Exploiting Rendering Mechanics in Desmos

[@qxtr5853]

We all love graphic cyalcularors :)

[@brando3465]

enlgish

[@doggfite]

The video is interesting, but god damn whatever this accent is is soul destroying

[@thatoneguy9734]

How do you misspell that badly

[@dl5200]

@@thatoneguy9734 watch the video, he pronounces it as cyalculator

[@thatoneguy9734]

@@dl5200 I was joking

[@MegaFooby]

This phenomenon is actually called aliasing incase anyone is curious enough to dive deeper into it. Fair warning, it is a very deep and complex rabbit hole

[@CalebRoenigk]

Does this mean that anti-aliasing is just the act of sub-sampling values and making corrective changes to the original value to be more accurate?

[@whenelvescry2625]

@@CalebRoenigk yeah. Sometimes you can just straight up double or quadruple the samplerate, or throw in a very slight low pass filter/gaussian blur

[@rsa5991]

@@CalebRoenigk Sub-sampling doesn't actually remove aliasing. However, averaging out the results does - because averaging is a low-pass filter. Actually, computer graphics has three different terms: "anti-aliasing", "texture filtering" and "motion blur" that... are all anti-aliasing! They just combat different aliasing. "Texture filtering" removes aliasing when sampling from texture. "Anti-aliasing" removes aliasing then rendering to the screen. "Motion blur" removes time aliasing (because "frames" are also samples, just in time)

[@adamp9553]

@@CalebRoenigk Yes, exactly. More accurate, but often limited given how many samples (and low-pass filter samples) are required for a desired accuracy. It can get pretty complex since some areas of an image need more samples than others, whereas super-sampling is just blind brute force.

[@borat1]

Holy shit this is complex. I def need to take calculus now lol

[@-NGC-6302-]

“Desmos is a perfectly balanced calculator with no exploits”

[@Schnort]

*The Spiffing Brit has entered the chat*

[@fuzz1252]

Tea sipping intensive

[@flowi1227]

is that the guy from the ruler of everything vid in your profile

[@-NGC-6302-]

First person to point that out

[@flowi1227]

@@-NGC-6302- woah

[@whenelvescry2625]

I decided to write my own graphing calculator in Java, and yes, this is a thing that happens. As other people pointed out, it's called aliasing, and it happens whenever a discrete (finite samplerate) method is used to approximate a continuous (infinite samplerate) phenomenon. Aliasing will introduce distortion into media like images and audio. This is always true at some level, no matter what you set the samplerate. However, smart boy Harry Nyquist figured out that if you set the samplerate to be twice the highest frequency present in the continuous signal, then you don't incur aliasing. For example, the highest samplerate that CDs support is 44 kHz, because human hearing only goes up to 22 kHz maximum. However, it's incredibly memory expensive to run the kind of sampling code that audio processing requires in a browser, and when you can zoom out on the level that desmos can, those improvements in detail are basically meaningless. Given how I'm struggling to write this damn thing, yall should be impressed that the most broken thing about desmos is a mathematical limitation that's been known for 100ish years

[@turolretar]

Who did you say - harry nesquick? I think i heard of him

[@MrMoon-hy6pn]

I thought human hearing topped out at ~20 kHz. Anyway i'm pretty sure the reason that 44.1 kHz was chosen was because of the Nyquist Theorem yes, but also because the audio needs to be low pass filtered. In ye old days of electronic audio processing this wasn't perfect so a little wiggle room was needed or what's called a transition band, so around 2.05 khz was chosen for that. 44.1 kHz was also the highest reasonable frequency that was still compatible with pal and ntsc, so that's convenient.

[@KittyRubz]

Harry NyQuil

[@fiskfisk33]

"Harry Nyquist figured out that if you set the samplerate to be twice the highest frequency present in the continuous signal, then you don't incur aliasing." Now, try to convince an audiophile!

[@wasabithumbs6294]

Before watching this I had figured Desmos uses some variation of the Marching Squares algorithm, I guess not though.

[@KentoNishi]

This video is brilliant, I've come across this same quirk when graphing things in Desmos myself and always wondered what was going on. Nicely done!

[@cartoonpower0]

ngl you sound exactly like the type of person who I would expect to make a video on graphing calculators

[@allenlark]

goob from meet the Robinsons

[@TheBookDoctor]

I can think of no higher compliment to bestow on anyone.

[@IMayHaveNukes]

He sounds like a deepfake text to speech program.

[@theemeraldboat9947]

> A fellow GD fan > Naturally inquisitive > Likes & uses Desmos > Interested in learning when and why systems break > Has a sense of humor > On top of all that, simply makes good videos I think I’ve just found the perfect KZbinr for me

[@gapplyz]

He literally mentioned "VSC song lol" in the desc

[@GeorgTheGr8]

Give this man a couple years and he will have figured out how to render Minecraft in desmos

[@thatguyalex2835]

I was gonna say the same thing, except he could use Desmos to render Crysis at 4K resolution. :) Rendering games and 3d stuff is a complex field of mathematics and science that I barely understand. All I know is that the highest end computers use ray tracing in their GPUs.. Lol

[@WotCorp]

That feeling when you realize that the VSC song is playing in the background

[@zhand3r420]

I saw his animation and i thought maybe he liked gd cuz creo popular in gd but then next vid boom vsc song

[@CXLVII]

I could hear it faintly. I had to put my phone up to my ear to hear it.

[@dragon_buster_10k]

I noticed it three seconds into the video lol

[@justin.campbell]

Absolutely awesome video. One quick note if anyone is having trouble with the javascript in the URL bar, put it into the console of inspect element. (ctrl+shift+i)

[@ego-lay_atman-bay]

Or just put it in a bookmark. This method works on mobile.

[@roaringdragon2628]

Even better, press f12 to open the console.

[@justin.campbell]

@@roaringdragon2628 Didn't know that, thanks!

[@xphreakyphilx]

it's aliasing because it's above the Nyquist limit of the rendering engine

[@pak-9]

video should be called 'man discovers aliasing' lol

[@jellydonut505]

@@pak-9 or desmos succs lol jk

[@marcorademan8433]

A great demonstration of aliasing and the Nyquist limit.

[@CathodeRayKobold]

So it's a moiree effect between the pixels on your screen and the periodicity of the wave.

[@hansdietrich83]

Yep. Also nnown as Aliasing in Computer Graphics

[@rsa5991]

@@hansdietrich83 Or in audio. Or in signal processing. Of course, computer graphics does stand out: they have at least three different aliasings.

[@danieljensen2626]

@@rsa5991 That's just because computer graphics have more dimensions than something like audio, otherwise it's basically the same as the aliasing you get with any kind of discrete signal.

[@ego-lay_atman-bay]

This is really interesting.I just found myself changing the number and seeing different results. I actually like this quirk.

[@someidiot6359]

I cant wait to rewatch this video 3 years later and understand what he’s talking about

[@mus1c3gg]

seriously, i think this is the only comment i can read in this whole page...

[@JaydenGarciaYT]

VSC background music.. the PTSD is real

[@T3sl4]

Neat fact, this property (aliasing, specifically at a vernier offset to the signal period) was used in the early days of electronic instruments (oscilloscopes), to obtain extremely high effective bandwidth. That is, to be able to inspect signals changing extremely quickly (several GHz -- taking a sample every 10s of picoseconds, say). They did this, back in the days of vacuum tubes and early transistors (1960s), where nothing was anywhere near fast enough to do that in real time. Let alone any kind of signal processing, like how we have digitizers, and whole-ass CPUs, running at these speeds today! The trick was to get a very accurate trigger from the signal; add a variable delay; then trigger an extremely fast pulse generator. The pulse goes into a switch, which samples the input signal. The samples then can be handled by ordinary circuitry; basically, little more than an ordinary television is needed. The trigger means you're always starting from a known point relative to the signal; equivalent to finding the canvas dimensions in your case. (Or kind of the reverse, because you're adjusting the sample rate to match the signal, but that's fine, it's all relative.) The delay, is easily created with conventional circuitry, and by making it electronically variable, and sweeping that delay value, the original waveform can be reconstructed -- assuming the signal is periodic, or even just repetitive really, so that you can take one or a few samples each time it passes by. This was possible because, although components weren't available to _amplify_ signals so fast, there are still ways to generate very simple waves, like pulses. The physics of certain components can be (ab)used for this purpose (like transistors in avalanche, or tunnel or step-recovery type diodes). So, as an EE, it brings me joy to see someone discover these old (not so well known, outside of certain circles) techniques for themselves. :D

[@laurenpinschannels]

This is super cool! do you have any suggestion for how I can share this with people in an easier way than linking them your KZbin comment?

[@T3sl4]

@@laurenpinschannels Hmm not sure. The best reference might be contemporary [1960s?] manuals, though I don't know of any offhand that nicely discuss the method. Tektronix was using it since at least 1962 I see.

[@hiibolt]

Well explained. I had the exact issue with writing a physics simulation for my teacher, and I followed the same train of thought. Amazing video.

[@phoenizboiisawesome]

I love the VSC background music

[@calathmann]

Weird how that works. You did a good job explaining it although I am going to have to watch it a few more times to understand

[@davidfranzen570]

Was not expecting the VSC song lol

[@Fanro3]

i cannot make my brain stop thinking about vsc this whole video

[@eshleyyy]

"After a mental breakdown..." - Desmos, probably

[@LDimno]

after a mental breakdown

[@groszak1]

Also, floating point numbers have signed zero. Notice how 1\div\sqrt{1\div\left(0x ight)} and 1\div\sqrt{1\div-\left(0x ight)} make different results.

[@asifalphakennybody8865]

That makes no sense stop lying

[@groszak1]

@@asifalphakennybody8865 What are you talking about? 1÷√(1÷0)=0 1÷√(1÷-0)=NaN

[@jacksonsmith2955]

@@asifalphakennybody8865 How does that make no sense? If you're talking about signed zero, floating points have an entire bit dedicated to sign to support -inf and +inf.

[@asifalphakennybody8865]

@@groszak1 ok but if 1\div/1 ight is equivalent to string theory your theory if fundamentally due to the fact that a myriad of 4s=3x/x1

[@Gears_AndGrinds]

@@asifalphakennybody8865 They're talking about how computers get those values not what their actual values are

[@Phoen1x883]

Thank you for the time left counter at the end. People like you make life better for the world.

[@jacksonsmith2955]

what's that for? legitimately curious

[@Phoen1x883]

@@jacksonsmith2955 Recommended videos pop up immediately after the video ends, so this lets mobile users know if it's safe to tap to bring up the controls.

[@Mark_Rober]

I still just love how you use Waterflame's music. He is my favourite musician so its really fun to watch you content :)

[@lotsofloops]

Have you seen this blog post from Desmos engineering? the way the sampling works is different for equations like x sin y=y sin x engineering.desmos.com/articles/press-a-key-in-the-calculator/#the-graphing-part-of-the-graphing-calculator

[@prototypemusic]

Its interpolation and aliasing, computers can't get infinite precision, so, when you get an enough high frequency wave, it will just ignore a lot of points. Nothing too complex, there are a myriad ways to alleviate aliasing though, I mostly came across it in audio applications, where a synth's memory and precision are limited, but I still have to accurately represent a wave might go up to 2 MiHz

[@asdasfdfgewqgrgyjh]

Loving the vids my man. Looks like youtube has finally decided to start shining a light on your channel. I hope you start making content again because this is great!

[@YOOOOOOOOOOOOOOOOOOOOOOOOOOOO]

I wanted to end my suffering everytime, he says calculator. cyalcyulyator

[@5omebody]

re: the "discrepancy" - it's more like, the mouse moves 10px while the graph moves 9997 units (of course, since you can either change the zoom level arbitrarily (idk about this one). you can definitely change the period of the function arbitrarily though so you could trivially just trial and error it until it barely becomes too fine for desmos to render every oscillation)

[@kodirovsshik]

I like how it's basically 4 minutes of big brain stuff with vsc song playing in the BG lol

[@blzrL]

OMG tbe VSC song caught me so offguard lmaooo

[@Kaiwala]

I'd love to pay attention to what you said but the VSC song is throwing me for a major loop right now

[@jasonpugliano]

VSC song go brrr

[@spiralhalo]

Generally speaking, I only trust a graphing calculator when zoomed in by a factor of infinity.

[@not_just_burnt]

this peep literally explained aliasing and intermodulation without saying those words. cool!)

[@kipplox7377]

BRUH WHAT I DID NOT EXPECT VSC LMAO

[@kipplox7377]

calc is a mental breakdown sometimes tbh

[@NANKAIDATTE]

calculator corr

[@NANKAIDATTE]

calculator core

[@NANKAIDATTE]

calculator core

[@NANKAIDATTE]

calculator core

[@Scout_21]

VSC jumpscare

[@ClementinesmWTF]

Really cool stuff. Usually when I break Desmos, it just decides to stop graphing literally everything or just make up its own numbers because of floating points. Also, your pronunciation of “calculator” sounds like you’re a supervillain (“cyalcyulyator”)

[@Bober26681]

The second I heard this music, I instantly thought: VSC

[@akraus53]

Welcome to the Nyquist Theorem

[@pvs_np]

What a nice song, Stalker by WaterFlame, in GD is know and related to an almost imposibble challenge to complete, sounds like what you're exactly looking for with those resolutions. Great job man.

[@ar7eniyan]

the aliasing comes from nyquist-shannon sampling theorem: to sample the function correctly, your sample rate needs to be at least twice as high as the function's highest frequency

[@laurenpinschannels]

what a very curious kind of wavetable synthesizer you've discovered! for more on aliasing, I'd recommend xiph's aliasing video ;) I'll bet the recommender will catch on and make it show up next to this one if people watch it!

[@Kazzy74]

Song is called stalker by waterflame if anyone was wondering

[@maplinxxgd5234]

VSC lmao, glad you caught that

[@not-applb]

After a mental breakdown...

[@lukostello]

The way you say "kyahlkyulahtor"

[@gdbreadloaf]

Vsc song omg HD reference

[@5ilkyYT]

ah yes vsc music

[@falxie_]

This seems like your standard Calculus student's thought process

[@seamusrichardson6011]

For firefox users, it doesn't work if you put it in your URL bar, but you can CTRL+shift+I, click on console and paste that there.

[@AmyLovesOwO]

I love this editing style.

[@____.__._.._]

Really helpfull, as i was trying to "fix" my Casio Graph-35+ struggling with drawing generalized sine waves. And yeah - the accuracy limit made such pairs of lines reapeating periodically, so i thought something is wrong with the graphing part of ROM, but actually no. Thanks :)

[@KaelVoker-d1e]

the early days of electronic instruments

[@kruumlauf5272]

I see the algorithm has taken effect the past few hours

[@haabyalexis]

Ayo wtf VSC song?? Cube game reference??😳

[@calebo56]

VSC song (good video)

[@victorfunnyman]

the VSC song

[@17thprime19]

I play VSC and one hour later a year old math Vid with the song is recommended to me. Hmm

[@chillnye1011]

student done with calculus' shit; breaks math, time, and space

[@ogdelantethegoatwwww]

“VSC song lmao”

[@zabotheother423]

You will do well in DSP my boy

[@mustardbeef6045]

I remember having to using this in school, putting a crapton of crazy stuff in involving exponents, sin, cos and tan until stuff broke. And I mean BROKE. There would be random dots appearing, lines would dead end, and sometimes a bunch of very short random lines would just fill the screen

[@Julian_H]

It isn't working for me - the graph looks fine as I scroll... Maybe it was fixed or it works differently on other browsers (I'm using firefox)?

[@Bluedragon2513]

I'm using Chrome and the graph also doesn't move for me D;

[@e_sd]

my guy is doing 5D math while we can only comprehend 2D math on a paper

[@guigazalu]

The code javascript:Calc.setMathBounds({left: 0,right: Math.ceil(2*Number(document.getElementsByTagName("canvas")[0].style.width.split("px")[0])*2)/2,bottom: -1.5,top: 1.5}); can be simplified to (running in the console, with Ctrl+Shift+K in Firefox): Calc.setMathBounds({ left: 0, right: Math.ceil(4 * parseFloat(document.querySelector("canvas").style.width)) / 2, bottom: -1.5, top: 1.5 });

[@isaackay5887]

Nice work!!!

[@shanemeadows-yaw1141]

Desmos when are you gonna give this man a job

[@ts4858]

i got recommended this from vcs song i'm assuming but this is cool video

[@groszak1]

In double precision, multiplying by 2^-1074 and then dividing by it effectively makes a round function. However, x×2^{-1074}÷2^{-1074} seems to optimize away. But as soon as you put another function like x²×2^{-1074}÷2^{-1074} then the round effect kicks in.

[@StormBurnX]

Instead of the Nyquist Frequency shall we call this the JohnDoesStuff Frequency?~

[@TheShockChicky]

Duuuude vsc song got me unaware

[@Siirxe]

Your next idea should be playing audio at MUCH higher quality than now by calculating the FFT of a song, then switching between the freqeuencies fast enough to do what you did now but with audio.

[@laeyak8504]

"VSC song lmao" Legend

[@CelestialxPanda]

You are the only calculator the world needs bro. 🤣🤣🤣🤣

[@Sm0llar]

The golden song❤

[@b0mbhead729]

Vsc song lol

[@AROAH]

This is some trickery on the level of stuff on the Sega Genesis

[@alexthomsonnz]

This feels like Ocean 8 but math

[@thesmug2750]

wow you "discovered" the nyquist sampling theorem

[@yourlocalprogramer]

Just because I heard the song, now make an animation of VSC in desmos

[@PGThe3G]

Or maybe vsc madness

[@kyriolexy179]

My man using VSC song in a highly technical math based video

[@Beregorn88]

And this is why we have Nyquist theorems

[@3O9XT]

my brain is having problems, welp, time to reboot

[@ykaaaaar]

this guy is gonna bend reality mark my words

[@salsa221]

your visuals look awesome. What do you use to make them?

[@KlausKlass]

I can't get it to work for some reason. It might be because I have a retina display so there might be less aliasing. The script works for seeing the spoofed graph, but nothing changes when moving it around. I have tried scaling my window but it still doesn't show the animation. Edit: it worked if I put Chrome in full screen and zoomed in on the page (using Cmd +)

[@tylerjames4956]

I was experiencing this same issue but ill try this I got it to work based off what you said and as long as I didn't change the width of the desmos equation window, thank you!

[@Kaixo]

Exactly how audio aliasing happens.

[@SachiN-Vishwakarm]

awsome maan......me too use this in trying to visualize various functions and often come through these glitches

[@digiorniboy]

I was watching this and thought to myself “wait a sec is that fucking stalker playing” and lo and behold

[@william1729]

I swear someone is going to make Bad Apple using this

[@SandraWilkes]

I have a baby question but I bet you'll know. I want to take a video of a student shooting a basketball. Or I could just shoot an image. Once I get the image on the axis, I want to trace it to show the parabola and find the vertex etc. Can you help me figure this out?

[@birdieman_1180]

Video makes me feel like I’m about to break into a vault wtf

[@eternal4074]

You can also make insane spirals by doing sin(xy) = x tan(y sin(x))

[@rheiagreenland4714]

Clearly desmos made a bargain with the devil in order to even begin to try to be able to graph the absolute nonsense we throw at it

[@kozynthetaquito5506]

"Graphing Cyalcyalater"

[@hollingharris659]

nice, ive idly wondered about how the rendering in desmos works before just from being bored as shit in math class and trying to draw stuff with equations instead of actually doing my work

[@slice-the-pi]

so basically a 1-dimensional Moire pattern! neat.