2D Rigid Body Collision Resolution

Hey everyone, author here!<p>To give some context, this is only part one in a series of blog posts I plan on writing about rigid body physics.<p>The post is aimed at people like myself, who aren&#x27;t game devs and don&#x27;t necessarily have a strong math background. Which is why I spend so much time explaining concepts that would appear almost trivial to someone who has experience in this area.<p>Happy to answer any questions you might have.

Oh! Look, a well-researched, deeply-explained, and <i>interactive</i> post.<p>Honestly, when I initially read the domain name and noticed the TLD is &quot;<i>.ski</i>&quot; I was thinking it is from the author who wrote about <i>Mecanical Watch</i> [1] and other cool stuff.. it turned out to be a totally different one but of similar quality. What&#x27;s the secret sauce behind this &quot;<i>.ski</i>&quot; TLD :)<p>___________________<p>1. <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=31261533">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=31261533</a>

One side project I am working on right now is a 2d space shooter I am developing with my son. The idea is to have top down look, have each player control some kind of ship and fly in an enclosed area filled with space debris and shot opponents. An important aspect of this game is that the space debris can be moved around the arena and used creatively to capture opponents, prevent them from achieving their goals, etc.<p>As part of the project I was thinking we will skip game engine altogether because I wanted to teach my son a bit more about how to structure the application, etc. I thought in future we would use a ready game engine but at least once we would go through the exercise of implementing everything.<p>Everything was fine until we approached the problem of collision detection and handling. That&#x27;s when things went downhill pretty quickly. Even with my theoretical math background I was soon consumed with just enormous amount of corner cases and finally decided to relent and use Box2d for this.<p>I am not a professional game developer, but I have over 20 years of development experience + math background and I still made the mistake of underestimating the problem. It really seems easy problem when you state it and just becomes exponentially more and more complex as you start digging into details.

I always enjoyed the explanation from the N game: <a href="https:&#x2F;&#x2F;www.metanetsoftware.com&#x2F;technique&#x2F;tutorialA.html" rel="nofollow">https:&#x2F;&#x2F;www.metanetsoftware.com&#x2F;technique&#x2F;tutorialA.html</a><p>Back when flash was everywhere.

I had fun building a TypeScript demo about this topic, involving balls that can bounce and collide. I learned a lot.<p>Code: <a href="https:&#x2F;&#x2F;github.com&#x2F;vandrieu&#x2F;canvas-bouncing-ball">https:&#x2F;&#x2F;github.com&#x2F;vandrieu&#x2F;canvas-bouncing-ball</a> (the collision logic is in src&#x2F;collision.ts)<p>Result&#x2F;Demo: <a href="https:&#x2F;&#x2F;vandrieu.github.io&#x2F;canvas-bouncing-ball&#x2F;" rel="nofollow">https:&#x2F;&#x2F;vandrieu.github.io&#x2F;canvas-bouncing-ball&#x2F;</a>

If you want to go further and go for rigid body dynamics and constraint, I found that series of blog post very useful: <a href="https:&#x2F;&#x2F;www.toptal.com&#x2F;game&#x2F;video-game-physics-part-i-an-introduction-to-rigid-body-dynamics" rel="nofollow">https:&#x2F;&#x2F;www.toptal.com&#x2F;game&#x2F;video-game-physics-part-i-an-int...</a>

Collisions are violations of the pairwise non-intersection constraint between bodies. Collision forces are Lagrange multipliers of these constraints. Collision normals are the (normalized) partial derivatives of the constraint function wrt one of the body&#x27;s configurations.

This is really cool! Love the explanations, the interactions, and especially the friendly tone of voice of the article. Looking forward to the ones following.

Making a 2d rigid-body physics engine is a really fun project. I made one myself in javascript before learning about linear algebra. And I dug deep into the maths to get it working. Despite months of work, I barely scratched the surface beyond the widely known basics.<p>Making a stable engine where objects don&#x27;t compress into one another or jitter is a rabbit hole without a bottom that even the most math-heavy articles I could find rarely touched.<p>I used a series of old articles by Christ Hecker to understand the maths myself. <a href="http:&#x2F;&#x2F;www.chrishecker.com&#x2F;Rigid_Body_Dynamics" rel="nofollow">http:&#x2F;&#x2F;www.chrishecker.com&#x2F;Rigid_Body_Dynamics</a>

To learn JS I started with canvas, and without any game dev experience, made a couple of cute little browser games. One is a galaga clone that, for the most part, works OK. The hard part is the projectile collisions. Instead of taking the position of your bullet now, and where it would be in the next time step, and seeing if it would intersect with the enemy hitboxes taken in the same way, I _only_ checked on the current timestep, which means your bullets can magically go around the enemies! Silly stuff. Maybe some day I&#x27;ll go back and fix it.

Wow, perfect timing. Some days ago I started to get interested in this, particularly in circle collisions. Keep it up, looking forward for the rest of the posts.

You probably don’t want rigid body collisions in most game mechanics. Player controllers, npc logic, etc. are hand crafted most of the time.

This is great. This reminds me of Chris Hecker&#x27;s Rigid Body Dynamics series from GDMag&#x2F;Gamasutra that I read (checks watch) almost 30 years ago! This is the classic&#x2F;canonical set of articles.<p><a href="https:&#x2F;&#x2F;chrishecker.com&#x2F;Rigid_Body_Dynamics" rel="nofollow">https:&#x2F;&#x2F;chrishecker.com&#x2F;Rigid_Body_Dynamics</a>

If you constrain your geometry to a tesselation, it gets much more precise, simple and fast.<p>Like those old atari games where everything was little square tiles &#x2F; pixels.<p>But little squares aren&#x27;t the most expressive geometry.<p>How about kisrhombille?<p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Kisrhombille" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Kisrhombille</a>

Huh. I always remembered it as being <i>s</i> because of French <i>sentier</i>, meaning &quot;path&quot;.<p>Besides that... Beautiful page, well done!

Guess this is a Shameless plug but I wrote an interesting program over 12 years ago using even then very old three Js which is not quite the metal but much less abstract than today&#x27;s tools. I&#x27;m always amazed when I check it and it&#x27;s still running<p><a href="http:&#x2F;&#x2F;busyboxes.org" rel="nofollow">http:&#x2F;&#x2F;busyboxes.org</a>

To dredge up a related oldie-but-goodie memory of blog posts:<p><a href="https:&#x2F;&#x2F;gafferongames.com&#x2F;categories&#x2F;game-physics&#x2F;" rel="nofollow">https:&#x2F;&#x2F;gafferongames.com&#x2F;categories&#x2F;game-physics&#x2F;</a>

I wish we had had this type of explanation in algebra on what to do with dot products.

My own attempts at 3d games failed to get good sweeping polygon polygon collision to work. IIRC I found one good demo video of a programmer demonstrating it on youtube but no code or articles or anything.

I do wish this kept going and went &quot;and as a last step, we need to add in torque&quot; because pretty much everyone stops at regular force vectors, but torque transfer is so ridiculously important.

Young high school and university students aspiring to become game designers should give some focus on their algebra, trigonometry and geometry :-)

Thanks! This will be something I check with my kid in highschool!

I know this post is focused on collision resolution, but I was still a little disappointed to see collision detection handwaved away. In my experience that&#x27;s where the real headscratchers are.

awesome article glad to read

The way this article is written with small simulations throughout the page and word highlights was reminding me of <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;</a> and then I noticed the domain name. It is very similar too <a href="https:&#x2F;&#x2F;www.sassnow.ski&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.sassnow.ski&#x2F;</a><p>Couldn&#x27;t be happier seeing more people going to same depths (or heights) to explain things to people. Will be looking forward to more articles like this as this just the very first one.