Game Physics Resources

Simple, easy to understand, but very good looking simulation.

I really recommend this article if you want to do a 2D vehicle game.

Demo project of 2D car physics with source code (C++). Works pretty well.

An article at the CodeProject.
Commented code included.

Haven't read this one.

You can find RK4 example in this article.

"Position" Verlet integrator modified so it is more accurate when you use non-constant acceleration (and you usually do) and/or non-constant time-step.

An iterative solver using impulses. Fast and gives very good (=good looking) results.
Described and implemented by Erin Catto in Box2D.

This implementation I uploaded here is a bit older, but it is much simpler then current Box2D version and easier to understand.

Be sure to read Catto's presentation included!

Very good article about soft body physics implemented in Hitman. This method is very easy (from my expiriences) to understand and implement and the result is good (it is probably not accurate as other methods, but it looks good).

Simulates objects as mass-points connected together.
Uses Verlet integrator.
Solves collisions using relaxation.

Good explanation of Verlet integration ("position" version).

One of the most popular engines you can use. It was used by many successful commercial games. Has really nice features like multi-thread support. It is also specially optimized for XBox360 and PS3 so you can port your games with ease.
It is free for non-commercial and commercial use.

Just found this after I completed this project :/

Just another cloth simulator. Didn't study it yet.

APE is a complete open source engine written in ActionScript.
It's a good example of how Verlet integrator can be used without many problems and accurancy lost - you usually don't need accurancy when creating games.

An action script engine based on Box2D. It is not released yet, but may be worth keeping an eye on it if you are ActionScript specialist as it seems it will be optimized for AS.

Dead project, continued by APE.

APE is a follow-up of the Flade engine. It still uses Verlet integrator, so be prepared for well working springs and mass-spring objects (softbody).
It looks REALLY usable and If I programmed for Flash, I would definitely give it a try.
There are also C++ and Java ports.

Direct port of the Box2D engine to AS3.

is a site of Bruno Heidelberger. There you can find interesting papers concerning soft-body simulations. However, they might not be very useful for practical use. But, maybe I just didn't get deep enough into their ideas.

Forums related to the Bullet Physics engine, but it gathers a lot of expirienced guys together.

Really interesting and fast engine written in pure C.
Currently under development.

Free for private use, but you have to pay a license fee to be allowed to use it for your commercial projects.

Written for XNA.

Dunno much about this one, but looks usable.

SoftBody physics simulator based on very special algorithm called FastLSM (obviously).
It is covered by multiple patents, so be careful with it's usage.
It's good to read the paper first before studying it.

My favourite soft body engine. Objects behave like a pack of jelly and bounce like crazy :)
Also there is a funny game created with it - JelloCar.

Haven't played with this one a lot, but the code looks clean and well commented.
Also it shows another use of the sequential impulses used in Box2D.

This is my most favourite engine. It's very well written and advanced with many nice features.
It is currently under heavy development by Erin Catto.
(so my mirror version is probably out of date)

Probably the most favourite physics engine at this time.
Currently under heavy development (so my mirror is probably outdated).
Used by many commercial and non-commercial projects.
Also be sure to visit it's forum as it is full of interesting information and people:)

Accurate physical simulator with different. Probably not so good for games, but interesting from the theoretical point of view.
Haven't played with it yet.

Implementation of impulse based dynamics described in Dr. Jan Bender's paper. Worth studying it from the theoretical point of view.
Also be sure to read his paper.

Just another study source:)
Uses sequential accumulated impulses described by Erin Catto (and used in his Box2D), so might be good to compare it to Box2D.
Still under development.

...is another open source collision detection library.
It says it is better then SOLID and RAPID, but you have to make your opinion by yourself:)

Another very popular engine, big rival to Bullet.
Used by many commercial and non-commercial projects.

An opensource library written in C++.
Dunno much about it.

Project aimed at simulating physics as "correct" as possible. Treates resting bodies in a very good way and also supports non-convex bodies.
Usually you can live without these features in your games, but might be interesting to look at.

..is an open source collision detection library written in C++.
It operates in 3 dimensions.
Coveres both broad phase (SAP) and narrow phase.

Recently released engine, still not known very well.
Has some nice features like support for many stacking objects or automatic object destruction-fragmentation, but doesn't seem very powerful to me at the first look.

I have no expiriences with this one.
It features swept collision test (for fast-moving objects), however it is the only remarkable feature in their list.
It is free for non-commerial use.

This pack contains many valuable papers, demos and source codes for car physics programming.
They include some of resources I mentioned in this section, but I think they deserve special space.

A little different and maybe not well known method for detecting collisions.

As a project for school I made a comparison of few broadphase collision detection algorithms using J2ME at mobile phones platform. Algorithms tested were SweepAndPrune(taken from Box2D Java port), UniformGrid and ImplicitGrid.
ImplicitGrid was clear winner for me.

Documentation (coll_test.html) is in english, but perhaps the numbers in the result table will be clear enough.

Haven't read yet.

If you are studying physics, you might understand his work :)
I currently don't much.

Solves problems in simulating multiple fluids with varying densities by altering the SPH method.

There is discussion about how to derive an equation needed by a constraint solver. You come to this problem when you want to simulate joints.

One part from the Siggraph '97 course by Baraff and Witkins.
Shows how to derive Euler and midpoint(aka Runge-Kutta) integrations. However, you need to know more about calculus to be able to get it clearly.

Coveres non-convex polygon detection, which might be useful for deformable bodies.
I haven't studied it much yet.

Haven't read, haven't tried.

C++ implementation of an array-based Sweep and Prune written by Pierre Terdiman. He claims it is pretty fast (according to his tests) and I trust him :)

It is based on his paper (below).

Haven't read this one yet.

Few math and physics slides/links.

And a little comparison to Verlet.

Good articles to get you started with springs.
Sample source code included.

Note that if you use position based dynamics (ie Verlet from Jakobsen), then you handle springs in a different way (by modifying their positions direclty without forces).

Maybe you can dig something up from there...

Haven't read this one. Targeted to 3D soft body simulations.

A collision detection method usable in 3D simulations. Haven't tried yet.

...is an algorithm developed by Alec Rivers under lead of professor Doug James for fast soft body simulations.
It also supports realtime destruction of the bodies as you can see in their video.
They concentrated on speed so it may be really usable for games. The algorithm is covered by some patents, but it seems like Alec will allow you to use it freely, if you contact him.

List of implementation I've found. Search for them in my resources or at google:)
- Box2D
- SOLID
- Farseer Physics Engine

...enabling you to handle moving objects and predict their collision in time. Found at Gamasutra, you probably need (free) membership to be able to read it.

When I was developing my own blob simulator, I had problems with choosing a right way to keep the volume of the blob. It still behaved like a baloon or a jelly or a gum ball. My desired behaviour was fluid-like body.
Finally I found a similar simulation on youtube and contacted it's author, Grant Kot.

The main idea is not to apply forces to mass-points, or add springs to the body, but to directly change mass-points' positions (and velocity, implicit). First you calculate how much you want to increase/decrease the volume and then you apply the value to all mass-points' normals (determined from the surface).

I plan to release some source-code of this when it will be ready, but if you need it right now, just contact me.

Good place to start at.
Also many helpful comments.

Touches almost everything you will encounter while playing with physics for games (rigid bodies and soft bodies to be more specific).

The best practice is usually to search these forums first. It is worth the time - if you find what you are looking for, you will certainly find many unrelated but very interesting threads:)

I think the title says it all.

I took few interesting ideas from this thesis, but generaly it is very math heavy to allow me to go deeper.

A guy from MollyRocket recorded a video lecture about the GJK algorithm. If you take a paper and review it few times, you shold be able to understand it even if you are not native english speaker.

Also, he mentions few optimizations (or tricks) which other sources don't mention.

Blog by Erin Catto, creator of the Box2D physics engine.

If you for some really strange reason don't own these books, you can at least try out some of these pieces of code. But without explanation, without comments. Snd sometimes there is no code to the article.

In other words - go and buy the books:)

Well known engine used in latests AAA titles. Pretty expensive and also not everyone can get it. Don't know what more to say about it :)

Impulse-based collision response described by Chris Hecker in his game physics articles.
Very straightforward and easy to read.

Probably to best articles to start with when you want to learn something about rigid body dynamics. It does not go into very deep theoretical details, but it should be clear enough to be understood by most of programmers.

Homepage of a famous guy:D

Probably to best articles to start with when you want to learn something about rigid body dynamics. It does not go into very deep theoretical details, but it should be clear enough to be understood by most of programmers.

Highly accurate and very advanced engine filled with features you've ever dreamed of:) Aimed especially at physical simulations, school projects etc. It is probably slower then other engines but haven't tested it yet. If you have enough free time I think it's worth playing with it.
It is free for non-commercial use.

Probably the first paper in which SAP appeared.
But I wouldn't put my hand into a fire for it :)

Theoretical paper about impulses.
Haven't studied it yet.

Few papers about impulse based rigid body dynamics. Had no time and need to read it yet.

A paper which describes "accumulated impulses" below.

My(=hardwire) personal rigid body physics engine I have written for mobile phones.
Doesn't support many fancy features, but it's pretty fast:)

Currently you have to pay small free if you want the full version and use it for your commercial projects.

Fully functional open source engine, so if you want to see how the simulation can be done, it's good source.
However, the objects behave a little bit strange - like a piece of jelly:)

Also, it implements gas-filled bodies described by Maciej Matyka.
Another interesting technique used is shape-matching, which is mostly the reason, why objects behave like a jelly.

If you are making a tile-based jump and run game, definitely take a look at these tutorials!

Extension of original SAP aimed to handle swept collision tests (it means it takes objects' velocities into account).

An introduction to car physics modelling for games.
If you are making a 3D vehicle physics this will be a good start.

Flash presentation explaining why it is good to care about collision detection in games.
Also coveres basic collision detection algorithms for tile-based games.

Nice and easy to understand tutorial with flash ilustrations.

SAT clearly explained including nice flash "movable pictures".
Also coveres poly-circle test.

Disscussion about networked physics.
Few ideas and maybe some source code, too :)

Slides of Gaffer's GDC2008 talk about networked physics.

Seems like something new in the industry because until now I can't remember a game which used physics simulation in multiplayer.

Traditional and accurate engine.
Seems it's not developed anymore.

In this paper you will find very brief and clean summary of all basic things related to rigid body simulation.
Source code included.

Interesting thing in this paper is that it supports nonconvex bodies, because most of the methods used assume all bodies are convex so they can optimize more.

It shows how to detect collision, simulate correct friction and solve stacking problems (using shock propagation).

This approach was implemented in JigLib library.

Still in beta, seems like it is not developed anymore.

One more time I link to these tutorials:)
There is a good performing (in my expiriences) method to find contact points.

Very nice series of tutorials, which are not very detailed, but included source code explains everything:)

Coveres SAT, simple (and fast) impulse collision reaction, swept test and some nice tricks.

Very nice series of tutorials, which are not very detailed, but included source code explains everything:)

Coveres SAT, simple (and fast) impulse collision reaction, swept test and some nice tricks.

Foudn this on Oliii's site. Nice example of creating bodies from rigid circles connected together.

Version optimized for soft bodies. Haven't tried this method.

The title says it all.

Quick summary of three most used Verlet integration methods: "position", "leapfrog", "velocity".

GDC talk by Erwin Coumans about using multi-threading to speed up collision detection and reaction.
It didn't fit to any other category so it's here:)

A programmer friendly approach for simulating both nonviscous and viscous fluids. It containts pseudocode and the math is not heavy.

Special section is devoted to collisions between fluid and rigid objects.

An implementation can be seen at Grant Kot's website.

Source code of this site if you want to use it somewhere.
It's my first bigger PHP project, be warned before you read it :D

Siggraph '97 course.
It needs you to know more math to be able to understand it, however if you do, it makes a lot of things clear.

Maybe the most popular series of articles about car physics.
However, if you are not writing the most sophisticated simulator, you probably don't need it:)

Found few handwritten notes and derivations at his sites:)
Maybe it will help someone.

Simplified explanation of impulse collision reaction for spheres.

This paper is similar to the one from Jakobsen. However, this simulation is more general and also easier to control.

They use explicit integrator, but mixed with Verlet. Also they use explicit velocity (instead of "last_pos") which allows user to manipulate velocity.
Collision response and all constraints (both equality and inequality) are solved using the same solver, which make it more general.

Another interesting thing is cooperation with rigid bodies - in their examples they simulated rigid rocks connected together via deformable cloth - really NEXT-GEN :D

A math light article suited well for programmers who want to start playing with fluids.

Source code included!

Basic idea of this approach is to apply force to all mass-points (along their surface normal) to keep them from collapsing.
Objects then behave like if they were filled with gas.

Another implementation of this method can be seen in JelloPhysics library.

This is not a "classical" method. However, if you need to query objects about their neighbourhood (and in broad phase you do:)) and your objects are moving very fast, you might try this out.

Links and resources they gathered while developing their car simulator.

Casting a ray through the data structures of the SAP is not that easy. If you need faster solution than bruteforce, take a look at this.

...is a book by Christer Ericsson.
It's worth the money and a really good start.

Haven't read. Haven't tried YET.

A famous article about grid based fluid simulations using Navier-Stokes equations. This method was improved in Practical Fluid Mechanics.

This is my Bachelor's Degree work about soft body simulation optimized for mobile phones. Unfortunately, it is in czech only.

However, you can visit the project's website to download the library for free!

Abstract: In the presented work I discuss possible options of implementing a~physical simulation that can be run on today's mobile phones. I describe several approaches from which I choose one and discuss it in more depth. Next, I talk about general methods of optimizing programs targeted to mobile phones and how they apply to the implemented physical simulation. Finally, I show a very simple game which demonstrates the power of the simulator and it's usability in praxis.

Part from a Siggraph '97 course.
Advanced math needed, however it is explained very clearly!

Part of a Siggraph '97 course.
It's about rigid body collision in general, however for broadphase they use SAP.

A part from a Siggraph '97 course.
Explained in a very straightforward way, I had no problems understanding it.
Sample source code provided.

Equations for 2nd and 4th order Runge-Kutta.

As explained by Baffer.

This site is loaded with large number of articles about fluid simulations as well as soft body physics.

This site is loaded with large number of articles about fluid simulations as well as soft body physics.

Nice description. Solves some practical issues, too.
The method described is implemented in Box2D.

Haven't read, haven't tried.

The title says it all.

One similar algorithm of shape matching is implemented in JelloPhysics engine.
This might give a more theoretical explanation of what it does.

Detailed description and comparison of most used integrators.

I have no expiriences with this one.
Free for non-commercial use.

Found this topic.
If you don't have much time to read through literature, you can try this out, but I am not sure how it will perform.

An attempt to simulate smoke using Navier-Stokes.

Article in the Game Programming Gems II book.
If you still don't have it -> go and buy it!

Nice example of points and springs written in C#. However, the code is not very clean and there are NO comments.

How to deal with stability(numerical and physical) issues when doing computer simulation.
More like an introduction to the problem.

Mick West used springs inside the body to keep the volume of the blob.
I must say his results are really nice. However if you have to decrease FPS or you can't afford too many mass-points and springs, this might not be good solution.
Also, you will not be able to completely remove instability issues IMHO (the body can deformate and won't be able to get back to the initial state).

He provides a source code, but I must say it's a real mess :)

If you need more accurate tires (not in 2D probably), you can try out this link.

In this paper they use the Verlet integrator for rigid body simulations...it's not a common approach today despite being very stable even when using stiff springs because of problems the Verlet integrator has.

What does the integrator do?