Building a Physics Engine with C++ and Simulating Machines

I talk about the basics of physics engine design and the theory behind rigid body constraint solvers. Here are all the resources you'll need to build a physics engine that is similar to the one I show in the video:
Source code of my physics engine:
github.com/ange-yaghi/simple-...
Euler method for solving differential equations:
en.wikipedia.org/wiki/Euler_m...
Runge-Kutta method for solving differential equations:
en.wikipedia.org/wiki/Runge%E...
Physically Based Modeling: Principles and Practice
www.cs.cmu.edu/~baraff/sigcour...
Source code of my real-time video encoder:
github.com/ange-yaghi/direct-...
Source code of my game engine:
github.com/ange-yaghi/delta-s...
#physics #simulation #programming
Check out my GitHub profile!
github.com/ange-yaghi
Join my Discord!
/ discord
Follow me on Instagram!
/ ange.the.great
If you like my work and would like to support me, consider donating!
ko-fi.com/angethegreat
Thanks for watching!

[@itskittyme]

"i wrote this advanced physics simulator" "oh and then i ran into some problems with making the video" "thus i quickly built my own screen capturing software which works better than this giant open source program that's been around since 2012" okay

[@abeecee]

if this is my competition looking for swe jobs, I might as well give up now lmao

[@deathTurgenev]

Then proceeds to say, sorry the code isn't optimized, I'm not an expert

[@EmergencyTemporalShift]

To be fair, taking a bunch of screenshots is easier than physics

[@HAWXLEADER]

Getting a raw image sequence out of your renderer is NOT "better" than this giant open source thing. It just does 1 thing and does it really well.

[@atypicalambience3487]

He uses ffmpeg which does all the hard work for you. You can literally feed it image files and it will just make it into a video.

[@theDemong0d]

No sleeping here, there is a huge lack of technical content on youtube at this level, these videos are killer. Keep it up. Would love to see the deep-dive on your fluid sims for your engine project.

[@Alexander_Sannikov]

I don't think you actually realize how much effort goes into creating a video like this. "At this level" there's extremely little content on the entire youtube.

[@theDemong0d]

@@Alexander_Sannikov I'm not sure exactly how to interpret this, but I never said it was easy. Also, that is not strictly true since there is an immense amount of highly technical content on youtube, just not in the realm of individuals writing interesting things from scratch, and not laid out to present novel experiments, Sebastian Lague-style.

[@Alexander_Sannikov]

@@theDemong0d what I mean is that 99% of sebastian league style content requires much less knowledge and effort than a video like this. UPD nvm, I think I read your original post wrong. I think I read "huge lack" as "huge block", or something like that.

[@RodyDavis]

+1000

[@dnull]

well, unfortunately, views explain why there's no much tech-focused game dev vids on youtube.

[@JubaProductionsStudios]

"OBS was making me nuts, so I made my own screen recorder" this guy is a legend haha

[@magmacodes9143]

You can do too. FFMPEG has been a fairly straightforward framework for making small screen recorders for a long time now.

[@vedantkanoujia]

@@magmacodes9143 ffmpeg is most vulnerable due to multiple support of library

[@dudearlo]

xD

[@XENON2028]

@@vedantkanoujia what

[@jakosloth]

Man's living my dream lol

[@AngeTheGreat]

Useful or pointless video? You tell me :D Thanks for watching 💪

[@puppergump4117]

Very useful, I will surely use it

[@Dicklesberg]

All your stuff is incredible. You’re going to have a million subs in the next 2 years if you keep it up. My advice is to not abandon your long form content in favor of shorts. Your issue earlier with the car rendering video was that you didn’t have critical mass of viewership. Now that your channel is blowing up, a long term project requiring a lot of work will likely be rewarded even more.

[@Mocorn]

I know exactly zero about programming and still watched the whole thing. Physics are fundamentally interesting stuff :)

[@isuckatthisgame]

For me, somewhat useless now, but very prompting to revise my old, long-forgotten knowledge and to learn even more.

[@user-yy3ki9rl6i]

im learning modeling and simulations next semester and this pretty much hypes me up! thanks for the content man, you just got a new sub.

[@lukewellcash]

Your videos should seriously get more attention then they do. Awesome work!

[@AngeTheGreat]

Thank you! As long as there are people out there that like my stuff and find it useful, I'm good ✌

[@marilynlucas5128]

@@AngeTheGreat You're truly great.

[@Alexander_Sannikov]

A note on implementation: your RK solver is very tightly coupled with the design of the system you're integrating. Usually it's best to try to decouple the integrator from the system itself and implement it more generically. For ordinary ODE's you just need a function that calculates a vector of derivatives from a vector of coordinates, and that's all your integrator needs. And your physics engine can _index_ into those arrays to access coordinates of any given rigid body.

[@AngeTheGreat]

Good idea! Might refactor that part, thanks for the suggestion

[@HilbertXVI]

Ordinary ordinary differential equations

[@revealingfacts4all]

He's also using public virtuals which tells me he's not very knowledgeable of c++

[@AngeTheGreat]

@@revealingfacts4all I don't claim to know it all and I like to assume that I know nothing anyway. What do you recommend I change?

[@Alexander_Sannikov]

@@revealingfacts4all I am curious as well as to why you think using public virtual functions somehow reflects his lack of C++ knowledge.

[@Cathal7707]

This is incredible. Constraint solving is stuff you do early on in an engineering degree but I never cared for it because I was always into the more computational stuff. Seeing you come at this from the computational side first has given me a whole new perspective.

[@grevel1376]

You got a new subscriber. I arrived to your channel by a reddit post with a link to your engine simulation video, and I guess now I'm binge watching all your videos. Amazing work man.

[@opti12]

All this goes far over my head but it's so impressive to see someone make things like this and to share it online, even creating a screenrecorder in the meantime. Crazy!

[@thierrybeaulieu4403]

I've studied physics for 2 years and computer science for another 3 years. I'm already thought of doing something like that, but it's very impressive to see how well you've done it. There are so many layers of complexity to what you're showing

[@scremeo8522]

As I'm currently preparing for an upcoming exam in numerical analysis, I find it interesting to see this really cool application of most of the methods I've learned! I'd like to write my own physics-engine right now, if I didn't have to study at the moment 😅

[@willi00willi]

I just got recommended this video today, and I am blown away! Can't wait to explore more of your channel's content

[@basile5490]

Just discovered your channel, and i see a lot of advanced, neat projects that really sparks my interest. This physics engine is very cool ! Im impressed to see that you make all that in C++, it genuinely makes me want to make similar stuff on a low level. That's really inspiring (even the nerdy mathematical details ! Along with the sources in the descriptions, those are the crunchy bit for me). Keeps up the awesome work !

[@AngeTheGreat]

Welcome to the channel! I try to work on projects that really challenge me and I'm glad that you enjoy my content. Hopefully my channel continues to help/inspire you in your software journey. Thanks for watching!

[@Ahsan_Fazal]

You're my new favorite KZbin content creator. WOW! This level of knowledge and expertise is something I rarely see on KZbin. KEEP UP THE GOOD WORK!!!

[@Alphaa101]

Where you are from?

[@freevbucksinthehoodprankgo4993]

I really enjoy watching your videos and trying to understand everything. I find that there is something satisfying in the way you explain things. Keep up the amazing work!

[@jojodi]

Awesome stuff! Highly recommend you look into iterative techniques (Gauss-Seidel, or more complex Conjugate Gradient). They are probably in fact easier to implement than the Gaussian Elimination, and you can terminate iterative approaches when the error is low enough. Convergence rates are almost always related to conditioning of the system being solved, which will depend on what combination of constraints you have in your simulation. Note that isn't worse than the elimination case: poor conditioning also causes numerical instability in that algorithm as well.

[@AngeTheGreat]

Excellent suggestion, you definitely know your stuff! I actually did implement Gauss-Seidel but I didn't mention it in the video because I didn't want to confuse people haha... But you're right that iterative approaches are great. Next step will be to implement Conjugate Gradient since that'll be faster and also slightly more robust (for redundant constraints, etc.). Thanks for watching and thanks for the suggestion!

[@GeorgeTsiros]

@@AngeTheGreat i saw no Gauss in the video, in fact, I don't think I saw any weapon of _any_ kind!

[@GeorgeTsiros]

oooh. nice.

[@chriswalsh5925]

Hey @brandon, what do you think of LevenBerg-Marquadt (probably mis-spelled!). I have read several papers recently where they use that for solving systems (not physics) as it is supposed to be very fast and more 'optimisable', removing zeros etc. Wondering if you thought it would be good for a physics engine?

[@GeorgeTsiros]

@@chriswalsh5925 there is only one way to find out... code it and test it! :> There _should_ be implementations online, already.

[@IONYVDFC]

Interesting to see someone reviving the (at least my) experience of writing a physics engine. It was really a brain crushing journey for me to do this in the 90' with less accuracy, much less computing power, my very immature knowledge of math, let alone internet resources on this topic. But I have strong memories indeed from my eureka moment after real-time simulating a cloth, and a few weeks later seeing the same idea rendered on a Silicon Graphics cluster on a computer fair in Brussels.

[@jroseme]

Super interesting and nice visuals to boot. It’s a relief to see an actual software application of this linear algebra stuff I’m learning.

[@Skeffles]

These simulations look awesome! Can't wait to hear about the project you're making this for.

[@AngeTheGreat]

Thank you! The follow-up should be out within the next few weeks :)

[@davidmc971]

KZbin algorithm please! Your content is an absolute gold mine of well explained experience in technical topics!

[@gaydogs]

man ur videos are so well made, i cant get enough of them

[@actuallydaneel]

every vid you make is just such a joy to watch, from the content to the editing it's just sublime. sincerely, good job.

[@AngeTheGreat]

Thank you, that means a lot to me! Glad you enjoyed it and hopefully I'll put out videos more consistently this year :)

[@actuallydaneel]

@@AngeTheGreat honestly, consistency isn't something i care about. take it at your own time and i'll enjoy whatever you put out, whenever you put it out.

[@mani_mincraft]

Honestly, this video is highly inspirational. Heck, I have even started studying derivatives and I hope to begin learning force constraints (like you were talking about in your video) next. thank you for being so inspiring.

[@Jamie-il1qu]

Man, such a good video, I found it genuinely very exciting. For me, this is like the idealized form of Nova, thanks for making it!

[@tamp1o]

Holy hell this is one of the greatest videos I have seen, especially for your sub count. These are better than my uni degree!

[@physicist1994]

One of the most underrated channels on youtube. Subscribed immediately with notifications on. Best wishes.

[@PathikritGhosh007]

This is bloody brilliant, mate. Awesome video. Going through your github right now. Was looking to learn how to make something as complex as a physics engine, and this came in super handy.

[@dragonminz602]

Absolutly loved the video. Honestly it is great to have some technical explanation. I have been writing some simple physics engines and now i know how to expand them. Many thanks

[@coopercone4293]

Love this video. You had a great balance between explaining the math deep enough to understand the video, but not too deep to the point where it became a math video and not a physics engine video. I also agree with others that there's a lack of high-quality and highly technical content. I will definitely be going through some of your other videos.

[@syntropy3020]

This is epic. Well done. Look forward to seeing more on this.

[@MrChaluliss]

Yo this is awesome. I know nothing about simulating physics, and am just now getting through the necessary maths and CS skills, so seeing it happen and actually wrapping my head around things is really amazing. Thanks for the cool video!

[@vintyprod]

Oh god that first animation you showed triggered my rigid body dynamics ptsd No but this video is actual gold. Thank you for making this. I’m so glad I found it. Also, thank you for including some of the math.

[@willianvinagre3338]

That's an amazing project! I loved the video, even though I couldn't understand the mathematical stuff, it was still entertaining. Great job with your content, I think you should get more attention with how good your videos are made!

[@AngeTheGreat]

Thank you! Don't worry about not understanding the math immediately, I didn't either. It's one of those things where I had to really sit down and study it seriously before I understood. It's also why I didn't talk about it much in the video 😂

[@henrydane6702]

This was absolutely incredible -- keep it up!

[@JoBot__]

This is pretty much my favorite kind of content.

[@TheGiantHog]

I can’t believe how you just glossed over some of the incredible work you did just to make this, easy sub man you’re killing it

[@chriswalsh5925]

excellent, I remember trying to understand that witkin paper like 20 years ago, eventually gave up and stuck with rigid body physics for the project I was on. Nice to see someone actually got it working! Great video!

[@roothacker4404]

Really incredible that these type of information is available for free!

[@AlexFlorias]

In the best way you’re content reminds me of those calming sessions in college studying on khan academy. Some things go over my head but your approach is so cool to watch, your content is criminally slept on!’

[@rafaellisboa8493]

awesome video, I LOVE the mathematical explanations, differential equations are my passion.

[@theastuteangler]

probably the best video on programming I've seen

[@stupidguy97]

Amazing quality. Subbed!

[@miroslavdimitrov5451]

Great work Ange. Keep it up, definitely a useful video!

[@AngeTheGreat]

Thanks Miro, glad it was useful to you and thanks for watching!

[@travezripley]

This is amazing, This video and the Engine video… Pretty much blew my mind.

[@ir3turnz675]

You deserve so much more subs keep it up man

[@resolversoftware5088]

Man this is tremendous!! It will be great if you make some tutorial series explaining in detail how build similar engine at least on basic level! Amazing information on your channel!

[@deotexh]

Such a genius, ahhhhh, I'll probably never get there if I wanted to Good job for your hard work to have gotten to that point!

[@marcus9157]

Awesome high quality video and explanation wise, I hope to see more content like this :)

[@AngeTheGreat]

Thank you! There will definitely be more content like this in the future :)

[@lorincszabo7411]

this was the most informative video on the subject i've ever seen :) triple thumbs up

[@MrAman47]

Great video, hope to see more of you!

[@Alexander_Sannikov]

Some constraints (such as rolling constraint, universal joint, etc) can be represented both as an extra body with simpler constraint attached to the bodies that you want to connect to start with, or with a more involved jacobian and no extra body. I recommend initially not wasting time implementing complex jacobians for joints that are not experiencing heavy load and implement them using just an extra body. If/when they become a problem, you can replace the extra body with a page of code for its jacobian, but they must converge to the same exact result in the limit of the extra body having zero mass.

[@AngeTheGreat]

Oh I see, might look into that. I think I might have gotten carried away with the rolling constraint, I really wanted to make it work for some reason lol

[@thomascromwell6840]

I'm amazed. I aspire to this level of work.

[@kloude_a4528]

awesome content! gets me inspire in a big way keep on keeping on!)

[@DBFIU]

Keep doing good work Ange, this is what youtube was made for.

[@AngeTheGreat]

Thanks 🙏

[@CurtisHamilton101]

Really cool to see the math behind it all.

[@krunkle5136]

Writing your own screen capture program? Legendary stuff.

[@hicham2668]

Working on my 3D engine in C++, this level of results was always my dream. Thank you for sharing.

[@fabianmuhlberger6153]

Wow, this would make a fantastic tool to teach technical mechanics. I would have loved to have an animation showing me this when learning dynamic

[@deathTurgenev]

Great video, please do more content like this, it's entertaining and inspirational

[@ronnylandsverk5037]

This is an awesome video for introducing computational methods in dynamics ❤

[@myingar20]

Very good and educational video! Thumbs up.

[@mastershooter64]

4:46 absolute madlad!! obs wasn't working properly and he just became thanos and was like "Fine, I'll do it myself" lmao

[@TheDoh007]

This is awesome! I'd love to see further work on this, particularly interested in magnets (and integrating electric component simulation if that's not too crazy)

[@garrettjensen4817]

I think 1 of 3 people who got excited when he talked about the Runge Kutta ODE method. One of the best imo

[@royhouwayek7892]

commenting to boost engagement because wow this is awesome

[@Carlos-kh5qu]

really great stuff, i may use it on a project eventually

[@Tantandev]

This was super entertaining! really cool project

[@AngeTheGreat]

Thank you! I've seen some of your videos too and love your work.

[@MrMitdac01]

Awesome. I love your explain and its great.

[@JimboMack]

Thanks a lot, found your channel today and now im in a C++ rabbit hole for the next 48 hours at least 😂 great video, with down to earth rational explanations 👌

[@albertlert]

Loved it! Thank you.

[@lucaslugao]

Really nice work, Ange. I wonder if you could get more performance by using hardware optimized solvers. I really like analytical mechanics and this is pure gold, keep going :)

[@neutron417]

The perfect intersection of Physics, Computer Science and Math

[@klibe]

the most i've done is remade 3d wireframe projection, and rotation of the camera is still not working, and you can see behind you, etc.. this is impressive and has blow my mind

[@Aethier-lostwoods]

I'm convinced you only uploaded this as a flex. And it worked.

[@teachd.marshal1066]

Long time no see, i've been waiting for ur video since i discovered this channel

[@AngeTheGreat]

Your wait is over! Thanks for watching 🙏

[@sripradpotukuchi9415]

really cool engine! the sims with the rolling constraint look awesome, so the tedious math was totally worth it 😅 physics aside, i really loved the visuals. great job!

[@AngeTheGreat]

I knew as soon as I started this project that rolling constraints were gonna be a thing, no matter how painful it was haha... Thanks for watching and glad you enjoyed it!

[@georgichalakov6727]

You really know what you are doing

[@t3v727]

I finally had some time to watch the video as well. You really made some cool stuff Ange. I realized that my maths got a bit rusty though but you made me excited about trying something into the direction of physics in games as well. Maybe it would be also a good idea to make a maths course for (game/graphics) programmers, too.

[@AngeTheGreat]

The math looks a bit scary but it actually isn't that bad! I'm excited to get flexed on by your next physics project lol. Also I might look into your idea for making a video about 3D math. Thanks for watching!

[@MrLP10o]

Dude, elaborate on the math part! It is nice to see the theory I've learned in University applied to create a physics engine! A video on the math explanation would be awesome

[@graham4133]

damn, seriously impressive stuff

[@fiflax4473]

installed quickly, thanks a lot

[@bluebaldwin]

Dude every time I watch your videos, I am amazed! What have you studied to learn so much? Very cool vid as always 👍🤙

[@AngeTheGreat]

Thank you and thanks for watching! Well I studied computer engineering in school but I've learned most of what I know from studying on my own. Maybe I just have too much time on my hands 😅

[@zgrpro]

this is literally insane!

[@DctrBread]

great video, i was looking into setting up a simulated double pendulum as a learning exercise, but after thinking it through for a bit i realized i would need to know more math.

[@lylesloth1275]

subscribed, epic guy, likes learning things, good at sharing things, good at explaining, epic, video liked.

[@David-ng9qh]

"Oh yeah by the wa. On a completely unrelated sidenote, OBS sucks, so I made my own video capture software." legend

[@novidtoshow]

Great work! Just a small nit, here... There are many ways to discretise the vector system: dx/dt = f(x,t) 1 - LHS: -------------- First, we can discretise the lefthand-side using the base definition of the derivative: dx/dt = (x(t+dt) - x(t) )/dt This one-side difference is the part they call "Euler". It's first order accurate, with errors being proportional to dt^2. 2 - RHS: -------------- Where in time you choose to evaluate the RHS is also important. The Forward-Euler method evaluates the RHS at t=t, thus: (x(t+dt) - x(t))/dt = f(x,t)

[@seesoftware]

What a madlad, obs didnt work, so he made his own version :D

[@spyrex3988]

dawg u are so smart it is insane

[@LucasDimoveo]

More videos like this please!

[@isaacenquist]

You can try using a symplectic integrator such as velocity verlet to increase numerical stability so that the energy/system does not diverge over time.

[@j.j.maverick9252]

very useful and really clear explanations. I think you judged the line between enough explanation vs too much maths exactly correct (for me anyhow!)

[@AngeTheGreat]

I spent a lot of time trying to determine where to draw that line haha... I'm glad that I got it right for at least some people, thanks a lot for watching and commenting!

[@Selbstzensur]

Brilliant Video, thanks for sharing. This is very inspiring.

[@ahmedsaadsabit1749]

look i am a youtube viewer since 2012, and my way of selecting which channel to subscribe is really anything but lenient. But this is a rare occasion when just by watching a few seconds of the video I've hit subscribe. NICE WORK DUDE FUCKING NICE HOW DO YOU DO IT

[@Daekanoid]

When you talked about the difficulty of differentiating the equations without making small mistakes, i got applied mechanics flashbacks. Oh god the hours I've spent trying to find the mistake only to assess that the problem was a misplaced exponent

[@kdashi5747]

I'd love to see a video about your Vim setup!

[@alfonsodonotsi6691]

This is amazing!!!

[@tensevo]

excellent, it would be great to see you tackle open source CAD for engineers. Thank you.

[@MScienceCat2851]

As someone who is learning C++ and is bad at math, this video is really is really giving me motiivation to continue

[@sanderbos4243]

This is epic, and the video encoder program you wrote on the side is also very useful! I am sure you know about the Phun/Algoodoo physics simulation program, man I spent so many hours in there. If you make a game that uses physics I'd love to see the same kind of features in there, like different shapes, gears & water!

[@AngeTheGreat]

Thank you! Not gonna lie, my encoder library is probably the only project I've made that could actually be useful to people lol... I can think of a lot of uses for it, especially for content creators. Regarding the use of this physics engine for a game, that may or may not already be happening... There will be a few follow-ups to this video which I'm pretty excited about. Thanks for watching!

[@sanderbos4243]

@@AngeTheGreat Your encoder library reminded me of .kkapture, you should look it up! It was written by the people behind the famous .kkrieger game demo. Look up "kkrieger: Making an Impossible FPS | Nostalgia Nerd" if you haven't seen that yet!