Spot a 'Vulgar Mechanick', how many of them do you know?

"A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in error, he knows not how to find it out and correct it; . . . Whereas he that is able to reason nimbly and judiciously about figure, force, and motion, is never at rest till he gets over every rub"

Isaac Newton wrote to Nathaniel Hawes on 25 May 1694.

Free BVH viewer released.

I just released a small viewer for the Biovision BVH mocap file format.

It can be downloaded from this page: http://jadnohra.net/?page_id=58

I did not plan to write this viewer, but I suddenly found myself having all the code I need for it while writing code for my animation research projects.

The 'Bigeye' UI library

I already had developed the 'Bigeye' UI library. This was I think the 4th UI library I had ever written. For this one, I had a couple of goals in mind: Small, OpenGL based but without state management headaches, easy integration of 3D scenes using render to texture, good looking with shadows, mouse-over, gradients, ttf and svg, no complex auto-layout/resizing support, no need for editor or text definition (at least not for the first versions). It took a number of weeks for this to happen, but I am very pleased with the results.

ImageMagick

A key idea was to use the ImageMagick library which is basically, photoshop/gimp in your code.

It allowed me to create nice and detailed widgets without having to prerender them in an image editor.

Compiling and linking ImageMagick can be quite a headache, but after that is done, using it is a lot of fun. I spent quite some time reading 'how to make a nice button' tutorials and trying things out in gimp before deciding on a look, one of the main inspirations was the Zbrush user interface. Colorpic was also a useful ally in debugging the looks and colors of various widget screenshots that I wanted to reproduce.

RenderState Management

For the UI I wanted to keep things simple, but still self managing, I went for a render tree approach, with automatic dependency management which was important for the 3D scenes rendered to textures. That way, RenderToTexture widgets could simply declare their dependency on a different (3D) RenderTree than their current tree (the main UI tree), and the Renderer would automatically take care of ordering the trees. Inside a tree, parents would render before their children.

The rendering would happen in three stages, building the render tree, figuring out dependencies, and then rendering in the right order.

For render states, again a simple design with one hashed state containing all the options needed for all the UI widgets (e.g: enabling transparency, texture, etc...). Each UI element would set it's desired render state instance, and the rest would happen automatically. Of course this is not the most flexible or performant design as code needs to be added to the render state structure and it can grow big, and for options that are not in the render state (e.g: line width) care must be taken to set them every time they are needed, but for a tiny UI like this, it does the job perfectly.

Biovision .BVH file format

Of all mocap formats, .BVH is the simplest, but many free mocap resources in bvh format exist on the internet, specially the .BVH conversion of the CMU mocap database is great. I will probably add .c3d support when I feel need it.

The format is relatively well documented on the internet. The fact that it uses Euler angles is usually the biggest source of headaches as I gathered from forums. I also had to try a couple of things out before finding out what the right way is. This included looking a the blender importer source code and even having fun writing a feature-incomplete bvh exporter for blender. A precise answer to the question of how to create a rotation matrix from the angles is nowhere to be found, because of that even some bvh viewers (bioviewer) got it wrong.

BVH euler rotation order

According to this very helpful resource: http://www.cs.wisc.edu/graphics/Courses/cs-838-1999/Jeff/BVH.html

one way to build the rotation matrix is to concatenate the matrices built from each angle in the order Y,X,Z. This is not entirely correct. The order should follow the one delcared in the bvh file itself, this means that if in the bvh file you see: "CHANNELS 3 Zrotation Xrotation Yrotation"

you concatenate with the order Y,X,Z but "CHANNELS 3 Xrotation Zrotation Yrotation" would require the order: Y,Z,X.

Since most files use the Y,X,Z order this bug can easily slip by.

Some of the CMU mocap files have a different order and look wrong in the viewers that got it wrong.

Of course, as usual, care must be taken about the coordinate systems and the order of matrix multiplications. Depending on you code, this might be different.

In a previous project of mine, I had a very elaborate runtime coordinate system conversion system, but this time I kept it simple and convert everything to an OpenGL compatible system when loading.

Code Dependencies

Everybody hates dependencies, but if you want to be productive, and pick the right ones, it is not so bad. In the past I avoided them like the plague, which was very educational, but this time around I am using the glm library (basically glsl on your pc) for math, strtk for strings (a great library which makes file parsing a ride in the park), glew for OpenGl extensions (which I need for rendering to texures using FBO), OpenGLUT and finally ImageMagick. I link all of them statically except for glew for now.

Viewer 'features'

The viewer loads bvh files using drag and drop and has the usual playback controls.

It analyzes the scale of the skeleton and the bounding box of the animation space, from that it decides on the best grid size, depth planes, camera position and camera movement speeds.

I implemented a simple 'turn table' camera controller (as inspired by Blender).

I also copied the way Blender renders Skeletons, without lighting for now.

If you download it and like it, let me know.

If you have any feature requests, let me know as well...

Stanford bunny released.

I was cleaning up my hard disk at home and I found the 'packet ray tracing project that was supposed to become the base of a photon mapper' I posted about in the past:

1. http://jadnohra-tech.blogspot.com/2008_09_01_archive.html#1603298383616017587
2. http://jadnohra-tech.blogspot.com/2008_10_01_archive.html#7537941235422943422
3. http://jadnohra-tech.blogspot.com/2008_10_01_archive.html#1222221128104057181
4. http://jadnohra-tech.blogspot.com/2008_10_01_archive.html#8986353999879708385
5. http://jadnohra-tech.blogspot.com/2008_10_01_archive.html#8721967187970184236
6. http://jadnohra-tech.blogspot.com/2008_10_01_archive.html#472543603436067225
7. http://jadnohra-tech.blogspot.com/2008_10_01_archive.html#1172483216700342377

Since I will have no time to take this anywhere anytime soon, I thought it might be a good idea to simply release the source code instead of backing it up into the dark corners of the web and a backup DVD.

The last version I am releasing dropped support for all primitives (e.g: spheres, quadrics) except for triangles and concentrated on triangles with SSE Packet tracing, BVH, and multi-core using OpenMP.

OpenMP is disabled in the delivered executable because my Visual Studio at home is the Express Edition and it does not include OpenMP.

SSE Packet tracing is also disabled because it does not support Lambert shading (I do not remember why though ... it's been a long time).

This means you will not see the 1 millions rays per sec I claim in one of the posts.

There is a number of build configurations and preprocessor options to play around with to enable / disable these options and other features.

In the executable, you can use numeric pad keys to rotate the camera and arrow keys to move the camera, when you do this, the program enters a low detail rendering mode until you release the keys. It is not great, but at least some kind of camera control is there.

The code depends on the 'WitchEngine' library (namespace 'WE' in code) which is the engine I had written for 'World of Football', but that is a LOT of code, so I spent 10 minutes only copying the code needed. It should therefore build with no problems, all you need is to point it to a DX9 SDK.

The download URL is: http://jadnohra.net/release/JadNohra_DistribPacketRaytracer.7z

AIGameDev Paris 2010, for the record.

Animation and math, starting 3000 BC.

http://sites.google.com/site/77neuronsprojectperelman/jad/animation-math

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Homegrown math study group.

Tom Lahore and me, and I am sure many others, find that there are not enough practical problems forcing us non-PhD / non-academic to delve into math as much as we like. It is a chicken and egg problem and we have strongly felt during the last years that we should do something about it and never had the discipline to do it consistently and therefore usefully. We will give this another shot at http://sites.google.com/site/77neuronsprojectperelman/

We will start by using the Khan academy videos (1 to 2 videos per week) and discuss them during sundays possibly using some online conference tool and use the wiki to share our thoughts. The Site is public so feel free to do it with us. Will we fail and stop in a month? I don't know ... we hope the fact that we do it in a group and that we use very low commitment (1 to 2 videos per week) will help.

That's what happens when you are researching human locomotion.

You find sentences like:

"Modern humans exhibit a much higher body fat content and reduced relative muscle mass than their ancestral counterparts, trends that are seen in domesticated animals generally (Allen and Mackey, 1982; O’Dea, 1991; Clutton-Brock, 1999)." (http://jeb.biologists.org/cgi/content/full/204/18/3235)

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More time = shorter letter

Yet another extremely valuable addition to my neuronal network. (Thanks to R.M)

http://dangerousintersection.org/2006/04/12/more-time-shorter-letter/

How true!

Anything must be something, except for nothing ...

We all have encountered and enjoyed seemingly mind convoluting statements like:
"This statement is false" or "I am a liar", such statements are basically 'unprovable'.

I have been reading about this while investigating logic and it's roots, mathematics, number theory, Goedel .... Some older posts are related to this.

Recently I decided to write down one such sentence that comes pretty naturally whenever you start thinking about what 'something' is.

Here is the complete sentence:
"Anything (any 'thing') must be 'something', except for nothing, which is of course also 'something', but on a different level of thingness, which goes up and down into itself to infinity."

The sentence flows pretty naturally when you are making it up, you start with:
"Anything must be something"
But then your mind remembers that there is an exception to that so you add:
"Except for nothing"
Again your mind jumps in, it cannot accept the void, this 'nothing' also fits the mind's intuitive notion of 'something', in the end, we just mentioned it, so it must be something, and this is where the fun starts, so you add:
"Nothing is also some kind of 'something'"
But then you fell uncomfortable, now nothing is nothing and something at the same time, but let's simply go on trying to explain how we feel about that:
"But on a different level of thingness"
The mind is trying to say that this nothing on one level (of 'thingness') is 'something', yes, but not on that same level), but now we have two levels, we needed those to resolve the paradox of nothing, but that's a problem, because on that new level we can probably do the same, and we can also think that the lower level is an upper level for some other level which has a 'nothing'. So we add:
"which goes up and down into itself to infinity."

So here we have it, nothing, something, a paradox and infinity all at the same time, plus the inability to make logical sense out of even the simplest everyday construct.

If you have been reading some Set theory, Number theory, Russel, Hilbert, Whitehead, Turing and friends all this would seem all too familiar: nothing could be the more formal 'Empty Set {}' ... and it's a long ride after that. So this is my layman's version of what all these geniuses and many others spent years thinking about, if that makes you interested, I suggest you read the most excellent book: "Godel, Escher, Bach: An Eternal Golden Braid"

I also found it interesting that this multi-level hierarchy of rules that we make up to reflect on a lower system from a higher system (escaping to the meta level as some colleagues would say) is inherent in the way we think, it is even mentioned in a seemingly unrelated game design book "Theory of Fun" and also a recurrent topic in our AI related discussions.

Next I will be investigating in more detailed the 'Completeness' part of this whole topic coming from Goedel's famous "Incompleteness theorem" that seems to be touching the physical limits of our brain and melting them in the core. More specifically completeness relative to what? Logic itself? probably, but, but ....

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The answer from above

While we game AI programmers noodle with our gross simplfications and regrettable /understandably unavoidable but also fun and challenging real-time performance constraints, we occasionally look up for any new answers from above, normally we are too busy to stay up to date, but it's the holidays and I am bored, I have no ps3 devkit here, nor a PC with a dev. environment to do some brainless coding... so I had to be brainful and start reading and so I stumbled upon this: "the currently available theories do not explain or engender anything resembling human-level general intelligence" what is meant here is theories coming from Information-processing psychology e.g: Cognitive Science and Cognitive Neuroscience. (source: http://www.cs.umd.edu/~nau/cmsc722/)

I wonder when such theories will start to be discovered and what kind of processing power we will have at the time and if they will good enough to allow the ones who will be peeking there at the time and spotting low hanging fruits to become famous applying them to video games (and other applications) being again, at the right time and place.

Now that's bad performance code! once and for all....

Translating an idea into a piece of code is an over-constrained problem, just like many other problems.

To decide how to code something, make a list of all points you think are important for it (maintainability, performance, easy to read by me, easy to reuse by me, flexible, many other pieces will depend on it, multi-platform, multi-compiler, link fast, compile fast, short names for faster typing, easy to read/understand/reuse for my colleagues, easy to read/understand/reuse for my clients, cryptic to prove I am 'old school' and can write assembly and you should be scared of discussing it with me, totally abstract to prove I don't care about performance and want to make a point that premature optimization is the source of all evil, totally lean and mean to prove that non-premature optimization is the road to a lame duck... you name it! I don't care what you put in there, the list can be very long and can include anything you like), score the points in your list based on their utility for the piece of code to be written with the very welcome possibility of zero utility for some of them (makes it less constrained).

You cannot compare apples to oranges? (e.g: maintainability vs. performance) ? yes you can (Yes son, you can compare apples to oranges... )! on top of that, you have no choice...

Finally, code/make compromises to maximize the total score, that's all there is to it and being an over-constrained problem for anything none-trivial it won't be completely obvious.

But the problem is clear, no need to call a programming style 'too old school' or another one 'too abstract' or 'too object oriented'. The higher the total score, the better ... that's it.

Now if u do not have the necessary coding skills, you might generate code that has a total score that is not the maximum possible ... but that is another topic.

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cool, now we can point to this instead of discussing it one more time ... saves more time for the 10,000 hours :)

http://www.youtube.com/watch?v=CtUuJo_DeyI

http://foodandretail.blogspot.com/2007/11/interlude-rule.html

http://www.youtube.com/watch?v=pIYUMwxKFzo

brought to by the AIGameDev IRC channel.

AI room + blackboard = geek art

I started out by wanting to draw a tree (the only thing I know how to 'draw' ... but then ... I had a Bob Ross happy accident)

PS3 game/FPS AI research

You gotta know your competition ... so I got me a PS3 and start taking notes while playing PS3 FPS's. As a side effect I am also enjoying Uncharted 2 MP.

Tech-radio silence

It has been some time since I posted anything but I am still alive and still scratching my brain the whole time, the reason for the radio-silence is that since September 2009 I am an AI coder at Guerrilla Games, it is a great experience.
I was going to take some pics but I found this:
http://ps3life.nl/nieuws/4528-een-kijkje-rond-en-in-guerrilla-studios/ this is how it looks like in here currently.
I was also interviewed at AiGameDev (http://aigamedev.com/insider/event/event-career-journey/), if you want to laugh at how sleepy the tone of my voice makes you will be probably be able to see it when it's posted as a video capture sometime in the near future.

More to come...

Irrationals on the border of existence and sqrt(2)

I have been reading a lot about abstract math, what numbers really are and are not, set theoretic number theory and related. The set theoretic approach even if I did not dig into the deepest depths of it, allowed me to be able to logically justify to myself the existence and nature of numbers.

I even bothered my wife (who could not care less) about the beauty I found in the irrational number: square root of 2, what I told her is the following:
I will prove to you how beautiful is math and that we should be grateful for all the people who contributed to it along the centuries of human thinking. I will give you a calculator and you can only use to to multiply, now with no other references, find me the exact square root of 2. Of course, one would proceed to multiply 1.1*1.1= 1.21 then 1.5*1.5=2.25, hence coming to the conclusion that 1.1 < style="font-weight: bold;">

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The following reductio ad absurdum argument showing the irrationality of √2 is less well-known. It uses the additional information 2 > √2 > 1 so that 1 > √2 − 1 > 0.

1. Assume that √2 is a rational number. This would mean that there exist positive integers m and n with n ≠ 0 such that m/n = √2. Then m = n√2 and m√2 = 2n.
2. We may assume that n is the smallest integer so that n√2 is an integer. That is, that the fraction m/n is in lowest terms.
3. Then
4. Since 1 > √2 − 1 > 0, it follows that n > n(√2 − 1) = m − n > 0.
5. So the fraction m/n for √2, which according to (2) is already in lowest terms, is represented by (3) in strictly lower terms. This is a contradiction, so the assumption that √2 is rational must be false.

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One could almost argue such numbers do not really exist, in the end, they are not called crazy/irrational (and have been fought) for no reason! The way I see it is that they don't at least as written out numbers, they do exist if we set a desired precision, this is why I am liking what I call a 'computationally theoretic number theory', no idea if it exists but you get my point. By setting a precision we can work with those things. One could argue that the number exists and that it's representation is sqrt(2), but this is not a number, the way I see it is that this is a rational (existing) number combined with an algorithm (or call it a function) that can transform this into another in this case irrational number, so either we imprecisely write down a number that approximates it to a given precision or we represent it as an algortihm (sqrt) and data (2) that expand to this 'inexisting' number, this is all layman terms and layman talk, and mathematicians will laugh, but I am recording these thoughts because, since I am a bit satisfied with what I know about this now, I will stop digging and go back to the actual reason I started to look into math again, and that is to solidify my math needed for a self designed auto-didactic machine learning 'course' in my free time. Another sqrt(2) existence thought occured to me in the car last weekend, imagine you have a piece of rubber of length 1, now you take it and stretch it to length 2, did you pass by sqrt(2)? you must have, so it exists? can one measure it? again only to some precision ... (even on the atomic/quantum level). almost mind boggling, this infinity of numbers, but it also makes sense, we allowed for it the moment we allowed ourselves to have a coma and numbers after it, after that recursively you have infinities of infinities of infinities ... but all still allow me not to explode when I look at the set theoretic number theory, basically it is ordering and number of things (in layman, mathematician laugh terms) ... between 1 and 2 there is an infinity of numbers, same as between 1 and 1.1 and 1 and 1.0001 ... in any case ... back to less mind boggling and much more practical stuff, in the spirit of the way ppl have been using numbers since ages for practical matter and not even really understanding what they are. and let me reiterate, please excuse the layman :( he's just trying to make sense of it within a very limited amount of time.

Addendum:
* bourbaki, one of my favorite persons for math discussions, does not think this post is utter non-sense and he just pointed me to:
http://en.wikipedia.org/wiki/List_of_paradoxes, http://en.wikipedia.org/wiki/Continuum_hypothesis

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Set theory is the branch of mathematics

Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.

The modern study of set theory was initiated by Cantor

Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor was a Germany mathematician, born in Russia. He is best known as the creator of set theory, which has become a foundations of mathematics in mathematics....
and Dedekind in the 1870s. After the discovery of paradoxes

Naive set theory

Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics , and the everyday usage of set theory concepts in most contemporary mathematics....
in informal set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms

Zermelo–Fraenkel set theory

Zermelo?Fraenkel set theory with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundations of mathematics....
, with the axiom of choice

Axiom of choice

In mathematics, the axiom of choice, or AC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if there are infinite set many bins and there is no "rule" for which object t...
, are the best-known.

Set theory, formalized using first-order logic

First-order logic

First-order logic is a formal deductive system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus , the lower predicate calculus, the language of first-order logic or predicate logic....
, is the most common foundational system for mathematics.

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Some References:
* http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Beginnings_of_set_theory.html
* http://www.absoluteastronomy.com/topics/Naive_set_theory
* http://en.wikipedia.org/wiki/Square_root_of_2#Proofs_of_irrationality
* The essence of discrete mathematics book
* ...


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At the end of the day, he would still be staring at the same blank sheet of paper.

Did it ever happen to you that you would sit to try to solve a new problem, and the more you would think about it the less it would make sense to you? if you would do that at your desk, would you then be considered non-productive? if you were a game developer be it technical, artistic or manager, sitting there and not typing for hours without making any progress would that be bad? well, Bertrand Russell, one of the most famous logicians of all times did exactly that, so you are ok :)


S = {x : x is a set and x !∈ x}.
In other words, S is the set of all sets that do not contain themselves.

In more 'naive' words:

* In Seville, there’s a barber who shaves all those people who do not shave themselves. Does the
barber shave himself or not? This is known as the “Barber of Seville problem”.

* Imagine a card. On one side is written, “The statement on the other side of this card is true.” and
on the other side is written, “The statement on the other side of this card is false.”

Bertrand Russell, one of the most famous logicians ever, struggled with this problem for a long time. In his autobiography, he describes just how hard he found the problem. Every morning, he said, he would sit down at his desk with a blank piece of paper in front of him. At the end of the day, he would still be staring at the same blank sheet of paper.

Russell’s final resolution to the problem is described in his “Principia Mathematica”, written with Alfred North Whitehead, in which he introduced a “Theory of Types” to get around his paradox. The basic idea was this: sets cannot contain themselves....

http://www.geometer.org/mathcircles/nothing.pdf

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Gödel, Mega-Mega-Giant of the week, July 2009

My steam gamer card, join to talk AI while blasting baddies :P

Not long ago I was dragged into playing L4D by the evil residents of the AiGameDev IRC channel, here is the result:



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Yes son, you can compare apples to oranges...

One of the things that bothered me while tweaking and tuning the Keltis AI heuristics, was that ultimately things sometimes boiled down to the need to compare apples to oranges, unfortunately I do not remember the exact details and I am too lazy to dig them up, but I know that I had to compare values that I was not able to reduce to a common unit to measure by (like risk per example), it was really a matter of preference, this is not a new problem, and with my head in the details, I failed to notice the obvious, this is an old topic called utility that economists have been using for decades, of course, as usual, I said 'aha' just after getting my head out of the details and shipping.
It was no big deal though, I ended up using utility without knowing it.

Utility is 'the' way to compare apples to oranges, but what brings me to today's rant is that I remembered this while reading in the context of my ongoing current research in applying Reinforcement Learning to Animation planning.
The question in question is about a very valid question [ :) :D :P ] about the 'essence' of Reinforcement Learning (similar to http://rlai.cs.ualberta.ca/RLAI/rewardhypothesis.html) :

Is it sensible to treat all preferences as numeric rewards on a single scale? Theoretically, yes. There is a theorem (North [4]) that if you believe four fairly simple axioms about preferences, then you can derive the existence of a real-valued utility function. (The only mildly controversial axiom is substitutability: that if you prefer A to B, then you must prefer a coin flip between A and C to a coin flip between B and C.) Practically, it depends. Users often find it hard to articulate their preferences as numbers. (Example: you have to design the controller for a nuclear power plant. How many dollars is a human life worth?)

source: http://www.eecs.umich.edu/~baveja/RLMasses/node5.html#SECTION00032000000000000000

I could not find the original in free electronic format: "D. W. North. A tutorial introduction to decision theory. IEEE Transactions on Systems Man and Cybernetics, SSC-4(3), Sept. 1968. "

If anyone can provide it I would be grateful, it is always very insightful to read about the essence of these things, this usually involves reading very old papers, and from my experience it is always worth it, it gives lots of confidence when applying things later and when doubts appear, because much thought and critical thinking went into each and every 'fact' we take today for granted, and for too naive tomorrow.

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