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My masters project involved a contribution to this:
https://rivet.hepforge.org/
Not that deep inelastic scattering is likely to find itself in a physics engine for a game hah.
I've said it before in the big programming thread that at least here in the UK physicists / electrical engineers are prized higher than CS graduates in more technical positions (obviously as far as graduate employment goes) in software.
I work for a company that makes graphics / capture cards as a software engineer and they only hire physicists / electrical engineers, a CS degree wouldn't have even got me an interview.
To be honest though, most of the stuff in a physics engine isn't all that complicated in terms of the pure physics involved, but actually getting it into a fully working model in a simulation is a different matter entirely.
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On March 29 2013 02:31 adwodon wrote:My masters project involved a contribution to this: https://rivet.hepforge.org/Not that deep inelastic scattering is likely to find itself in a physics engine for a game hah. I've said it before in the big programming thread that at least here in the UK physicists / electrical engineers are prized higher than CS graduates in more technical positions (obviously as far as graduate employment goes) in software. I work for a company that makes graphics / capture cards as a software engineer and they only hire physicists / electrical engineers, a CS degree wouldn't have even got me an interview. To be honest though, most of the stuff in a physics engine isn't all that complicated in terms of the pure physics involved, but actually getting it into a fully working model in a simulation is a different matter entirely.
I was under the impression that lagrangian mechanics were very high level physics?
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United States24667 Posts
Lagrangians aren't that difficult to set up, and once you apply the euler-lagrange equation you get the differential equations (second order) which give the equations of motion. You can simply plug them into any DSolve equivalent to get numerical solutions for the equations of motion (in simple cases they can just be solved using typical undergraduate ODE solving methods).
Of course, some software like Mathematica will do the whole thing for you as long as you can come up with the actual expression for the Lagrangian, which for simple systems isn't that difficult. You just need to express the kinetic and potential energy in terms of some useful variables (generalized coordinates), and then say L = T - U. Punch it into your software and the work is done for you!
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On March 29 2013 03:15 micronesia wrote:
Lagrangians aren't that difficult to set up, and once you apply the euler-lagrange equation you get the differential equations (second order) which give the equations of motion. You can simply plug them into any DSolve equivalent to get numerical solutions for the equations of motion (in simple cases they can just be solved using typical undergraduate ODE solving methods).
Of course, some software like Mathematica will do the whole thing for you as long as you can come up with the actual expression for the Lagrangian, which for simple systems isn't that difficult. You just need to express the kinetic and potential energy in terms of some useful variables (generalized coordinates), and then say L = T - U. Punch it into your software and the work is done for you!
Interesting. Might I point you to this? http://twvideo01.ubm-us.net/o1/vault/gdc09/slides/04-GDC09_Catto_Erin_Solver.pdf
I would like to learn to understand why this sort of math setup works for modelling and solving constraint equations. The general process for modelling and solving a constraint goes like this:
- Create equation of position to model the constraint.
- Derive equation to end up with one in terms of velocity.
- Isolate velocity terms.
- Identify Jacobian by inspection.
Then the rest is just a programmer using the Jacobian in a few lines of code (10-20 or so) in order to model complex behavioral constraints.
Could you perhaps shed some light on where all this is mathematically grounded?
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United States24667 Posts
On March 29 2013 03:26 CecilSunkure wrote:Show nested quote +On March 29 2013 03:15 micronesia wrote:
Lagrangians aren't that difficult to set up, and once you apply the euler-lagrange equation you get the differential equations (second order) which give the equations of motion. You can simply plug them into any DSolve equivalent to get numerical solutions for the equations of motion (in simple cases they can just be solved using typical undergraduate ODE solving methods).
Of course, some software like Mathematica will do the whole thing for you as long as you can come up with the actual expression for the Lagrangian, which for simple systems isn't that difficult. You just need to express the kinetic and potential energy in terms of some useful variables (generalized coordinates), and then say L = T - U. Punch it into your software and the work is done for you! Interesting. Might I point you to this? http://twvideo01.ubm-us.net/o1/vault/gdc09/slides/04-GDC09_Catto_Erin_Solver.pdfI would like to learn to understand why this sort of math setup works for modelling and solving constraint equations. The general process for modelling and solving a constraint goes like this: - Create equation of position to model the constraint.
- Derive equation to end up with one in terms of velocity.
- Isolate velocity terms.
- Identify Jacobian by inspection.
Then the rest is just a programmer using the Jacobian in a few lines of code (10-20 or so) in order to model complex behavioral constraints. Could you perhaps shed some light on where all this is mathematically grounded?
That is going in depth with more specific examples than I am used to, but I will help as much as I can. Remember how I said you set up the Lagrangian using generalized coordinates? Sometimes you can choose generalized coordinates such that position constraints are build into the coordinates. For example, if modeling a simple pendulum, instead of using x, y, and a constraint equation (effectively reducing two variables to one), you can use the generalized coordinate theta, which is the angle between the string and the -y axis. The length of the string can be treated as a constant, and you no longer need to worry about constraints... you build them IN TO your Lagrangian by using a smart coordinate transformation (x = Lsin(theta), y=-Lcos(theta)).
Unfortunately you can't always get away with this trick so you need to actually come up with the constraint equation(s). The constraint equation is always of the form f(x1,x2,...xn) = 0, where x1, x2, etc are each of the variables. The Euler-Lagrange equation usually says:
dL/dx - d/dt(dL/dx_prime) = 0, once for x1, again for x2, etc through all your variables (often it's just 1 or 2 variables)
However, when you have explicit constraint equations (unlike the pendulum example where we avoided it) you actually do:
dL/dx - d/dt(dL/dx_prime) - df/dx = 0, again once for each variable x1, x2, etc... just substitute xn for x in that equation
I'm doing this from memory so I would look it up in a classical mechanics textbook before taking my word for it. I'm not sure if the built-in Euler-Lagrange functions in software like Mathematica will handle the constraint equations for you or if you need to set up the Euler-Lagrange equations yourself by hand.
If you (or anyone else) is interested in a more in-depth guide to lagrangian mechanics I could probably write it, and I would actually reference my texts to be sure I was using proper notation and not making mistakes.
edit: btw I neglected to mention that the Euler-Lagrange equation is basically a summary of the calculus of variations, which is a very useful mathematical tool for classical mechanics, but it can be used in other places as well.
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On March 29 2013 03:37 micronesia wrote:
If you (or anyone else) is interested in a more in-depth guide to lagrangian mechanics I could probably write it, and I would actually reference my texts to be sure I was using proper notation and not making mistakes.
Yes I'd be very interested in seeing that!
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United States24667 Posts
Okay I'll plan to put something together. Once again, it won't be geared towards as detailed of an application as how that Blizzard guy was working. It should provide a good basis provided the reader has a math background, however.
The hardest part is going to be writing out the math in an easy to read way since I'm not that familiar with latex.
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On March 29 2013 03:49 micronesia wrote:
Okay I'll plan to put something together. Once again, it won't be geared towards as detailed of an application as how that Blizzard guy was working. It should provide a good basis provided the reader has a math background, however.
The hardest part is going to be writing out the math in an easy to read way since I'm not that familiar with latex.
Exciting, thanks for putting something together, I appreciate it a lot 
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ooooh I would love to read that, please do!
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On March 28 2013 20:35 Otolia wrote:Show nested quote +On March 28 2013 12:15 CecilSunkure wrote:
tldr; physics programming isn't a job position that has any demand (in my own opinion). Like micronesia said, a physics programming is the mother of all computational science bar computational mathematics (but mathematicians are always secluded). Weather forecast, Finance, behavior modelling all of this is done by physicists. For example, the best programmers in my theoritical physics class have written projects like : behavioral spreading of diseases, chaotic rebound (that was mine) or weather propagation. Those were simplistic but for most of us that was our first real code ever and we all wrote in C.
Yeah, I think the above statement was meant to be scoped by the games industry in particular. In research labs that kind of talent is very in demand.
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On March 29 2013 12:45 i.of.the.storm wrote:Show nested quote +On March 28 2013 20:35 Otolia wrote:On March 28 2013 12:15 CecilSunkure wrote:
tldr; physics programming isn't a job position that has any demand (in my own opinion). Like micronesia said, a physics programming is the mother of all computational science bar computational mathematics (but mathematicians are always secluded). Weather forecast, Finance, behavior modelling all of this is done by physicists. For example, the best programmers in my theoritical physics class have written projects like : behavioral spreading of diseases, chaotic rebound (that was mine) or weather propagation. Those were simplistic but for most of us that was our first real code ever and we all wrote in C. Yeah, I think the above statement was meant to be scoped by the games industry in particular. In research labs that kind of talent is very in demand.
Ah yes, to clarify I meant for the games industry only. I don't know about the state of other industries.
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I think this kind of blog really puts into perspective how much hard work you have to put into a physics program. That said kudos to blizz for putting in its physics engine that sometimes honestly does wow me.
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On March 28 2013 11:23 CecilSunkure wrote:Show nested quote +On March 28 2013 11:11 micronesia wrote:
Something to keep in mind about coding physics engines (and other things like that): it's more effective to have a science specialist learn coding in order to apply expertise to a program than it is to try to teach the scientific expertise to someone who purely knows how to code.
For a simple 2d engine this may not be the case, but it is true in the 'working world' for the most part.
Thank you for sharing this... sounds interesting.
edit: you might want to suggest how people can learn the physics necessary to come up with their own engines! We can't all have degrees in physics :p I would tend to agree. Most people aren't capable of writing this sort of thing on their own. And the funny thing is, is that in 2D the complexity isn't all that much simpler than in 3D. They are actually very similar, and often times just "adding another dimension" is all that is required to make such a transition. However scientists and mathmaticians are absolutely terrible at programming. They can't really be used for any commercial products because of this. So what is really needed, is someone that is great with mathematics and specializes in computer science. These types of people however are quite rare.
Engineers can be pretty good though. I took a three programming classes while learning chemical engineering and it was easy as pie. Some of the purely engineering software you basically have to have a minor in computer science to just interact with it (most older-generation, some of the newer ones have reversed the trend). Side note on the scientists since I saw so many friends go from a mechanical or chemical engineering over to programming jobs and software engineering.
Sad about know-how, but cool article & pictures!
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Bisutopia19229 Posts
Just write an article about the dot product and cross product and you just solved all your problems for physics in game development. Add in matrices if you want to be more advanced.
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Italy12246 Posts
Lagrangians are fucking awesome i remember being completely blown away when i first figured them out lol.
If you need help with Latex i can ask a friend of mine. He's also helped with sorting out the pdf for the PvZ guide.
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i dont think you would need that much knowledge for basic engines.
1 semester in physics is all i had regarding classical mechanics and analysis I+II gets you differential equations, manifolds and minimizing/maximizing with conditions. What more could you possibly want for an engine :D
I think the point where its easier to use a physics guy over a computerscience/programmer guy would be for labs that go much beyond those things.
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On March 29 2013 21:32 LaNague wrote:
i dont think you would need that much knowledge for basic engines.
1 semester in physics is all i had regarding classical mechanics and analysis I+II gets you differential equations, manifolds and minimizing/maximizing with conditions. What more could you possibly want for an engine :D
I think the point where its easier to use a physics guy over a computerscience/programmer guy would be for labs that go much beyond those things.
On March 29 2013 19:54 BisuDagger wrote:
Just write an article about the dot product and cross product and you just solved all your problems for physics in game development. Add in matrices if you want to be more advanced.
It's not that simple. Things start to get very complicated very fast. Having things bounce off one another and rotate with friction is very complicated, and joints are equally so in terms of mathematics. The computer science aspect of creating a high-quality robust physics engine usable in a game is also equally as difficult.
So when I see people say things like what I've quoted above, it's really that you guys just don't know what you're talking about unless you're referring to the simplest of simulations.
Edit: On a more light-hearted note, yeah you use a ridiculous amount of dot/cross products  You even use dot product in crazy places where it's not actually a dot product in theory, but the computation is the same haha
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Wow this looks complex, glad my game won't need to have this stuff in it :D. Collision detection is so easy in comparison
By the way I love your stuff cecil, your game layout TL knowhow article is an amazing reference.
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On March 30 2013 13:22 Rollin wrote:Wow this looks complex, glad my game won't need to have this stuff in it :D. Collision detection is so easy in comparison By the way I love your stuff cecil, your game layout TL knowhow article is an amazing reference.
Awe why thank you for the compliments
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EPT
