daimi.au.dk/~bang/



APPLICATIONS

http://www.cs.cornell.edu/courses/cs567/2007sp/a4SmokeControl/index.html : Interactive Smoke Control, java based.

http://www-evasion.imag.fr/Membres/Fabrice.Neyret/Etudiants/sujet3Master2009_10-en.html : Amplifying smoke simulation, C++ & OpenGL - no sample codes.

http://www.win.tue.nl/~alext/COURSES/INFO_VIS/SOFTWARE/smoke.html : Real-time smoke simulation, C/C++ & OpenGL (using FTTW) - sample codes provided.


The Little Grasshopper - graphics programming tips

FANTASTIC SITE WITH FREQUENT PAPERS UPDATE


By Christopher Batty

http://animationphysics.wordpress.com/

The infamous Ke-Sen Huang

http://kesen.realtimerendering.com/


Focused:

Thyson Brochu - interest in fluid dynamics

http://www.cs.ubc.ca/~tbrochu/Tyson_Brochu.html

Philip Fu - Prof in NTU, good general links to many important graphics knowledge.

http://www3.ntu.edu.sg/home/cwfu/



HAPPILY FLUID DYNAMICS DUDES

(Pure Mechanical Engineering Numerical Method, Computer Graphics almost always reduces some terms)

I was reading this forum and thought it is a good one and everyone should read this too:

http://www.physicsforums.com/showthread.php?t=287547

Here it is recommended to read: http://courses.cit.cornell.edu/fluent/cfd/intro.pdf


Computational Fluid Dynamics: The Basics with Applications by John David Anderson

Making life easier when writing engineering paper

To self:

1. Always write the equations, no matter if it's only the alpha sign in Math Equation (Latex equivalent) so as to save you from more grief later when copying the text for full dissertation.

2. Always keep a good citation method. EndNote doesn't install at all for me, Memento does not work on Word 2003. Need to find an alternative.

3. Write summary at the same time when reading the paper for the 2nd time. First time is for understanding and scribbling.

4. IEEE: Mark equation with (x) right justified. Refer to equation later with "Therefore, (x)..." without using Equation (x) or Eq (x). However, to begin a sentence, we should "Equation x..."

5. IEEE: Annotate tables and figures with "Figure x: bla bla" and "Table x: bla bla". Refer to figure and table with abbreviation "Fig" and "Table". Tables are numbered with Roman numerals.

Infinite: Start early... Who am I kidding? I kick myself every sem. I thought I'd be wiser by now.

A Few Tips on How to Use PowerPoint for Mathematical Presentations

I've included this tip from the link at the bottom of the post to help me with the equations in PowerPoint.. This is not my own post.

What These Are About

These tips may help you produce math-heavy PowerPoint presentations more efficiently, and get them to look better. They assume familiarity with the basics of PowerPoint. They do not argue for or against using PowerPoint for your presentations (there are many pros and cons). They were born out of a conversation among graduate students in the MIT theory group sometime in 1999 or 2000, when many of us were discovering PowerPoint and agreed that a page for sharing tips would be useful. Some of them are probably getting out of date as newer versions of PowerPoint come out.

They are maintained by Leonid Reyzin. Please contact me if you have additional tips you think should be included, or if you find something wrong (or no longer applicable).

Machine Independence

One of the biggest headaches with PowerPoint is the difficulty of getting it to look the same on different machines. To that end:

• Make sure your file includes fonts. This is accomplished by going to the "File" menu, selecting "Save As," and checking the "Embed TrueType" check box in the dialog box that pops up. Then click "Save." Your file will likely become very large once you do this, and you may need to compress it to get it to fit a single floppy (see also "Miscellaneous PowerPoint Tips," below, for how to deal with large files).
• If you use Equation Editor/MathType, you need to embed those fonts, as well. Unfortunately, PowerPoint doesn't know you are using those fonts simply because an equation is embedded (it treats equations as graphics); thus, you need to make sure that at least one character from each font used in your equations appears somewhere (e.g., on a special slide, or as white on white, or just a space) in an ordinary PowerPoint textbox. The fonts you are interested in are MTExtra, Euclid Math One and Euclid Math Two. Then use "Embed TrueType" option described above. (Thanks to Bob Mathews for the tip.)

Making Overlays

Get everything you want onto one slide, and get in its final form. Then split it into overlays as follows: copy it as many times as the number of overlays, and simply "hide" parts on each slide. To hide a part, change its color to white, or cover it up with a white rectangle. Do not delete text, because that will move other text around, and your overlays won't match. Instead, change its color to white.

Typesetting Math

One way to typeset mathematical formulas and symbols in PowerPoint is to use TexPoint add-in. I haven't tried it myself, but have heard good things about it. Just save often, because PowerPoint's tendency to crash apparently only increases when the add-in is used (in particular, when the LaTeX interpreter is closed improperly).

If you prefer to use "straight" PowerPoint, here are some tips.

1. Getting it to look good
   • Italicize only what should be italicized. Generally, this means only Roman and Greek variable names (italicizing uppercase Greek is optional). Be sure to not italicize plus and minus signs, function like log and cos, numerals, parentheses, etc. If in doubt about what should be italicized in a particular formula, typeset it in LaTeX and then mimic LaTeX's output in PowerPoint. To toggle italics, just use Ctrl-i.
   • Use Times New Roman or a similar font. Sans serif fonts, such as Helvetica, are not good for math (although they may be good for the rest of your presentation). It's ok to have one font for math and another for the text (the slides class of LaTeX does that, in fact). To change fonts without using the mouse, use Ctrl-Shift-f and arrow keys.
   • You can also change fonts and styles by using the "format painter" button: simply get one character to look right, and then use the format painter to copy its format to other similar characters. (Thanks to Shane Scott for this tip.)
   • Do not use a hyphen for a minus sign. A much better minus sign is an en-dash. Unfortunately, it is a bit hard to get in PowerPoint. See "Inserting non-standard characters" below.
   • When you copy math around, make sure it has the same font size as the surrounding text. PowerPoint will not always automatically get it right.

2. Inserting non-standard characters.
   • To insert Greek letters, simply type the "corresponding" Roman letter (e.g., "a" for alpha, "t" for tau, "q" for theta), and then change its font to Symbol. Same for "sum" and "product" symbols: simply use capital sigma and capital pi.
   • Standart Unicode symbols for integrals don't look any good. You may want to use the curve-line tool to make one and then copy it around. (Thanks to Nikola Venkov for this tip.)
   • To insert the many special symbols that are available in Microsoft Word (such as en- and em-dashes, ©, etc.), simply open up Microsoft Word, and insert them using the menu "Insert" then "Symbol." The "Special Characters" tab is particularly useful, and contains handy keyboard shortcuts. Once you get it in Microsoft Word, simply select it, copy it, and then paste into your PowerPoint text. Make sure the result has the correct font and size. Then you can copy it around your PowerPoint file whenever you need it.
   • More recent versions of PowerPoint have the "Symbol..." item in the "Insert" menu (the corresponding toolbar button is available, as well: see "Miscellaneous PowerPoint tips," below). You can insert characters from various fonts.
   • A host of characters is available in the "Character Map" accessory. (Go to the "Start" button, then "Applications," then "Accessories," then "Character Map.") Trying different fonts to find what you need; Symbol font is particularly useful for math. You can select and copy characters, then paste over to PowerPoint. Moreover, if you click on a particular character, you get the "keyboard code" for it displayed at the bottom. Once you learn the keyboard code, you can type it directly in PowerPoint without having to copy and paste. For example, the code for an en-dash (which is good for minus signs) in Times New Roman font is Alt-0150 (hold down Alt, press 0150 on the numeric keypad, then let go of Alt). The code may be different in other fonts.

3. Subscripts and superscripts
   • To make subscripts and superscripts using the menus, select the character you need, then go to "Format" then "Font." Note that you can get double superscripts, subscripts of superscripts, etc., by varying the "offset" amount.
   • It is faster to make standard subscripts and superscripts using the keyboard. Ctrl-= toggles the subscript flag, and Ctrl-+ (same as Ctrl-Shift-=) toggles the superscript flag. For example, to get a_ixⁱ, type "a, Ctrl-=, i, Ctrl-=, x, Ctrl-+, i, Ctrl-+" (don't forget to turn on italics at the beginning by "Ctrl-i").
   • You can also get buttons for making subscripts and superscripts on your toolbar. See "Miscellaneous PowerPoint Tips" below. Or you can use the format painter: get a single subscript to look right, and then copy its format to other subscripts (see "Getting it to look good" above).

4. More complex formulas.
   • You may avoid using Equation Editor/MathType (see "Machine Independence" above) by utilizing multiple text boxes instead. You can move them around to get them in the right positions. Note that large parentheses, brackets, braces, and other useful shapes are available under "AutoShapes" (most likely on your drawing toolbar). Once you get a formula to look right, group all of its components (see "Drawing" below), so you can easily move it around and copy it.

Drawing

• Learn to use "Group," "Ungroup" and "Regroup" in your "Draw" menu (also on your right-click menu). "Regroup" is particularly handy if you need to ungroup to modify something little. You don't have to reselect everything to group it back: simply choose "Regroup."
• To select multiple objects, hold down the Shift key as you click on them with the mouse.
• It is a pain to select text boxes, because when you click inside them, you get to edit text. If that happens, press "escape," and the text box becomes selected. Alternatively, hold down the Shift key as you click. Conversly, if you've selected a text box and now want to edit its text, press "enter."
• It is often easier to nudge objects by selecting them and using arrow keys, rather than by using the mouse.
• Connectors (available under "AutoShapes" on your drawing toolbar) are great when drawing graphs, trees, etc. They can be made to stick to an object, so when you move nodes around, edges adhere to them.

Layout and Design Tips

• You do not have to be stuck with the standard boring slide style. Play around with it by going to the Edit menu, and selecting Master, then Slide Master.
• When giving a talk that will be projected (rather than printed out on transparencies), the color combination that is easiest on the eyes is yellow (or white) on a blue background. (Thanks to Steven Rudich for this tip.)
• To make small caps font style (equivalent to LaTeX's \textsc command), type in all uppercase letters. Then select all the letters you actually want to be in small caps (i.e., not the ones you want to actually be uppercase, such as first letters of sentences), and simply make the font about four points smaller. (Thanks to Amit Sahai for this tip.)
• To start a new line without starting a new paragraph: press "Shift-Enter."

Miscellaneous PowerPoint Tips

• You can customize your toolbars. In particular, it is handy to have buttons for "Format-Subscript," "Format-Superscript," and "Insert-Symbol." Go to the Tools menu, then Customize, then click on the "Commands" tab. Then simply find a command you want by looking at the various categories, and drag it out of the dialog directly onto a toolbar you want. (Thanks to Amit Sahai for this tip.)
• If AutoCorrect annoys you (e.g., you have a variable named "i" and don't want PowerPoint to automatically capitalize it every time), check out the menu "Tools" then "AutoCorrect." If it doesn't annoy you but is just occasionally wrong, you can undo what it just corrected by pressing Ctrl-Z or selecting "Undo" in the "Edit" menu.
• If you file is too large to fit on a single floppy and you need to take it with you, use the "Pack and Go" command in the File menu. Be sure to check the boxes that "Include linked files" and "Embed TrueType fonts" in the dialog boxes that follow. Prepare a large box of floppies, as PowerPoint manages to only enlarge your file as it "compresses" it. However, the packing and restoration procedure is automated, and beats trying to split the file into multiple chunks yourself. Don't forget to label the floppy disks in numerical order; run the application that is included on the first floppy to restore the file to another computer.

http://www.cs.bu.edu/~reyzin/pptips.html

Creating mathematical symbols with MS Word

There are four sections to this document

• Before you can use the Equation Editor
• (Very) Basic operation of the Equation Editor
• Shortcut Keys are your very best friend
• Simonds tips on using the equation editor

Before you can use the Equation Editor

The other three sections of this document will work only if the Microsoft Equation Editor has been installed on the machine you are using; the Equation Editor comes with Microsoft Office but is not installed under a standard installation. The computers in the Sylvania CRC and Sylvania math classrooms all have the Equation Editor installed. On your home machine you probably will need to load your Microsoft office CD and do a custom install to install the Equation Editor. (It's easier to do than the phrase "custom install" implies. J ) All of the maneuvers described in this section of the document will need to be done at most once.

After installing the Equation Editor, you also want to customize your toolbar so that the Equation Editor button is easily accessible. (The button is already on the CRC and math classroom machines.)

The menu shown in Figure 1 was opened by selecting Tools - Customize from the toolbar menu across the top of the screen, then selecting the commands file-tab at the top of the dialogue box, then selecting the insert category on the left side of the box, and finally scrolling down on the right-side of the box until the Equation Editor button was in view. Once you have located the Equation Editor button, left-click and drag the button up to your toolbar menu.

Figure 1: Customizing your Toolbar

(Very) Basic operation of the Equation Editor

Once your Equation Editor button is in place, all you need to do to open an Equation Box is left-click that button. Upon your click an Equation Box like that shown in Figure 2 will appear as well as the Equation Editor Menu shown in Figure 3. (As a side note I should mention that the Equation Editor Menu has the unfortunate habit of sometimes opening directly on top of the location at which you are typing. L Should this happen, simply left-click and drag the solid strip across the top of the box until the box is out of the way.)

Figure 2: Equation Box

Figure 3: Equation Editor Menu

The Equation Editor Menu can be used to insert both symbols and templates for complicated mathematical expressions. For example, Figure 4 shows what you click to insert the Pi symbol; Figure 5 shows what to click to insert a fraction template.

Figure 4: Inserting a Pi symbol Figure 5: Inserting a Fraction Template

Once a template has been inserted into your Equation Box, you need to look and see where inside the template the cursor is flashing. You then go ahead and type the information that goes into that location. To move to the next location in the template you press the Tab key. You also press the Tab key to exit the template. When you are done typing in your expression, you left-click anywhere outside of the Equation Box. If you need to edit an existing Equation Box you simply double-click anywhere over the expression contained within the box.

Shortcut Keys are your very best friend

Mousing all of your math symbols and templates gets real old real fast; thankfully there are shortcut keys that enable you to avoid your mouse in most circumstances. The shortcut keys are found in the Help Menu when you have an Equation Box open. I have copied the most commonly used shortcut keys into figures 6, 7, and 8.	Figure 6: Shortcut Keys for selected Math Templates
Figure 7: Shortcut Keys for after the fact symbol Embellishments	Figure 8: Shortcut keys for selected math symbols

Simonds tips on using the equation editor

• Always add a full space before and after an equal sign, before and after a plus or minus sign, after a limit sign or integral sign, and before each limit on a definite integral. A full space is created inside an equation box by pressing Ctrl+Shift+Space Bar.

• Always add a half space between a coefficient and a variable and before and after the arrow sign in a limit. A half space is created by pressing Ctrl+Space Bar.

• To line up your equal signs (J ) you need to use the format/align option shown in Figure 9.

Figure 9: Gotta' line up them equal signs!

• You can add text inside an Equation box by selecting Style - Text from the toolbar menu. (See Figure 10.)

Figure 10: Adding text inside an Equation Box

• Sometimes you might want to insert text along with a multistep simplification or other type process. One way to achieve this is with a matrix. For example, the simplification shown in Figure 11 was typed using a matrix with 7 rows and two columns. The style used in the left column was "Math" while the style used in the right column was "Text." I always insert a blank row between every line to avoid crowding - that's why the matrix had seven rows as opposed to four. The appropriate Menu and Dialogue Box are shown in Figures 12 and 13.

Figure 11: Adding text along with mathematics

Figure 12: The Matrix Menu Bar

Figure 13: The Matrix Dialogue Box

Finally, you will find below is a keystroke guide for creating the expression .

1. Open an Equation Box
2. press Ctrl+t, u
3. type in "lim" (don't type the quotes J )
4. press Tab
5. type in "h"
6. press Ctrl+Space Bar
7. press Ctrl+k, a
8. press Ctrl+Space Bar
9. type in "0"
10. press Tab
11. press Ctrl+Shift+Space Bar
12. press Ctrl+f
13. press Ctrl+9
14. type in "3"
15. press Ctrl+shift+Space Bar
16. type in "+"
17. press Ctrl+shift+Space Bar
18. type in "h"
19. press Tab
20. press Ctrl+h
21. type "2"
22. press Tab
23. press Ctrl+Shift+Space Bar
24. type in "-"
25. press Ctrl+Shift+Space Bar
26. type in "9"
27. press Tab
28. type in "h"
29. press Tab
30. click anywhere outside the Equation Box to close the equation box

Blatantly copied from: http://spot.pcc.edu/~ssimonds/thisandthat/msword.htm

All about Matrix

Matrix multiplication

REMEMBER!

AB != BA ==> matrix multiplication is not commutative.
Cols in A == Rows in B (right, down)

Inverse

For a matrix M to have an inverse, it's determinant |M| != 0.

Given M is a 2x2 matrix.

m1 m2
m3 m4 = M

3 2
6 4 = M

det[M] = |M| = (m1)(m4) - (m2)(m3) = (3)(4) - (2)(6) = 0 _QED

!! Remember this arrowing only works till 3x3 matrix. Anything more will need to manually compute. Will come back to this.

Matrix inverse

M^-1 = 1/ |M| x (adjoint M)
... Crap... So hard to draw matrix. Ok Nvm. Come back to this later.

Mathworld Wolfram does a better job explaining it. Here: http://mathworld.wolfram.com/MatrixInverse.html


Ok... I should not spend so much time on this. Gotta hand in computer vision assignment in 10 days. Come back to this later.

Yum Char: Discussions over dim sums

Had lunch with Quark. Haven't seen him in a long time. He's only free this week.(Oh ya, Quark, if you are reading this, the site I was telling you about is www.modepass.com).

Talked. Mostly on computer graphics, computer vision, AI and machine learning. Even in the computer engineering field, there's so many different classifications. We had a lot of ideas for a lot of things. We just need to sleep less to get things done.
Also, Quark and I come from the same school of thought. At least I am not alone. One of the first thing we have to realise as grad candidates is the fact that we are... grad candidates. So we have to think like researcher and less about application. However, I do not believe in wasting my time on things that is not useful in life. Quark agrees with me. We're more of the bottom-up than top-down people. Cool. Well, he finished his Masters way back and he still thinks like this.

Anyways, tried the annotation joke about Web2.0 on him. He totally gets it! Lol. I tried it on my colleague a few days ago. Fell flat.

So good talking to someone who understands what I am doing now!

I tried with some of my colleagues but heck, they don't even have a strong grasp of telco knowledge. Wait. that is not true. The only idiots I've met are all from this company. Oh well enough of that.

Anyways one of the idea we had was how to convey mathematical theorems and algorithms in human language. The tv series NUMB3RS did that moderately well. (I have the hots for Prof Eppes but that is another story altogether).

Here is a site: http://www.weallusematheveryday.com/tools/waumed/home.htm, deriving the whole idea from NUMB3RS to teach maths. I think it's alright. But definitely worth a visit.


Season:
2: Episode 14 - Harvest -- Hidden Markov Model.

Markov Chain Links - predicting probability of certain states in the future from what we know of the present. (Ex, was the weather yesterday: sunny, cloudy or raining. therefore what's the probability that it will rain today?)

Hidden Markov Model - In the event when we are not able to observe the actual state but only the outcome that is connected to the state by a certain probability distribution. (extend from above example, we do not know if it rained yesterday but the sales of umbrellas for yesterday was high).

Representing 3D on 2D

One of the thing I felt most important to CG is the fact that we are trying to represent 3-dimesional objects on 2 dimensions, our computer screen.

Therefore, besides the X and Y axis, the Z axis is utilised for perspective control (orthogonal and modelview, will come back to this in a moment); ex: Z_near, Z_far.

Initially on my GL assignment I made the mistake of drawing my ground plane on X & Y axis, causing all my models to seem like they're stuck on their side to the wall. Wrong! Should draw the ground plane on the X and Z axis!

When drawing & loading model vertices, always remember... counterclockwise to look at the front side. Right hand rule.

CG works by: modelling --> animating --> rendering.

Texture mapping= rendering the surface without requiring additional polygons to represent minute details.

Coordinate system

This I gotta find out more: model space, world space, eye space, normalised projection space, normalised device space, image space.

2D TRANSFORMATION

translation
rotation
scaling
homogeneous coordinates
composite transformation


Rigid Motion (Euclidean Transformation) preserves the distance and angle : Identity, Translation, Rotation. ∴ Shape and orientation does not change!


Linear Transformation: Identity, Rotation, Scaling, Shearing, Reflection.

Affine Transformation: add translation to linear transformations ∴ giving us affine transformation.


3D TRANSFORMATION

homogeneous coordinate
translation, scaling
rotation
composite transformation
change the orthonormal basis

3D Affine Transformation Matrix... absolutely beautiful. Draw it tomorrow.


3D Viewing and Projection

World to Eye Coordinate Transformation
Eye Coordinate System
(related to orthonormal basis)

Grr... Projection Transformation.

2 types of projection: perspective & parallel. The key factor here is COP (Center Of Projection). If projection plane is finite == perspective. Infinite projection plane == parallel.


*****Will come back and finish this. Now I need to sleep. And have mathematical nightmares.
















Oooh... I need to come back to these:
http://www.faqs.org/faqs/graphics/algorithms-faq/
http://kesen.huang.googlepages.com/

Maths: Binormial Co-efficient

Binormial co-efficient

(ⁿ_i) = n! / i!(n-i)!

Binormial theorem

(x + y)ⁿ = ∑ⁿ_i=0 (ⁿ_i) xⁱ y^n-i

in relation to FFD:

conventional polynomial basis: 1 t t² t³
Bernstein polynomial basis: (1-t)³ 3(1-t)²t 3(1-t)t² t³


1-D example (real line)

given an arbitrary point, v, on a line of P0, P1, P2, P3.

P₀=0
P₁=1
P₂=2
P₃=3

v is given as x. t is given as the length of v to P0 divided by P3 to P0.

in general mathematical terms:

v = ∑ ³_i=0 P _i W _i (t)


W = weight = scalar = constant

in this context:

t= ||v P₀|| / ||P₃ P₀|| = x/3

∴ using dot product:

v = 1 • W₁(t) + 2 • W₂(t) + 3 • W₃(t)

(P0 is ignored because P0=0; where the multiplication will results in 0)

= (³₁)t¹ (1-t²) + 2 • (³₂)t²(1-t) + 3 • (³₃)t³

= 3t (1-t²) + 6 t²(1-t) + 3 t³

=3t [ (1-t)² + 2t(1-t) + t² ]

=3t [ (1-t) + t ] ² = 3t = x

I've spent 2 hours searching for this post!!!

http://archive.atomicmpc.com.au/forums.asp?s=2&c=10&t=2770&p=0


and this:

http://archive.atomicmpc.com.au/forums.asp?s=2&c=10&t=3197

Read read read!

Teching... somewhat: Fonts

Those who knows me will know I am somewhat obsessed with fonts.

So I was a little upset when I reviewed and realised that almost all my fonts are in serif. You see, even though I do not claim to know much about graphics, I know one thing.

Only use sans-serif font with online/web publishing. So imagine how pissed I was when I realised vanity blog was mostly in serif.
So here is the part where you need to change in:
Layout--> Edit Html

Add a new variable for the new font type.




Adjust the font accordingly in your post body structure.

.post-body {
font:$postfont;
font-size/* */:/**/small;
font-size: /**/small;
}


To understand briefly the need of serif & sans-serif font distinction for print and online publishing, go here:


http://www.scribe.com.au/tip-w017.htm


Ascii character for html.

Maths symbols for html.