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Physics For Game Developers
Programmers who want to get serious about game physics will love David M. Bourg's Physics for Game Developers. As I've said, the subject is inherently very difficult, and the book assumes that you are already familiar with vector and matrix arithmetic up to college level, integration and differentiation, and at least you hazily recall your mechanics/physics lessons from school. You also won't be afraid to wade through Bourg's carefully documented derivations of formulae for various physical effects, and his well-commented source code.
The book starts off by recapping the basic concepts of mass, centre of gravity, moment of inertia and inertia tensors. Bourg assumes that you have a working grasp of these subjects, and I admit that I had to go back to some of my A-level mechanics text books. He then goes straight into kinematics, where he uses standard (but forgotten!) integration techniques to calculate velocities from accelerations and positions from velocities. His examples are excellent, although a few exercises wouldn't have gone amiss. The chapter on forces covers a great many different types of forces such as springs and buoyancy, but curiously omits the important subject of contact forces (the normal force that a table, for instance, exerts on your computer monitor to stop it falling through the floor). In fact contact forces don't appear until much later in the book. Particles, rigid bodies and impulses (forces from collisions) are introduced in chapters 4 and 5.
At this point I have to say I was a little bit confused. What did this have to do with game programming? Everyone knows that games spend most of their time running round a single big "main loop," working out the forces on each object, looking for collisions and working out which keys the user is pressing. It doesn't seem imaginable that a game programmer could completely solve all the equations of motion by pure integration at the beginning of the game, and then just run the positions of the players through the graphics engine like a movie!
I already knew a little about this from what I'd found from the web, but what most games actually do is calculate all the forces on all the objects (players, scenery, etc.) in the game, and then integrate them at each step. Some of these forces will be generated by human players pressing keys on the keyboard or wiggling the joystick, and that's how the objects end up moving. Pure integration isn't usually possible, so the physics engine performs numerical integration - a kind of fast approximation to the pure "closed form" solution. Numerical integration is itself a tricky subject, but it's the meat-and-veg of good game programming. Surprisingly, numerical integration and a realistic main loop doesn't appear until chapter 11 (172 pages into the book). I skipped straight to this section, and I suggest you do so too...
The chapter on numerical integration is excellent and contains the first realistic gaming (or at least simulation) code. Many games I've examined use simple numerical integration, like this:
// At each step ... A = acceleration, dt = time step
Vx += Ax * dt;
Vy += Ay * dt;
Sx += Vx * dt;
Sy += Vy * dt;
Unfortunately this method (Euler's method) is very inaccurate and unstable: if you tried to simulate planets orbiting around a sun using this method, they'd soon fly off into outer space unrealistically. Bourg gives an excellent introduction to better methods such as the "improved Euler" method and the popular Runge-Kutta method, and he covers them in a context which will make it clear how to use these methods in your own programs.
The book reaches a crescendo with three fully developed simulations: two hovercraft which you can drive around and jolt into each other like bumper cars -- they spin around realistically; a flight simulator; and a 3D car which can be crashed into blocks that bounce around. Again the source code is meticulously commented and generally well written. My only two reservations about the code are: It would be nice if Bourg had chosen to use OpenGL instead of Direct3D so that those of us without regular access to Windows could actually compile and run the examples. The book would make an ideal companion to the OpenGL Red Book. And coming firmly from the Windows camp, Bourg's examples are full of all the horrors of Win32 APIs and Hungarian Notation. But maybe that's just my personal preference :-)
So in summary: The Bad Points:
- Measurement systems: Bourg moves uneasily between the English/US system and the European SI units. So we get examples which combine ft/s, meters, slugs and kilograms, uneasily converting between the two. He should have chosen one system and stuck with it.
- A common complaint about computer books: I've just spent 25 quid on a book which will sit open on my desk for months. Is it too much to ask that it be ring bound?
- Some subjects are not explained in enough depth. Particularly: moments, contact forces, impulse methods. Bourg should probably have written a chapter or three on collision detection.
- The chapters are presented in a very strange order. Move chapters 6-10 until later, or introduce numerical integration earlier.
- A few of the illustrations are inaccurate.
and The Good Points:
- Considerably better than the usual round of maths/physics text books which make up this field. In fact, this is really one of only about 2 or 3 significant books in this area which are pitched for game developers as opposed to mathematicians, and it's certainly the best.
- The areas which are covered are done well, in significant depth, with a good bibliography where you can find out more.
- The commentary on the difficult equations is good, and Bourg resists the temptation to derive many of the formulae he presents, instead referring interested readers to other references.
- Code is well documented and explained.
And now I suppose I have no excuse not to resurrect XRacer :-)
You can purchase Physics for Game Developers at Fatbrain
i've played a lot of games, and gone 'wow' at some of the eye candy, but if you've played baldur's gate for PS2 you know that the coolest thing that has ever been coded for a game is the WATER for this game. you leave a wake behind you when you walk through it, you splash when you jump in, and ripples interact and reflect from the shore. maybe the physics aren't 'perfect' or whatever, but the realism of the water was enough to really 'immerse' myself into the game.
-sam
burn the computers. go back to the abacus.
I remember a good old game called "4D Stunts Driving" or something... That had a pretty interesting physic. Often it was sufficient to just bump into another car and you would go up in flames and millions of pieces. Or, if you reached high enough speed in the jumps, you could get such an angle, you would fly right into the athmosphere, and if you changed the camera POV, you could maybe see the car as a few pixels high in the sky. I think that, though, is part of the charm with this game. That, and the music :)
Will work for bandwidth
So pair up a couple of guys. One to worry about the artistic design, and another to worry about realistic physics.
Robotiq.com is heavily tested on animals
Some people aren't into super realistic physics. Some don't want to read a 300 page manual for a flight sim and spend weeks figuring out the flight model. They would rather just grab a joystick and start playing like in Wing Commander.
Its called "Physics for Scientists and Engineers".
Lets face it, the best physics is REAL physics.
If you want your game to have good physics, then slap a good physics engine (based on real formulae) into it!
Good quote, too many chars. Seriously, the slashdot 120 char limit sucks!
I really doubt that your method of numeric integration is going to be that critical an influence on the quality of game play. In fact I think that you ability to simulate physics without really doing the math would be more important. I doubt anyone is going to be timing a car's drop off of a cliff in Carmegeddon to determine what gravitational constant is used in the game.
I think it is more important to include as many effects as you can: gravity, linear momentum, angular momentum, elastic/inelastic collisions, friction (surface and wind), than it is to model the effects perfectly.
In fact one could argue that it is to the game designer's benefit to use an innaccurate and exaggerated physics model. Most real world collisons with the guard rail on a race course are relatively unspectacular (by design) - but that would be oh so boring in a racing game now wouldn't it?
-josh
Is it just me, or does that describe Pong perfectly?
Note: Greatest game of all time referes to the classic version, 2 controls, 1 console, 1 tv, 1 wasted childhood.
Wax-Museum Fire Results In Hundreds Of New Danny DeVito Statues
I just started playing Camageddon 3 TDR again(with the cheats ON sice I wanted to try out the missions), and I didn't observe until now, but your car falls in slow motion, ALL THE TIME. heh. Still,, fun game.
Even on games where there doesn't appear to be any need for modular physics, there will always be some mod author that sees a need. Say you are writing a racer, you might think that the physics should be fixed to real-world physics, but the mod author that wants to write a 'dune buggies on the moon' mod, is going to disagree with you, so keep it modular :)
The game may be three years old, with (originally) dodgy graphics, but it had the best car physics engine of any PC driving game. You could actually get a feeling for what the car was doing, how it was sliding etc, and in a '67 F1 car, which slides a lot, that was a big help.
It's still one of the most popular games in the driving sim community, with new mods and graphics appearing almost daily, but in the end it's the physics that draws people in. Yah it's hard to drive, but it should be hard to drive, and once you learn it, you'll never look back.
..although i picked the cheapest form of delivery so it won't be here for a bit more time...
i read thru the sample chapter [here] it's all about particle physics. i was quite impressive, i enjoy the *conversational* style that most o'reilly books have.
i implemented all of the examples in java using java3d.
i hope the book meets my expectations....
Maybe this book has an answer to a question that's been on my back burner for a while, and for which I've been unable to find a good answer for while surfing.
;)
Suppose you have a device that records lateral acceleration, longnitudnal acceleration, and forward velocity, with 100 samples per second, and stores them in a text file, one sample per line, one value per column.
Given the file parsing routine is a gimme and thus provided the values for elapsed_time, LatG, LongG, and FwdV, produce a function that will return the current X and Y co-ordinates of the vehicle, so that its ground track can be represented in a diagram.
Anybody got any good sources of information (or better yet, an existing library) for how to do this?
No, this is not an exam question.
DG
Want to learn about race cars? Read my Book
I agree, in some games, realistic physics can make a big difference. I remember when I first played Super Mario Bros. 1 on the NES, seeing how the fireball bounces along in a straight line until it gets to a hole, and actually falls down, I was rather impressed. (Small things, small minds, whatever. I liked it.)
However, in modern 3D-type games, it's important to pick and choose where you spend your time coding in the physics. In a racing game, it's a lot more important to spend time making sure the cars handle correctly than how realistically the trees sway in the background.
Unfortunately, there just isn't the time to make everything about the game perfect, and it's sad to see when a program has missed it's spot because of delays in implementing useless features.
I want a FPS that lets you blow holes in walls, accurately representing physical damage from weapons. Imagine Counter-Strike with realistic bullet physics: ricochets, windage, and weapon recoil that isn't predefined.
Hacking physics though, now that's a job and a half: figuring out a quick and dirty method of approximating the complexities of the real-world, and still have it look natural, making it look like a real environment filled with objects that have familiar properties and behaviours. And then blowing them up, REAL GOOD.
Tribe 2 has the best game physics ever in my opinion. It's a shame that there arne't people playing it anymore. The only reason it went down the tubes is because there aren't enough non-mod servers. Just about every server runs some variant on the game. As soon as I get a new computer I'm setting up a non-mod Tribes 2 server and me and my friends will rock the house again.
The GeekNights podcast is going strong. Listen!
There was a good article a while back in one of the mags (Scientific American?) i get about a team putting even more physics into games. If you shoot someone in the shoulder, they spin a bit etc. They were trying to make bullet hits look more real (as in reaction not gore). Anyone have a link?
As fascinating as the book sounds, individual developers or teams that are writing (and debugging, and debugging, and debugging) code to calculate the acceleration of a mass on a curved path are not using their time productively.
These functions are based on laws of physics, and should be the last thing to be reinvented.
Game development as a whole will be of a far higher quality when games don't have to be developed one molecule at a time.
I remember reading an article with a game developer a while back, who pointed out that the key for physics in a game wasn't realism, but consistancy.
He was developing a racing game, and says in order to make the game more fun, he had to sink the center of gravity for all of the cars several feet below the pavement, so that the cars wouldn't tip over when making hi speed turns.
As long as all the cars behaved the same way, it didn't matter that you were "cheating".
When playing your game, the user is entering your world, and learns a new set of rules. As long as you present your set of rules as consitant, it doesn't matter if they don't correspond with how things behave in "real" life.
Captain_Frisk - wannabe game designer.
http://www.d6.com/users/checker/dynamics.htm
provides an excellent, and free alternative to purchasing a weighty tome on the subject. Chris covers the details of rigid body mechanics in a thorough, but light manner.
I went to a physics lecture at GDC, the most memorable part of which was Chris saying:
"Here's how it's going to go... you're going to write your first rigid body dynamics simulator. You're going to simulate a cube dropping onto a plane. You'll run the program, the cube will drop, hit the plane... and disappear."
So, so true.
I agree with you on the ever-compounding inaccuracy of dead-reckoning.
:)
The good news is that I only have to do it for 30-60 second stretches.
I've also heard that one can correct somehow the wander/error from the integrated acceleration values by examining the forward speed value (which is produced by a separate sensor) - ie, work out the velocity from the accelerometers, and then compare the magnitude to the forward speed sensor, and correct the ground track from that. I haven't a clue on how that works, but I've seen evidence that it can be done.
As for what the project is... see farnorthracing.com
.
Want to learn about race cars? Read my Book
Excepting the possibility that the N64 version is completely different from the PC version, you are completely clueless. Carmageddon, of ALL the games you could have chosen, was a pioneer in game physics. It was the very first game that I played that had a real rigid-body simulator built into the engine.
Say what you will about the gameplay, or the physical settings (gravity was too low), but you can't say it had sucky physics. The cars and environmental objects interacted in an incredibly realistic manner. It was miles ahead of Re-Volt in that department.
I don't know that I really agree with the idea that physics need to be wildly realistic in the 'games' that I play. Honestly, I don't want to know what kind of recoil the rocket launcher in Half-Life would inflict on my character. I'm happier just watching the rocket track nice and straight towards my target instead of attempting to pick myself up off of the ground where I slid to a stop from the highly realistic recoil.
On the other hand, when I play a 'simulation' the physics are quite important. The best physics I've found in a sim are in a 3-year-old game: Grand Prix Legends. You're racing 1967-era Formula One cars, which means skinny tires, no downforce, high powered...which is a combination for difficult driving. But the physics engine is spectacular: you touch the gas when in neutral, you can feel the torque twist the body of the car; each wheel has its own model; touch the gas a bit to hard in a corner and be prepared to swap ends of the car, etc., etc.
The graphics are what you'd expect for a 3 year old game, but a dedicated community has sprung up to support the sim with everything from replay analysers, new tracks and graphics, and even a movie maker!
It seems that if you make a sim with good enough physics behind it, the fans of it can create new 'eye candy' to keep the sim looking good. But if you have crappy gameplay (see: Andretti Racing) and good graphics, the game will quickly be relegated to the bargin bin when something prettier comes along.
-Mark
I'll bet that in at least 90% of the games out there realistic physics would completely ruin the whole fun. What is the point of interacting with a fake environment when the environment reacts the exact same way real life reacts? Racing games are a good example. People want cares to handle well, generally. They don't want realism, in real life operating cars at high speeds is a lot more difficult than most games.
And in *any* game where people jump, realistic jumping becomes completely pointless. People want to be superhuman. Imagine quake with realistic physics....
Realism is not the high mark of games in all aspects, that is the whole point of games, to escape reality...
XML is like violence. If it doesn't solve the problem, use more.
Has anyone else seen the quake II secret level that has less gravity. Jumping, the remains of oponents, those bouncing gernades.. everything was like it was on the moon.. Lots of fun..
Now thats physics
Yeah, the technology wasn't always realistic (how exactly did the balls of flame track down and chase the pedestrians -- I mean zombies) but it was a CONSISTENT model.
I loved pondering... "OK, so I need to get the speed up powerup and hit this ramp at such a speed at this angle to bounce off the wall of the building and fly JUST over the tower to get that platinum power up and land on the building over there."
DO NOT DISTURB THE SE
In my opinion, the most difficult aspect of writing a good 3D game is coding complex physics
IMNSHO, getting good human motion is the hardest. Sure, EA does great motion capture for their sports sims, but where else do you see this in the industry? Download the Wolfenstien single player demo and see how stiff the models look (especially in the intro).
I think getting realistic physics is important, but, since most of it can be reduced to math anyway, GHz machines and loads of memory, combined with good programming, should be able to get it right. Making motion look good is far more important to my enjoying the game, and much more difficult.
On a side note....
Has anyone else noticed how this seems to be what sets WETA's effect in LOTR apart from the rest? Instead of generating a digital army, they film a bunch of guys walking in armor, then copy/paste/randomize to make a realistic hoard of warriors.
The cave troll, while the rendering was supurb, was entirly motion-captured. They had some actor plodding around with a big stick and ping-pong balls taped to his joints. They seem to understand that they can make everything look perfect in a still image, but the motion will still look fake.
I'd rather have someone respond than be modded up.
The VV algorithm has a lot of advantages: it's simple, stable provided dt is small enough, and unlike straight Verlet is self-starting given an initial velocity set.
Eric
"Seven Deadly Sins? I thought it was a to-do list!"
Some of my all time favorite games are great because they move 'right'. Can you imagine playing Spindizzy or Marble Madness with crap physics? I can, on a dire MM ripoff. It was frankly painful. The unexpected coolness that can result from engines that do things properly is very nice - although they cheated on the amount of kickback to do it, rocket jumping would never exist if they hadn't used impulses and momentum to control movement rather than old style 'move forward if the player pushes forward' arcade method.
"I Know You Are But What Am I?"
Actually, the game is not working out the forces of each object. This is why most objects in 3d fps games are static. Beyond basic collision detection, there is no interaction with the objects. If there are interactive objects in your game, the math involved in calculating the physics of a 3d pack of cigarettes or a 3d can of cola would not only take an enormous ammount of coding to bring to light, but also put undo load on the CPU.
When we worked on Ghost Recon, one of the big problems with physics involved calculating the way the trees swayed in the wind(believe it or not). Part of the solution involved going from multiple wind directions to a single one. The users wouldn't notice it. Heck, we could have made the trees static, thus relieving the system of about 40% of it's performance hit, but we wanted some level of realism in the background and atmosphere.
Is that it gives you all the important physics equations that I learned throughout freshman and sophomore years of college all in one place. They equations are easy to find (though the variables used aren't the traditional ones in physics).
The book is a good reference to have. To me this would be good to have because I already "learned" all of this, but like most don't remember all of it. Having all these equations right in front of you will enable you to remember everything swiftly and apply what you need to.
Like most O'Reilly books, this is a good reference to have, and I think it should be bought by people that already know most of the basic physics stuff.
"Time is long and life is short, so begin to live while you still can." -EV
Half life is based on a heavily modified quake 1 engine with some quake2 code thrown in for good mesure.
autopr0n is like, down and stuff.
Quote: "A common complaint about computer books: I've just spent 25 quid on a book which will sit open on my desk for months. Is it too much to ask that it be ring bound?"
The book is not ring bound because it costs 25 quid (= British Pounds).
'Twould be far too easy to stick it through a photocopier or scanner if it were.
Not confused enough? http://translate.google.com/translate?u=www.slashdot.jp&hl=en&ie=UTF8&sl=ja&tl=en
Carma 2 had fun physics on the PC too.
The N64 version sucked, bad, as far as physics. That is what the original poster was complaining about.
I've had enough abrasive sigs. Kittens are cute and fuzzy.
I'm still waiting for Physics for Cartoon Developers: just how long should a character remain suspended after realizing he's in mid-air? We'll need pure math computation methods for ordinary cartoons and numerical methods for interactive cartoon games.
What do you mean they cut the power? How can they cut the power, man? They're animals!
This is a refresher course in high school physics, sometimes freshman college physics, but the author does not have any kind of perspective on game development. It's easy to pick up a book about physics and implement what's in there. The equations are well known. But that kind of implementation is much, much, too hardcore for game use, where you need to devote 15% of each frame to physics calculations.
The trick is coming up with a way to seem like you're doing much more than you really can. The book gives little help there, as trickery and non-traditional techniques can buy you a lot more than just implementing standard mechanics.
I think that the most glaring physics error commonly seen in many games -- especially platformers and FPSers -- is violations of inertia. Take almost any game where 1) your character can jump and 2) there are horizontally moving platforms of some sort. Stand on a moving platform and jump as it moves. In almost every single game you play your character will jump straight up in the air and the platform will move out from under the character, even though real physics should have the character continually moving in the direction of the vehicle (air resistance isn't that strong or your characters wouldn't be able to move at all).
I think that I've seen one game (whose name escapes me atm) that actually got it more or less correct -- and I think that was just a game engine quirk that caused it.
STOP MISUSING APOSTROPHES, YOU MORONS!!!
The real solution here would be to stay with real world physics. "Real World" physics work on the moon too. If a physics library would allow you to specify mass instead of weight and also the mass of the main body to witch he is on the surface, this library would indeed encompass ANY physical situation. You could even have a "G-Field" which could temporarily change the value of G (the gravitational constant) or even your mass to make you be able to "defy the laws of physics" and jump 20 feet in the air while you have said "G Field" suit on.
:)
I think accurate physics MUST be present in most motion-oriented games so that the control feels more natural (i.e. feels like what would happen in THIS universe). You can change masses, gravitational constants, whatever, to make objects in your world to WHATEVER you want them to do, but F=ma should still apply
I am a flight-sim junkie, and a former military pilot (before anybody asks, I am NPQ, not physically qualified to fly anymore). I have owned maybe two dozen different flight simulator programs over the past fifteen years.
My favourite for a long time has been Austin Meyer's X-Plane. X-Plane uses an engineering process called "blade element theory" to approximate the true behaviour of an aircraft in flight. And it does this fairly well; I think X-Plane does the best job of any of the PC-based sims at mimicing the actual feel of the aircraft.
X-Plane doesn't have the "eye candy" of MSFS-2002 or any of the Flight Unlimited series, but as far as accurately modeling flight physics, X-Plane is head and shoulders above the competetion.
Runge-Kutta is a complex method for quickly and accurately solving differential equations by numerical means. It is used instead of simple Euler iteration because it is equivalent in speed and gives much more accurate results. It works by adjusting the timestep dynamically to skip over regions where the system is changing slowly, and to integrate more carefully when the system is changing quickly.
This is all well and good when you are trying to do something important, like simulating heat flow within in a heatsink. But for simulating the orbits of planets around a star, for example? What a waste of time! The orbit is elliptical, so just simulate a freaking ellipse!
What about space missiles? Do you need Euler integration? No! There is a closed-form solution to the linear acceleration problem -- it's a quadratic. This procedure does not give low error. It gives zero error.
I read this guy's articles several months ago. I thought he was off his rocker then, and I still think so now.
So there I am trying to solve a ballistics problem for a game. I need to drop artillery shells on target, based on launch speed, required horizontal distance and gravity, but not, thankfully, air resistance or other accelerations. We need this to work right, but more than that, we need it to work quickly for an imminent product demo, so a co-worker is thrown at it as well. He has his Halliday and Resnick Fundamentals of Physics Extended Third Edition, and a couple of years of college maths.
So we get to work. I do a quick napkin calculate and can solve for the range based on the speed, angle and gravity, but I can't figure out how to solve the equation for the angle. It's fairly easy, but I'm an absolute duffer at maths (it nearly dropped me out of college). My coworker has started right, trying to solve it for the angle.
Five minutes later, I'm done, and I mean done. I'm dropping shells within spitting distance of the target. "Oh, you solved it then?" asks co-worker. Heh, not exactly. I'm pumping angles into my napkin equation and doing a bsearch until I get a distance that looks close enough.
Coworker is outraged! It's inefficient, he claims, which is technically true, but it's a few iterations happening every few seconds at most, which isn't even worth our time profiling. It's not perfect, which is also true. But our engine is using cheap and nasty "X += dX * dt" anyway, so even a perfect calculation wouldn't be accurate.
My points: it's hitting the target. We hit the time target. It's a game.
Sure, physics has a place, and it's aesthetically appealing, but as long as you get the results that you need, the method isn't important. The games that you think have great physics? Probably fudged nine ways from Sunday to make them feel great.
If you were blocking sigs, you wouldn't have to read this.
I've found in my limited (hobby only) game programming experience that real physics make for boring run 'n' jump games, but they make for wonderful projectile games. Think ballistics (Scorched Earth, Quake, etc...).
Another pet peeve i have is that a lot of these sort of things never really mention one killer point. When computing whatever delta t for updating a scene, it is best to use a moving average of the last n frames (i use 32, kept in a rotating ring buffer), because that keeps an unusually long or short frame from fucking up any calcultions.
---
Play Six Pack Man. I
Actually, some of the people I work with have been doing research on trying to simulate cartoon physics, it's VERY difficult! It's basically research into getting game characters to stretch or compact realistically when accelerating or colliding with walls/floors. In terms of "real" physics, this is close to soft-body dynamics, which is MUCH harder than the rigid-body dynamics presented in this book...
Dan
In the summer i took a numerical methods course using "Introduction to Numerical Methods and MATLAB: Implementations and Applications" by Recktenwald. If you can use procedural languages, you can read/write Matlab scripts. I'd give the link to the course website, but the prof changes the password every term; it's a damn shame, too. He's a fellow of the IEEE, really smart guy. Had good course notes.
sigs are for suckers
Just because this book tells you how to program more realistic models, does NOT mean they have to be realistic. For example, you can set gravity to 9.8m/s^2, or hell set it to 4.9m/s^2 and have it be the moon. Or if you JUST want higher jumps, increase the force you apply when jumping.
The important thing this book (I assume) lets you do is generate better MODELS. These models can be parameterized on all sorts of things. The outcome doesn't have to be more realistic, but the interactions will be more consistent and reliable. In this way, the interactions of the forces (even if gravity is half or what it is normally) can still be realistic.
"Of all days, the day on which one has not laughed is the most surely the one wasted." -Sebastian Roch Nicol
For those of you interested in the physics of motion (mechanics), I would suggest you pick up the books "Vector Mechanics for Engineers" by Prof. Beer and Prof. Johnston. It is easily the best book for mechanics I have personally read. And it is modular in the sense you can skip some chapters if they're not interesting without going "DUH" while reading the later ones. Although it says 'For engineers,' the books are understandable even if you haven't got too much math experience. If you're scared of vectors, they also have a "Mechanics for Engineers."
-Shaunak.
I'm reminded of folks in high school who would get hot under the collar arguing that the Arduin rules for magic and hit points were more realistic than the D&D versions, or the realism of different types of dragons . . .
hawk
hawk
I think I just figured out why my ground tracks are such a bloody mess.
The acceleration values I have are taken _with respect to the vehicle's axis_ not the world co-ordinates' axis.
So I somehow have to translate the co-ordinate systems before I can apply the acceleration to the vehicle....
Any ideas on how to do that?
.
Want to learn about race cars? Read my Book
The main problem with realistic physics in video games is that it really isn't possible to do it.
What's that you say? But this whole post is about how you can do it? Nope sorry, but I don't know of any games today that really model what is going on in terms of 3D solid mechanics. Once one body interacts with another the calculations get staggering complex. Likewise do you really think that the flight sim calculates the flow around the aircraft to get it to behave right? Of course not.
What most games actually do is model everything as a point mass and then add a handful of other parameters to take into account solid body rotations. Collisions and other more complex events are handled with simple rules of thumb. Or in other words they are fudged. Provided they are fudged well it doesn't really matter. This is what many simulation games do (like Terminus). If you are very lucky they may actually calculate the stall of an aircraft using bernoulli's principle at a few key points. However it far easier to supply a stall angle and stick with that.
So when we talk about "game physics" keep in mind that some of the best game physics of all is completely fictitious. It just has to look and feel right, it doesn't have to be right especially when being right would take way to much processor power.
So far I've gotten all my Karma from telling people they are wrong... :)
A very simple (*) way to model downforce is to drop the centre of gravity of the model so that it is below the ground. Other variables such as tire grip also have to be changed as well but these are generally constants.
(*) Downforce changes with vehicle speed so this is a very simple model.
wot no sig
Realistic physics in games will never catch on. Lara Croft would keep falling over forwards.
11.0010010000111111011010101000100010000101101000
As someone else pointed out, there's a straightforward way to approach game physics, based on what you learn in a first-year dynamics course, and it won't work. Free flight is easy. Contacts and collisions are hard.
Detecting contacts between objects is complicated, but well-understood. There are several free collision-detection engines available, and many research papers. The time bounds are quite good; only slightly worse than O(N) with the better algorithms. Writing a collision detection system is a big job, but the theory is tractible.
Taking appropriate action when you detect a contact is the hard part of the problem. Bouncing balls are easy. Multiple irregular objects with multiple contacts, slipping and sliding, are hard. Most current games simplify their collision geometry down to cubes or spheres and botch the hard cases ("But my sword went right through him and he didn't even notice!") The latest generation of games is just starting to get contact right. In another year, correct contact handling will be a "must-have" for commercial games.
If you simulate contacts between objects with a spring and a damper, you run into numerical stiffness during integration. Soft objects at slow speeds will bounce fine. In a hard collision, the forces become huge for short periods. The simple integration algorithms will result in huge errors, and the objects will go flying off into space.
If you simulate contacts between objects as impulses (an impulse is an infinite force applied for zero time, but with a finite energy transfer), two objects bouncing off each other will work great. More than one contact per object doesn't work too well. Resting contact doesn't work; objects may fall through each other. And everything bounces like it's a pool ball, because all collisions take zero time.
If you try to do everything with constraints, resting contact works. But combinations of sliding and resting contact result in wierd corner cases that are hard to get right. Trying to solve contact, rather than simulate it, leads to static indeterminacy. (Think of a table with four legs, slightly different in length. How the table behaves is very sensitive to small changes in leg length. Numerical solutions of multipoint contact problems become similarly sensitive). This is the approach Baraff preaches at SIGGRAPH, but few others have been able to implement it.
After a few years on the problem, I developed Falling Bodies, which successfully solves this problem well enough to simulate a human figure falling down a circular staircase. It can be done. I hammered through the spring-damper problem by using unusual and robust integration techniques. This is computationally expensive, but sound.
If you're developing a commercial game, and need working physics, go with the Havok engine. They have a rigid body engine, a soft-body system, and a specialized vehicle simulation engine. (Yes, vehicle physics in games typically has fake components. In most racing games, the tires are impossibly good and the vehicle CG is impossibly low. But you need a real physics engine to fake it properly.) It's not cheap, but you're not going to solve this problem in a few months. Major developers have blown years on this problem and failed. Trespasser, from Dreamworks, went down the drain that way.
This is a very interesting point -- I imagine that a lot of modern game development has to do with squeezing as much as possible out of each frame....and for the same reasons that 3D graphics programming is more than just "calculate primative, raterize, clip scene, etc." but actually uses well-designed algorithms to make this process more efficient.
Do you have any links/books/info on the "trickery and non-traditional techniques" that game developers might use?
--Noah
Ferrari and other exotic car rentals in New York
I picked up this book just last night at Borders... flipped through it, and thought it was really interesting. I'm not particularly interested in programming games, but I am interested in doing simulations. Can anyone recommend any other books that would get one into this?
Libertarianism is rich wolves and poor sheep playing gambler's ruin for dinner.
As it turns out, the book cites several gamasutra articles as references.
Libertarianism is rich wolves and poor sheep playing gambler's ruin for dinner.
Unfortunately this method (Euler's method) is very inaccurate and unstable
This is only true if you're simulating a standalone system (like the orbiting planet example). In real games, the player is constantly pressing the controller, collisions are occurring, and the "AI" is making decisions. Stepwise integration makes perfect sense in that case. Calling it "inaccurate and unstable" shows a lack of game development experience.
I wonder why I didn't have a better subject line. Hm. Anyway, you're right, the cars could be flying in weird trajectories, it made the game very funny, very playable!
Will work for bandwidth
Carmageddon is an addictive game not due to the physically simulated space but due to the simple fact of being able to crash someone's eye balls after you run them over with your truck over and over and over and over and over again! (the sound of crashing bones is what makes that game addictive)
You can't handle the truth.
Not quite sure how to take your comment on my degree :) I'm also getting a degree in CS so it's a lot of juggling to be doing. I'm putting the priority on CS.
Why? If somebody does something stupid and they get stuck it's their own fault. That's how it is in real life, why should we expect anything different from a realistic game? Otherwise you have to define what can and cannot be destroyed, and you end up with something just like the "deformable" terrain we currently have in some games, except it's got a whole lot of unnecessary math chewing up your clock cycles.
Under capitalism man exploits man. Under communism it's the other way around.
True, but you need realistic physics as a starting point. Some of the driving and crashes in Midnight Club and GTA3 are certaily unrealiztic, but you can see hoe they are based on a realistic physics model that was tweaked for gameplay purposes.
It amazes me how people can drool through a
calculus course and then proclaim themselves
experts on slashdot.
First of all, Simpson's method does not
create an "exponential polynome." It models
a curve locally as a parabola.
Second, this method is useless in many situations
where one integrates over time. Simpson's rule
is designed to find the area under a curve.
Yes, distance is just area under a velocity
curve, but you are not given the velocities
a priori. You have to solve for them on the
spot, and even worse, velocities can be
influenced by the current position. In fluids
and soft-body deformations, things can get
even uglier. Some of the better methods for
numerically integrating through time involve
estimating the next values in time and solving a
system of equations using old and new values to
get a more accurate result (very hand-wavy explanation).
This is a subject on which I am as close to a world expert as it's possible to get. If you are familiar with MMOG development, you may have heard of MUD-Dev. If you do a search for my name and "physmud" you'll turn up hundreds of articles on the simulation of physics in a game engine. I used to simulate multi-day trajectories of orbital and ballistic bodies for SDI purposes for a living. I know just about all there is to know about this kind of modeling, and where you can take a shortcut, how to do a numerical approximation in n or nlogn steps when possible, what the inaccuracies introduced by each approximation would be... sometimes, I know how to do an exact solution to a transformation in a far smaller amount of time, using a jacobian transformation on complex geometries with an angular integration... but the reason I know this is, I learned on the job, and I took a degree (plus a bit) in physics, and I read all the books I could find. So, it is with regret that I say this book was not terribly good. I've seen better in a text entitled "An Introduction to Computer Simulation Methods, Applications to Physical Systems", a not too well written textbook with source in BASIC, but at least featuring a fair breakdown in the nature of algorithms, numerical integration, efficiency and accuracy, etc. A much better choice, IMO, would be "Numerical Recipies in C", though it's a little more advanced... "Numerical Methods for Physics" is hard to find, but very good. "Numerical Methods for Scientists and Engineers" is not the same book, and while very good for numerical analysis, it isn't an ideal book for learning simulation techniques. If you're interested in related fields, try looking on Amazon under Books/Subjects/Science/Mathematics/Applied/Compute r Mathematics. There's stuff on 3D graphics algorithms, signal processing, crypto, genetic algorithms, organic and physical chemistry sims, and more... just be aware that there are a lot of books on using Matlab/Mathematica/Maple/etc.
-- Still waiting for the Nike endorsement
How is this a troll?
Hrm. Seems my last five comments have each been modded down one point. Fortunetly for me, I could care less.
autopr0n is like, down and stuff.
So now, given the theta angle, we can transform the car-coodinates accelerations into world-coordinates accelerations, and then we process the Verlet algorithm to get positions.
Soooo then... how to determine the theta angle, given that there is no compass on the vehicle?
I don't think I've defined the problem clearly enough:
Imagine you have a car, parked on a flat plane of infinate size. The car is stationary, at the origin, with the nose aligned with the Y axis (so, for the moment, the car axis and the world axis are aligned)
Inside the car is a pair of accelerometers (one along the car's x axis, the other along the car's y axis), and a speedometer (which provides car-y-axis velocity) The car is then driven around in a path, while the accelerometers and speedometer record values at a fixed sample rate.
Given the resulting data stream, and assuming no slip, give the stream of world (x,y) coordinates that correspond to each car (x-accel, y-accel, y-velocity) coordinate.
Seems like we're modt of the way there...
.
Want to learn about race cars? Read my Book
> Is it only me, or Halo (on Xbox) has some of the worst physics engine I've EVER seen?
;-)
It's just you.
When you're in the jeep, look for the blue carat ^ in the middle of the screen. What makes the jeep so difficult to drive at first, is that arrow points to where your jeep will go, irregardless of where your wheels are pointed. If you grok that, handling the jeep is just 2nd nature.
Cheers
.. that the physics-based formulas are just *one* part of a physics engine.
Collision Detection (CD), and more importantly Collision Response (CR) determine the "feel" for your game. You can have the most accurate physics in the world, but if your CD/CR sucks, chances are, you're bringing the game down too.
Check the archives of Game Dev Algorithms if you want more info.
If it is done like most books today, it is simply glued. If color isn't a necessary component of the printing, you could "break" the spine, carefully remove the leaves (I think that is the term) or pages (if it is real cheap), from the book, photocopy them, and ring-bind or spiral bind it yourself.
If it is well bound (ie, with sewing, cloth, hardback, etc), then cut the pages out and photocopy them, then ring-bind it.
Now, I am not one for destroying books in this manner (or any manner - I love books), especially such an expensive one - but if you really need ring-bound books...
Reason is the Path to God - Anon
First, physics is inherently descriptive and approximate anyway, so if there is a "real" physics, it has yet to be discovered. Physicists are always working with approximations and numerical methods, but it's best to go as far as you can with "exact" solutions and generalities. Then, when you need to start doing numerical work, you have some place to start from. You can't do numerical integration unless you know what to integrate.
Second, the usual 100-level undergrad textbook in physics tells you a lot of things that you probably don't need to know when designing games (like E&M and some quantum mechanics), but also leaves out the more practical aspects of classical mechanics when dealing with less-than-ideal objects. Once you work with the motion of objects that are not spherically symmetric, you need mechanics at the next level, and you need to work with matrices and vectors. This stuff isn't difficult, but it's not in the typical undergrad textbook. And it does require a bit of mathematics, like most things that are worthwhile.
So it sounds to me like this book does have an important niche to fill, combining undergrad classical mechanics, a sampling of junior-level classical mechanics, and some numerical methods to boot.
Or maybe, since we're talking about games with realistic physics, give them some way to remove/get around the obstacle, such as being able to climb over it, or blast it with an improvised explosive which would perhaps cost them a lot of their ammo, or dig their way out with a shovel.
Or, there could be limits placed on what can or cannot be destroyed based on the difficulty level the user selects.
My point is that there are plenty of other ways of dealing with these sorts of problems. They may cause a lot of headaches for the coders, but so will realistic physics.
Where I'd personally like to see realistic physics is in space flight simulators. It really iritates me that the majority of them ignore the basic mechanics of movement in the absence of gravity and atmosphere. Given that gravity and atmosphere produce most of the complications in dynamics, it doesn't make much sense to me why they do that, other than that it's cheaper to slap new graphics over an existing flight sim engine than to create a new one that actually works right.
Under capitalism man exploits man. Under communism it's the other way around.
I have to say I've only played the PC version, but in Carmageddon the physics are very "floaty" and it's that way for a reason!
As Carmageddon is all about massive jumps and stunts and air time (as well as crashes and pedestrians), they made the physics of the game enhance the gameplay aspects they wanted to emphisize.
"There is more worth loving than we have strength to love." - Brian Jay Stanley
In my opinion, the most difficult aspect of writing a good 3D game is coding complex physics
And here I was thinking the hardest parts of writing a 3D game were managing oodles of content as fast as possible, creating believable AI that doesn't get instantly panned, creating tools for designers and artists that are not only easy enough to not cause lost time but also complex enough to do everything they require, and generally trying to make a game fun based on an unproven concept (ignoring genre cookie-cutting games).
The most important part of making a game is making it fun. People aren't going to give a rats ass if a game has decent physics if it's a bore to play. Case in point, Trespasser - the most complex physics system seen in a game, and also the biggest flop and butt of game developer jokes for years to come (although that could just be because of Seamus Blackley, but I'm not going to go onto a tangent).
My point is, games are fun first, realistic second. If a game is extremely realistic, it's a simulation. Some may not see the difference, but I'm guaranteed you would after playing an hour of both Railway Tycoon II (Turn-based game based on railroad era) and Microsoft Train Simulation/Trainz (Simulations where you drive a train). The difference here is that one is fun and non-realistic, the other isn't fun to non-trainspotters but is extremely realistic. I'll let you imagine which one makes more money.