Physics For Game Developers

Richard Jones writes: "In my opinion, the most difficult aspect of writing a good 3D game is coding complex physics. If you can take away all the flashy graphics, texture maps, light and shadows from a game, and it's still at least 75% as playable and addictive, then you have an excellent game. But too many programmers seem to be ready to concentrate on the graphics, neglecting the underlying physics which make the game playable. If you compare, say, Re-volt with its fabulously detailed models of remote-controlled cars, and Carmageddon which on the N64 at least has sucky physics, well I know which one I'm still playing." He's contributed his review (below) of a book intended to help game programmers make games that aren't sucky. Physics For Game Developers author David M. Bourg pages 326 publisher O'Reilly rating 8 reviewer Richard Jones ISBN 0-596-00006-5 summary A good introduction to the difficult subject of writing 3D games and simulations with accurate physics, let down by a few minor snags.

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

Comments

Re:Don't need to be that exact

[skoda]

There's a difference between "unrealistic" and "unstable".

Unrealistic suggests that it doesn't behave as in the real world -- but that doesn't mean it isn't modeled on the same principles (acceleration, momentum, etc.) And you still want to simulate it consistently; it should "feel" right.

But an unstable computation method can "blow up", regardless of realistic or unrealistic "physics."

Consider:
Jump pads in games like Quake or Unreal are "unrealistic". But they are modeled at least partially on physics. But to make them work right, in all their unrealistic glory, the computation method must be stable.

If it wasn't stable, then you might something like:
- Multiple, successive jumps on one would lead to a "blow up" where the player would be wildly, and unexpectedly shot through the roof and to the outer edge of the game universe.

For both realistic and cartoon physics, you need accurate and stable computation methods.

Chris Hecker's Physics tutorials are FREE!

[strags]

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.

Games vs. Simulations

[dreadpiratemark]

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

Who wants realistic physics?

[Junta]

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...

Cartoon Physics

[devnullkac]

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.

Re:throw physics out the door...

[Dimensio]

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.

Lara Croft

[Stephen]

Realistic physics in games will never catch on. Lara Croft would keep falling over forwards.