Typo at the end! Should be b^(n+m) = b^n * b^m Btw, support me for more videos: GLSL Course: simondev.teachable.com/p/glsl-shaders-from-scratch Patreon: www.patreon.com/simondevyt

Holy crap! A long time ago, I was writing a multiplayer top-down shooter and I ran into a weird issue where the camera would start jittering like crazy, some kind of de-sync between the client and server. I never figured it out and just lost hope in the project, abandoning it. Fast forward *15 years* and at the end of a video about interpolation, there's a quick side-note about a common mistake when interpolating positions. And, if memory serves, that is *exactly* what I did with the camera. ...Holy crap..!

i like the part where he said "It's lerping time!" and lerped all over the place

Thanks, Simon. I'm lerping as a programmer but smoothing and shaping my path.

This video needs to be waaayyy longer. I want more!

This is exactly what I needed for my game. Camera Log Zoom and Frame Rate independent tracking for aiming. Thank you so much, Simon! Subscribed.

Your smooth voice and professional animation and videos design gives your videos such nice aesthetics! Also love the knowledge you share with us

Nice linear/log zoom example! I was just staring at a linear fade in and thinking it didn't look good. I'll have to give log a try

Hey Simon, I finally got around to implementing Lerps and I am very happy I kept your vid around. Helped a ton!

That's an effective lesson, explaining all these concepts, functions, and implementations in such short time.

I didn't check the math exactly but the last example when you are following the target, you are effectively solving a differential equation. The initial fix by multiplying by timestep should be forward Euler method. Using the exponential is an exact solution to the differential equation, hence the frame rate independence. However, it is exact solution only if the target is stationary(maybe also in the case of linear movement). Therefore it is still not frame rate independent but the error is much much lower.

Absolutely astonishing video! I was aware of the lerp itself, but these tiny things, like the interpolation of colors to get nice gradients, which are very quickly overlooked while programming. I'm amazed by the solutions. Thank you very much!

There is a mistake at 8:07 IG b^(m+n ) = b^m * b^n not b^(m+n) = b^m + b^n.

I love these videos, covering basic concepts and tool sided in game development. I always learn new things and get a deeper understand of what I'm doing, and what I could do better. Thank you so much!

A bunch of awesome concepts in just enough detail, great video!

I've experienced 2 of the issues mentioned with deltaTime lerping and the camera zoom lerping problem. I found ways around both at the time but this video was very insightful and i've made some notes for these in the future as i'm sure i'll run into them again. I knew how lerp worked but i was always curious about smoothstep, it was funny cuz i've experimented with lerping between lerps so was a suprise that i was on the right track just didn't think of the sqrt. Great video Thanks!

This is gold. Thank you for all the effort you put into this beautiful video

That bit at the end is especially brilliant! Thanks for the video!

Wow, I don't think I've seen such a useful video before, and it only was released a week or two ago. Major props, thanks for sharing

Yes! I've been looking for something like this! Thanks so much for making this video, now I know how to derive lerp functions

Good to see you making videos again! I always learn something.

Interesting stuff. My favorite functions in Unity game development always has been lerp and slerp because they are easy to use and extremely useful in many situations. Also I love their names

Thank you! This helps me _understand_ the functions. Cheers!

I gotta thank you a lot especially for that last one. My camera was lerping weirdly on different frame rates and that solved my problem!

Thank you Simon! I'm studying CS and this is amazingly useful.

Loved this so much Simon! Thanks for the video 🙆🏻‍♂️

I didn't know I needed this video until now, thanks!

Amazing stuff. I've done all these kinds of things without LERP (e.g., moving objects, color transitions, camera tracking). So it will be interesting to see how I use these commands to improve my programs.

Great video. Really interesting to see how functions can combine to make smooth step.

it's like all the fun parts of cs course without the boring parts

Absolutely blown away by the insights offered by these videos. There is a lot of how to do XYZ game dev videos on KZfaq. But the depth and breadth covered on this channel🤌 You are a rare and beautiful beast. Thank you.

I will appreciate more math videos like this. thanks

I wish this video existed when I was getting to know all about these functions myself! Great video!

that frame-time independent lerp will be useful, thanks!

Love how you always seem to be able to simplify things to make it easy to understand

Thanks. That was really interesting and inspiring!

Great timing, just implemented this in my little engine!

very nice, i like it a lot. short and on topic.

Super cool video. Love to see more of those math videos :)

I could see how I could have a whole library of different variations to lerp with some better names for what you want to do. Like the smoothstep. Thank you for this, it sounds awesome.

I've been doing smooth lerping as shown at the end wrong all this time! I did the exact same as the same as the second example, slapping on delta time. I was never satisfied with how it looked with low framerates as it gets jittery, so I tended to add some additional checks to make it not freak out.

Hey, so some people (like me) might be calculating their lerp rate as t = K * (targetFrameRate / frameRate) instead of t = muchLargerConstant * frameTime {i.e. t = .35 * (60 / 240) instead of t = 21 * (1 / 240); this is if the result is supposed to be equally large, t = .0875 in both cases} bc they wanted to be able to write constants (K values) that were equal to the actual used lerp rate at a target frame rate, meaning a lerp rate between 0 and 1. If you use a K value from 0-1 in the second equation, your t value will be very low and cause slow lerping, thus you have to use a K value that is (targetFrameRate) times as large as the first equation (21 = .35 * 60) to get the same result. Basically, if you are ok with small lerp rates, then the second equation works fine with K being a 0-1 value, and the use of the equation presented in the video gives similar results. Using my method, however, means that your constants will not work the same way in the new frame rate independent lerp function. And if you, like me, instead of refiguring many different lerp constants, want to use the same constants to get the same result except truly frame independent, then you can use this method. After some fiddling with math, I found that you can add an extra constant out front of the (new) equation so that it becomes: t = A(1.0 - pow(K, frameTime)), where: A = K / (1.0 - pow(K, (1 / targetFrameRate))) It probably goes without saying, but this has the same effect if you were previously using something like: t = targetFrameRate * K * frameTime, as that is the same as my original equation. There is probably a shorter version of calculating A, but I didn't bother trying to condense it. A stands for Adjust, as it adjusts the result of the new function to be identical to the result of K * (targetFrameRate / frameRate) at a given targetFrameRate and all subsequent rates for different real frame rates to be much closer to the original function as well, allowing you to use the same K value used while utilizing t = K * (targetFrameRate / frameRate) (Note: There is nothing wrong with the equations in the video, they just give small lerp values that you might be required to adjust later since you can't use a K value greater than 1 in the new equation). The constant A only needs to be calculated once upon creation of the object that uses A (assuming K is indeed a constant). In summary, this provides a way for t values from the new equation to be close to the old equation using the same k values. I hope this helps anyone looking to implement this function in an already largely completed version of their project! And here is a Desmos graph I set up to help understand why this might be useful: www.desmos.com/calculator/sylkom3bze Try getting rid of A on the purple line and f on the blue line. That illustrates the exact way the original equations were portrayed in the video.

super helpful! thank you so much.

Every time I go to write I a comment you're ahead of me explaining what I know from intuition, but way better than I could. Then adding to that something I don't know. brb gonna bing your videos.

Crazy good videos thank you!

Great video, thank you!

I wish I had this channel when I was younger.

This video earned you a subscription. Very nice work.

One of the best explanations

Fantastic video - thank you

Wow! That was beautiful 🤩 I need to learn math today

I didn't know about the slerp function until now, and it is SUPER helpful! I'm a 3d artist, and I often face the problem of having to interpolate between two normal maps. When searching how to do this, there are tones of unhelpful answers. some say to just interpolate between the raw pixel values (which never looks right). Others say to use an overlay blend operation, which does an ok approximation. I have never once heard someone mention slerp! One great property is that you can rotate one normal map by the other by using t=2, or t=-1 to rotate it in the opposite direction.

lost me at the end lol but very good video on some game maths fundementals. Nice refresher after not having dabbled in stuff like shaders in a while

What I like about lerp is how it can be cheated to be smooth, like you showed. But also in shaders how it can be used for shapes and patterns. Where T is a value of 0 to 1, meaning black to white with grey in between. So by feeding it a black and white pattern "aka any colored image but only one of the 3 colors" then you can use lerp to paint effects onto a surface. Say you have a texture with spots you want lit up. You just use the non lit part into the A, the lit part into the B. And the black and white part into T. So now it lights up the white parts of the texture while smoothing out in the greys.

thanks for these videos.. these are pretty dope :D

Teacher Simon. Thank you for the great tutorial. God bless you. Can I request a video on "How will I learn to code if I could start over"

Oh my god, learning the right way to lerp positions independently of framerate IS a must and I never thought of it... Totally required for online games where position matters.

1:13 Using this in conjunction with ‘B*t + A*(1-t)’ was an idea I never heard before and will be SO MUCH more useful than having to go into desmos to hand craft functions whenever I need interpolation, so thank you for all this! I know this was probably the simplest concept for others, but I work in a sim tool that doesn’t offer interpolation functions and I only really need them when making nice animations. But this is so much cleaner than reimplementing complex functions...

Thanks especially for the last part. I am the person who always used deltaT. I will do better now. ;)

very nice. thank you.

You da best, Simon!

I love this, thanks

very very cool! thank you!

2:18 From what I understand this can be achieved using integer math as well. I've heard you can do something similar on 8 bit platforms using the following: char speed = 0; unsigned char accel = 0; void gametick(){ accel++; if (accel) { if (speed > 0 && speed < 0x7f) { speed++; } } Essentially accel acts as a timer that increments speed whenever accel overflows. If you wanted to achieve an effect like x^3 or sqrt(x) you could AND accel with a bitmask that grows or shrinks based on the value of speed.

Very good video, keep it up

This is really cool

I'm not sure if what happened at 7:47 was a genuine audio screwup or you faked out censoring the word "infuriating" but I love it

I'm currently working on a game that has some events that sometimes causes a spike in the frame time, if I happened to be moving the camera in a specific way during those events the camera starts to freak out shaking all over the place. I ironed out some time consuming events to minimize the problemas but never understood why the camera of all things was suffering from the fps drops... until now

Watched this a second time, realized already had given a thumbs up.

Love IT, thank u

Great video

Sorry... shouldn't it be b^m * b^n = b^(m+n). Is it different if the numbers are strictly between 1 and 0?

this video is great thanks

useful stuff i found here

One content, two languages. What I have now written may have a perfect mirror in another language.!!!!!!!!!!! Hack in the brainlll

Awesome!!

Sadly... I slept at math, so thank you! 😂

I like your examples of UI animation. This animation you've done are not simulative, right? The animations you've shown doesn't take velocity or other physical properties in consideration, right? Is it possible for you to do a video on spring-based system and normal curves? Great video!

amazing video, you should leave a little more time at the end of the video, so the recommended videos appear there. Currently the explanation of method #3 get interrupted for being at the end of the video

Serious tidbits my man

I had no idea about the naive position lerp being framerate-dependent. The more you know!

Thank you for this!

That last pitfall has filled me with terror.

Post this on your twitter! KZfaq’s algo highly values the first few hours!

I only subbed bc of that cheeky little gag you did.

Very nice

lerping is the most underrated field in math

I always wondered how texture filtering worked, yet never considered lerp.

How do you generate the voice on these videos? It sound super real 👍

Look at this remind me abt bezier curves is just lines lerping together

this video should have been in 60fps

omg definitely use quaternions to interpolate between two random rotations ;D

instant subscribe!

2:43 "A parabola..." *shows a bell curve*

As a web frontend programmer for an online store, I rarely get to very fancy animations... I rarely end up using anything except a linear interpolation and very rarely ease in out. But if I did use anything more fancy it would be annoying as heck to use. Because in a tool such as a webshop any animation must finish in under a second, usually between 200 ms and 400 ms not to feel frustratingly sluggish. Only when doing large distance animations such as dialogs animating onto or off the screen I get to use up to 1.2 seconds long animations; but usually half of it is basically transparent anyway.

I wonder if the log function for zoom in zoom out should not be a sqrt function for natural view, because then your velocity with which you distance in or out is constant, as the area you cover increases with the sqr of the distance.

note to self: slerp = spherical linear interpolation

Is there a course that teaches you the various ways to apply this? I’ve been having very limited success in experimenting by myself and I think I need, like, a legit teacher to help me step by step

After plotting a few of the smoothstep family of functions, it seems like it gets steeper and steeper in the middle. Does it converge towards the discontinuous step function, or towards a "smoothest" step function ? My intuition would be the former, since the nth derivative of S_n is made to be zero at x=0 and x=1 on purpose, the taylor series should be 0 + O(x^n) and 1 + O(x^n) respectively, and thus should converge to 0 and 1, with a discontinuity in the middle. Maybe the function isn't analytical, but all smoothstep functions are polynomials and therefore analytical, so I don't think that's possible...

on the 3rd method, frame independent lerp thing, its ilke K = 1 - pow ( K , frameTime) we're using the variable K when declaring it is odd. shouldn't it be pow(constant , frameTime) ?