A solid reason for doing your own physics and reinventing the wheel is to build a nice understanding before you throw it all away and use a more functional physics library where we take for granted some of the things that are possible with it.
Furthermore, in order to understand how to make a physics engine, I recommend looking at and using pre-existing engines (like Box2D for example) to see how they solve certain problems.
Agreed! It requires a lot of math to even do something simple like a ball rolling down a slope. In most cases it's better to use a physics library and the most popular 2D physics sim, used in games like Limbo and Angry Birds, is called Box2D. p5play uses a JS implementation of it which is superior to matter.js and also easier to use.
Nice one! For your "overlap correction", I think the proper way to go is to get the particles' relative velocities along the impact vector. Based on this relative velocity and the magnitude of the overlap, you can then compute the time dt by which your simulation overshot the actual collision due to finite framerates, backpropagate the particles by this time step, then update the velocities, and move them forward in time by dt again.
Now shut off the wall bouncing, make the particles wrap around, and add a spaceship that lets you shoot the particles. Pew Pew Pew! Asteroids, with collision physics!
The next step: Adding the elastic bodies! Let's add some deformation upon bouncing! ;-))) As a mechanical engineer and amateur programmer, I have really enjoyed this video.
@@AmeeliaK Yeah, that's the silliness of the terminology. Rigid bodies make elastic collisions, while elastic bodies make inelastic collisions. Not to mention the plasticity.
That's what I thought he was going to do at first. You could get a pretty good approximation by simply having them accelerate away from each other when they overlap, and the amount of acceleration would be a function of the distance between them relative to the sum of their radii. Drawing it would be a bit harder, but you could just remove the curves where they overlap and draw a straight chord to show that they're mashed together.
@@oldadajbych8123 not quite. Rigid bodies can do elastic and inelastic collisions (and everything in between), and soft bodies can do the same. The elasticity of a collision is the ability for the objects to return to their original shape. For rigid bodies, this happens on the microscopic level and at a very small time interval.
Just more, please! Whatever you've got the time and energy for. I love your videos; particularly the live stream VODs, because I enjoy watching the entire process (no pun intended) warts and all. Finally, thank you so much for all your hard work and energy fostering such a wonderfully inclusive instructive community!! ❤
one of the best videos actually, I tried to do the math like 8 years ago without using linear algebra (I did not know why linear algebra exists back then). I did the simulation using C# GDX library I believe, and that definitely impacted my choice to be an engineer.
I wish Daniel would have been around when I started to learn coding. Would love to see you do a follow up with inelastic collisions (including some coefficient of friction/heat).
I remember doing this for 'fun' in the late 90's, with *_NO_* idea of the math beforehand. I did rather well, in my own opinion, but could only really handle velocities where objects couldnt pass 'through' each other between frames.
Objects passing through each other sounds like a fascinating problem to solve. Assuming that there was a good solution, it makes me wonder how far you could raise ∆t before it breaks. I mean, you might have had more than one collision between frames. It's a real head scratcher.
@@nagualdesign Never ended up solving it, but I considered checking whether they were moving towards each other both before and after adding their velocity vectors - if they were getting closer before, and further away after, then the closest point wouldve been somewhere 'during' the frame, but trying to figure out exactly where and when..... and then I got a new job, and significantly less free time.
@TheCodingTrain Yes it took a long time, and it was so fun to see how JavaScript was before ES6, you struggling with if/else statements and arrow functions hahaha I didn't know that it was you that made the first Nature of Code book! I read that while I was learning about JS a few years ago, and today I'm a web developer!
As I tried to make a breakout game, I could never figure out how the ball should bounce after it hits something. You have solved my several decade old question. Thank you. Love the show!
It requires a lot of math to even do something simple like a ball rolling down a slope. In most cases it's better to use a physics library and the most popular 2D physics sim, used in games like Limbo and Angry Birds, is called Box2D. p5play uses a JS implementation of it which is superior to matter.js and also easier to use.
One of the things I love the most about the code train is exactly solving problems with pure vanilla js, It's most important to learn the strategies, calculations and ideas behind the simulations so to make good and confident usage of ready solutions, you'll have a much deeper and better understanding allowing you to use the libraries more effectively, and when you face a problem that the library doesn't solve, you're equipped with the base knowledge to explore the solution yourself... Video with no special library are the best ones
This is simply amazing. I'm definitely impressed by how you developed the entire collision detection from scratch. The explanations were clear, and the walk around the code was pretty detailed. Good job!
bought the book immediately -- you manage to explain complex problems with fun and humility like nobody else, truly refreshing! you make it look easy/approachable and this requires a deep understanding of the problem and a lot of talent & work. TL;DR = thank you!
I was working on EXACTLY this, and I got stuck about 1 week ago. Decided to take a break, cause I didn't really want to go over elastic and plastic (non-elastic) high school theory. LOL. now this is here, so I guess it's time go get back to the project... Thank you, Daniel!
Watching this after I made a 3D rigid body physics engine. I remember the days when I first made this, glad to see you're making it easy and fun for beginners!
Haven't been keeping up with the community for a bit because of studies. It's good to see a coding challenge after a bit! I'm excited about the Nature of Code launch. Hopefully it becomes available in India soon. Cheers Dan!
Very cool that you did this video! A few months ago, inspired by some of your other videos, I tried to solve exactly this problem. Without the math education, I never quite got it right. I ended up with some very odd results. I'm five minutes into the video, I've got my old attempt that I wrote in Lua opened up, and I'm excited to see where I went wrong! Also I pre-ordered your book months ago! I'm a big fan!
Erin Catto, the guy behind the Box2d physics library, posted a cool video "Solver2d Results" where he puts 8 different solvers through a variety of physics simulation tests.
The better solution to collision detection of moving circles is to extend the circle into a 3D sheared cylinder and then you solve for the time when the two cylinders touch. A hint is find the distance function between the two circles in motion, then find a solution for when the distance equals the two radii added together, another hint is you can use the squared distance and the sum of the radii squared (r1+r2)², an equation for the diatance could be d(t) = ||(p1 + v1t) - (p2 + v2t)||
Your end result immediately made me think of Brownian Motion. I know it's not the same thing but, adding a little random walking to the particles might be cool. 🤙🏻
Hey Dan, nice vídeo as always. I am glad you are back, I love your videos and they make me happy! I am looking forward for the new The Nature of Code. I did all chapters of the old one, it was a great experience! I also have the "Learning Processing" book, another great book!
27:00 I agree the correction has to be done. The system can enter physically invalid states because of finite time steps and the overlap correction resets the system to the last valid state which was traversed during the last state transition
Your videos are fascinating to me. Your on-video energy is spectacular! Personally, all my personal and work projects are in Rust as opposed to the JS you use. No matter, your videos are ultra interesting. Thank you!
I'd love to see the histogram of speeds and do some thermodynamics! Add other interactions (with radial potentials) and even spin for magnetism models... Physics are your oyster!
Awesome video! As you mentioned, I would like to see how you got the simulation of many particles to run at 60 FPS using a quadtree. A supplemental video like that would allow us to take this to the next level. Thank you!
Mathematics and physics are important for a programmer. I had to come up with an algorithm for a grenade with a shock fuse, I came up with it. But usually programmers just use a collision callback and detonate a grenade in this callback. Although this is the wrong decision, it is necessary to track the impact, the grenade can be hit not only by a collision with solid geometry, but also by some external force. In general, I use changes in the velocity vector, subtract the current velocity vector from the past and look at its length, this is the impact velocity, if above the threshold, then the ball inside the UDZ presses on the spring-loaded plate on which the striker is fixed with sufficient force so that this striker initiates a capsule, which causes a grenade explosion. The code turned out to be very simple and reliable, the main thing is that it simulates the real UDZ of the RGO and RGN grenades quite well.
There is a different way to work out the equations of the collision that you might find helpful. Transform v1 and v2 into center of mass and relative velocities. COM is same before/after. Vrel(after)=-a×Vrel(before). a=1 for elastic, a=0 for perfect inelastic. 0
Super interesting video! Please do the quadtree version. For gamedev/software design the optimization part is the most important/fun! Thank you very much for the free culture you are providing.
Might be cool to go over fixes for tunneling (when one object is moving fast enough towards a ting/small object, it can move completely through that object instead of detecting the collision and resolving it correctly)
Let's see that inelastic collision example. I wanna hear a nice crisp *Crack* of a billiard ball, or maybe somehow deform the shape in the axis of collision slightly for animation?
Very nice. Can you colour and simulate diffusion by mass of the particles? And yes please do inelastic and make an annoying sound for each collision! Great work
Completely not related to the content of this video, but what techniques do you use to remove all of the silent portions of your video. Is it a manual process, or have you found an automatic process? I face this daunting aspect for every video I make. Another question, why did I enjoy this video so much?!? Haha
Physics professor here with a small gripe. While there are plenty of people who use the word 'conserved' the way you did ("momentum and kinetic energy are conserved in elastic collisions") that is not how I would describe it when communicating this idea. Quantities are either conserved quantities or they are not. What it means to be a conserved quantity is that the total amount in the entire universe remains constant; it cannot be created or destroyed. Momentum is a conserved quantity, so it is always conserved. Kinetic energy (by itself) is not a conserved quantity, and so it is never conserved. There are no collisions in which both momentum and energy aren't conserved. What you're talking about is whether the total amount of a quantity within a specific system will remain constant or not. This is different from conservation because it depends entirely on our choice of systems. If you consider both of the objects in an elastic collision then both total momentum and total kinetic energy remain constant, but if you consider only one of the objects in that same collision neither remains constant. To put this into more coding terms, whether a quantity is conserved or not is a global property while whether it is constant in a particular interaction is local. So I would say that momentum and kinetic energy remain constant in an elastic collision. To use the word "conserved" in this context implies that sometimes momentum isn't conserved (and that kinetic energy is sometimes a conserved quantity, which it is not).
I enjoy experimenting with problems like this, and watching your process. I especially like the idea of using a quad tree to reduce calculations. How do you handle the case where two objects have passed thru each other during the time between each step of the draw loop, and the collision is not detected?
Hey Dan, thanks for all the amazing videos over the years! I just pre-ordered a copy of the new book, but I wanted to ask a question: will there be a PDF version included so that I can always have it with me? I love physical books and believe they're the best medium for focused reading, but they're not always super handy to move around with and reference quickly. Thanks!
(v2 - v1)•(x2 - x1) and (v1 - v2)•(x1 - x2) are the same, they therefore trivially have the same sign. The difference in sign is only due to the last term, after the fraction.
dude! you gave me the nudge necessary to also preorder. I remember the first edition and reading it online was fun. now it'll be in my library forever, aside my unopen vinyls (I have vinyls but no turntables, what a weird thing to do)
I would allways, check for screen bounderies , top, bottom, left , right , if sphere is coliding with these bounderies, then increment or decrement x, y acordingly. Like , if x> 800 { x=x-1 } This is the simple way of doing it.
When redistributing the overlap, the distribution should be proportional to their velocity, not just divided equally between the two. Also, it might be possible that pushing them back would move them off-limit, behind a wall.
As alway, a truly nice video. A good recollection of all the 'nature of code' spirit and how to code it ! So nice... What next to do ? Optimize your algorithm and implementation in BASIC to make it run on your vintage Apple ][. May it be able to handle just a dozen of particules ?
At 29:55 my Roku streaming box lost its mind trying to decode the video with all the moving stuff in the corner. Everything turned into MPEG artifacts. It was quite fascinating. Also while I don't enjoy Javascript, the book is interesting to me because I know all the cryptic maths will be explained in code that I can read and make sense of.
2:25 hey, if you do make your own game with something like C or C++ from scratch, u cant just make this simplification. every frame has a different dT relative the the previous frame. always check the dt of the current frame and use that for your physics.
ok, 40s in im buying that book, building your own physics engine. is multiplying by -1 quicker than v=-v . first principles is actuall alot less scary than most people think, even thermodynamics.
now try continuous collision detection. for a start, you can find the time t at which two particles will collide using the quadratic formula with the terms: a = ||v1-v2|| b = 2*dot(v1-v2, p1-p2) c = ||p1-p2|| - (r1+r2)^2
