Game Physics

Adder_Noir

Hi I was wondering which of the following titles I should buy with regards to building a fairly simple physics engine for a game idea I have. I don't want to rush in I want to spend my money wisely. The titles are (roughly) as follows:

Real Time Collision Detection
Game Physics
Game Physics Engine Development

They'e all in the Morgan Kaufman series. I know the last title might seem the obvious choice but I would like to be sure before I buy. For your information it is intended to be used with an existing game engine which I presume already has collision detection built in. Does that I wonder rule out the first topic title? This also makes me think is the Game Physics Engine Development thus going too far seeing as the game engine is already there?

Would I be best looking at Game Physics as it is the physic concepts I wish to learn about the most at the moment rather than actually transferring them to code. Maybe I've answered my own question I'm not too sure I could do with some help thanks chaps

Danger

Are you sure that any of them will be beneficial? Do you have a chance to review them to make sure that they're not just duplicates of stuff that you already know? It would probably be worth your while to investigate other sources as well. Shop around.

Adder_Noir

Nice idea, I'll do that

I think they go quite deep, I've read a few of the customer reviews and apparently the books are quite complex as is game physics apparently. No major surprise there. I bought a book to brush up on my calculus aswell.

I think on the strength of the reveiws I'd probably go for the game physics one but again I'll stay undecided until I know for sure or someone else contributes who's been there.

Thanks for the reply.

Danger

You're more than welcome. Another thing that I forgot to mention is the possibility of joining, or at least contacting, a game-programmers' community. If it's anything like special-effects, or costuming or home-made jet engines, there's probably at least one site out there that's PFish in its eagerness to help novices along. You might end up learning all that you want to without buying anything.

Adder_Noir

I've had a good read through Chris Heckers website and it appears that the differential and integral are used to 'jump' between evaluations for position, velocity, and acceleration.

I wonder indeed though which quantity must be evaluated first? I would expect the dynamics is used to evaluate forces and thus resultant acceleration, which is then integrated with respect to 'physics-frame-rate' time to find velocity and positional changes.

Could someone help me and confirm if that last affirmation is indeed correct?

Thanks

Danger

I'm outta this one. I don't even know what half of those things mean.
Good luck with it, though.

ranger

I'm not sure about the specifics in doing this with game physics. But given a rate of change, one can integrate to get back to the original. So if you have a function that describes the objects acceleration, you'll integrate it a couple of times to get to the original positional function.

Adder_Noir

Thanks for the replies both of you Ranger I do now believe that is indeed the case thanks for pointing that out.

technobot

Yes, this is correct. First you find all the forces, then you convert that to accelerations, then you intergrate to find the velocities, and finally the positions of the objects. Though iirc, the more advanced physics engines work with momentum (and perhaps some other quantity) instead of velocities and accelerations. But I don't remember the details of how or why it is done.

In any case, the difficult part with a physics engine is exactly how to calculate the forces, and how to intergrate everything, such that the simulation will be stable, but at the same time fast enough and accurate enough. As you may be able to guess, there are different approaches and algorithms, with different performance characteristics.

Adder_Noir

Thanks technobot! That's helped my understanding of it alot

jostpuur

As long as your questions are physics and mathematics related, you probably get good answers here, but check out http://gamedev.net/ for specificly game programming related matters. They have a good discussion forum.

Adder_Noir

Thanks jostpuur

I've just been reading through Chris Hecker's articles (his first one) and he introduced a Euler Integrator. He was working with a force equation (the dynamics part I assume) relating velocity to air resistance of a moving body.

f=-v

Which when applied to the f=ma equation comes out as:

ma=-v thus a=-v/m

so dv/dt=-v/m

Fine with me. He then plots a velocity plot and states that the dv/dt part of the preceeding equation is used to model the gradient of the velocity plot at any instantaneous point. Followed that bit. He then states that if you go a short distance along the gradient denoted as (the distance) 'h' you have the following formula:

yn+1=yn + h(dy/dx)

Which in the force equation evaluated above and thinking of it on the velocity plot:

vn+1=vn + h(dv/dt)

Which becomes:

vn+1=vn + h(-v/m)

Which gives us the next velocity point on the graph. He states this is an integrator. This I don't follow. How can something which does not evaluate the area under a graph be described as an integrator? I see that it is getting the next velocity point on the graph (well roughly, h puts an error in) but how is it integrating?

Am I putting the cart before the horse a bit? Is the above formula meant to be used to trace the line of a graph before it exists after being given some initial conditions?

I have another question which can wait because if I ask it now it will just confuse people replying to this thread.

Thanks for the help offered so far

ranger

All he seems to be saying here is that the equation gives you the rate of change of velocity - (dv/dt = acceleration).

But it seems that he calls this an integrator because it evaluates the velocity at any given point; given that you have the acceleration (-v/m). So you enter an acceleration and out comes the velocity i.e. it is integrating acceleration.

Adder_Noir

Acceleration in, velocity out is indeed an integtrator. I didn't see that before. Thanks ranger

rcgldr

You're correct. Forces are calcuated, then numerical integration is done to determine velocity and position. Don't forget that angular stuff is done as well, such as yaw rate. I'm not sure if torques are calculated, then numerically integrated to give yaw rates and orientation. There's also pitch effects as well (acceleration and braking).

Slip angle (angle between direction tire is pointed versus direction tire is moving), along with downforce, and tire physics determines pavement force reaction that accelerates the car (in addition to aerodynamic forces).

Personally, I would just use a canned method for collision modeling. Trying to get it near perfect isn't worth the efforct since accidents should be relatively rare, and would waste CPU bandwidth (unless it's a Nascar simulation with all the crashes). Bouncing or sliding along walls might be important.

For a source in racing game simulation development, a guy named Todd Wasson has been doing a lot of work in this area. Click on contact on the first link for email address:

http://www.performancesimulations.com

http://www.virtualrc.com

Adder_Noir

Thankyou Jeff that's very kind. I aim ultimately to produce a military simulator. I have now ordered one relevant book to help me although I expect the journey to be a long an arduous one through several different texts.

I am indeed interested in things such as yaw rate and slip given that the game will include tanks and the like. I wonder if Todd would be prepared to enlighten me on certain issues regarding torque and slip and the like as I would expect racing games to be hot in this area.

In fact I'll drop him an e-mail now. Thanks again

Adder_Noir

For those whom are interested here is Chris Hecker's Integrator proof. Whether or not it's absolutely correct I don't know but I think it is.

Not that dv/dt is given by -v/m and f is taken to be f=-v (air resistance style).

I plotted in blue the series (Series 1) which uses the equations of motion to accurately predict velocity. I plotted in magenta the copycat profile (Series 2) using the integrator Chris talks about. You can see the slight error difference as the plot progresses but it's only small at that defined value of h.

Equations of motion plots are bounded in green whilst integrator data is bounded by blue on the sheet. Hope someone finds it useful.

http://www.savefile.com/files/843884