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The Simple Yet Powerful Math We Don't Talk About - Freya Holmer I Neat Corp


Пікірлер • 178

  • Matthew Winston
    Matthew Winston  Жыл бұрын +119

    Freya, the rare true Rockstar. The integration of Art, Code, and Math each enabling a richer understanding and utilization of each other.
    Reminiscent of Gödel, Escher, Bach. You may find this presentation moving!

    • t 77
      t 77 Ай бұрын

      @Data Rake calling a young person the actual next Isaac Newton can easily come off as a bit disingenuous by going over the top, which can feel like there's ulterior motives involved, which invalidates the compliment, is all. That's not hating on the compliment 😎

    • Data Rake
      Data Rake 2 ай бұрын +2

      The people commenting here hating on your comment are ridiculous. Looks like they never left their moms basement.

    • Nachfüllbarer Trank
      Nachfüllbarer Trank 2 ай бұрын +4

      some ppl got salty over your compliments lol

    • hack huck
      hack huck 5 ай бұрын

      Fettes DoubleDislike für Matthew Winston ! 👎👎

  • Marcos
    Marcos 4 ай бұрын +40

    Freya set the bar on a whole new level for what means to be a technical artist. Math and code Goddess.

  • razveck
    razveck 2 жыл бұрын +30

    I struggle with the mapping issue she mentioned on a regular basis. I have to remap things all the time. I didn't know there was an inverse lerp function, and this will save me countless hours in the future

    • ThePC007
      ThePC007 11 ай бұрын +1

      If I understand things correctly it's just the _map_ function that's provided in the Arduino framework. I've found this function so useful that I started using it in non-Arduino projects as well.

  • Luce Quesbe
    Luce Quesbe  Жыл бұрын +18

    Using lerp as a way to overlay texture is so simple and yet elegant! I never thought of that (even though I'm guessing it's already being used for that purpose everywhere anyway -- painter's algorithm being less efficient)

  • Aaron Rumley
    Aaron Rumley  Жыл бұрын +45

    this was such an awesome description of lerp and inverse lerp! It really helped solidify my understanding of them, and I've already found several use cases in my game that I have easily been able to accomplish!
    listened twice - understood lerp.
    listened three times - understood inverse lerp.
    listened four times - understood remap.

    • supendi Xu
      supendi Xu  Жыл бұрын +1

      Lol turns out I'm not the only one who is rewatching haha

  • hund 44
    hund 44  Жыл бұрын +6

    In blender there is the "map range" function which is just a generalised version of lerp and iv lerp. It takes input range minimum and maximun, output range minimum maximum and the value as inputs and outputs the remapped value. For a normal lerp the input bounds are just 0 and 1. And it also does extrapolation aswell but this can be turned off if not desired.

  • Conner Anderson
    Conner Anderson  Жыл бұрын +9

    Had no idea about remap. I was trying to build up some calculation from scratch to figure out how to lerp between 3 different gradients over time in a shader. I was losing my mind trying to see how I could keep one gradient up longer than the others. This helped me so much.

  • big mistqke
    big mistqke  Жыл бұрын +5

    Would love an in-depth breakdown of that water shader. Looks absolutely gorgeous.

  • Winters
    Winters  Жыл бұрын +3

    You have a very good way of explaining complex stuff in an easy to understand manner. Thank you for this very enlightening talk!

  • DigilusionStudios
    DigilusionStudios  Жыл бұрын +3

    Looking at the points and vectors you have to make a bezier curve are the same kind of ideas that Tony Derose talks about used in the development of the Toy Story movies with the Catmull-Clark equations. He gave a TedTalk in 2013 using a SubDiv program making curves into full circles for 3D geometry used in Pixar just by splitting the midpoints.

  • Pepperized
    Pepperized 3 жыл бұрын +76

    Fantastic talk, thank you Freya

  • sachin tumbre
    sachin tumbre 3 жыл бұрын +14

    Awesomly simple explanation of complexy looking math functions. Opens up so many possibilities and scope for creativity, also Thanks for uploading this video

  • M. Sierra
    M. Sierra 10 ай бұрын

    Surprised to not have seen distance maps in this talks. Animation using distance maps and lerp is a really nice usecase as well I think :)

  • Angel Sola
    Angel Sola Ай бұрын

    I truly admire this woman and her deep knowledge. Bravo Freya! Keep it up

  • Robert Durham
    Robert Durham 3 ай бұрын

    Freya Holmer : Game Devs :: Felicia Day : Nerdcore
    They both do a fantastic job engaging with their communites, and emit such a positive vibe.
    Freya has so much educational content on her channel though, she's probably become Big(O) in the function that determines my interest in math.

  • Joseph Merrill
    Joseph Merrill Ай бұрын

    Unrelated but adjacent, I'm interested in whether the 3D fractal program, Mandelbulb 3D can be sped up. Apparently the fractal generators on the back end need higher resolution than actual graphical resolution and therefor requires Large Floating Point numbers and apparently (I'm told) this means we can't use GPUs. One idea I have for that program is whether they could at least separate out the post processing and assign that to GPUs. But I wonder if there are other ways to speed up fractal generation, possibly get it on a GPU platform. IDK.

  • Venkata Ramayya
    Venkata Ramayya  Жыл бұрын

    Thanks for a wonderful and simple explanation of LERP etc.!!!

  • Kenbomp
    Kenbomp  Жыл бұрын +3

    Really shows how powerful formulas are. The pictures are good for examples. But the formulas are so elegant.

  • Slime Pixel
    Slime Pixel 3 ай бұрын

    This was great explanation!
    Thank you!

  • Anouar Aja
    Anouar Aja 2 жыл бұрын +131

    Freya Holmer, The Shader Goddess

    • Lucasinatur
      Lucasinatur 2 ай бұрын

      @P L I know about these forms. They were used a lot but went out of use in the modern Era. Bringing them back in words like God or actor is just dumb.

    • classic max
      classic max 2 ай бұрын +2

      ​@Lucasinatur except the point of using 'goddess' is often precisely the fact that it's gendered. an element of the intended meaning is lost when you just say 'god' instead. to call a woman a goddess of something is not just to say she's good at it or knowledgeable about it, but also to emphasize her femininity.

    • Hipxel
      Hipxel 3 ай бұрын

      Sounds like a boss battle

    • Lucasinatur
      Lucasinatur 4 ай бұрын +1

      @ark Because I know from German (my mother tongue with this problem) that it is really annoying. Some people use weird non-standardized language to "include" everyone. Like "Lehrer" means teacher and "Lehrerin" means female teacher. "Lehrer" can mean both but some people think that's bad. But the root of the problem is the word "Lehrerin" because if it didn't exist, you couldn't interpret "Lehrer" as male-only.
      English had this too and some forms survived like goddess. But don't emphasise them if not neccessary because it will just lead to a lot of headaches when talking about groups of people.

  • Titus Grothaus
    Titus Grothaus  Жыл бұрын

    Awesome talk - it was very eye opening for me with the great visual examples. thx !

  • DePistolero
    DePistolero 3 жыл бұрын +17

    I took a picture of that as well, yes using my phone right from the laptop screen... And Remaper made my whole day.... I am so happy for it.... Thank you!!!

  • Metal Emissary
    Metal Emissary 4 ай бұрын

    Freya taught me a lot of the things I know today

  • Constant Dupuis
    Constant Dupuis 3 жыл бұрын +4

    Very good overview and clear illustrations

  • Roman Salnikov
    Roman Salnikov  Жыл бұрын

    I really liked it, I'm impressed. Watched in one breath. I'ts very interesting and informative!

  • SRal
    SRal 2 ай бұрын

    This was really fun to watch :) Thank you

  • Roderick Sibelius
    Roderick Sibelius 2 ай бұрын +1

    Mathematics is the tool of all Engineering Sciences and Technology, it is awesome that we have 'computers' today with the use of programming we can create graphics and animation in colors: visualization, and to computer games. Engineering design is the most indispensable tool for use of this. Thank You for educating us.

  • Kidan Nelson
    Kidan Nelson 5 ай бұрын

    I have no idea if its because of freya but Unity shadergraph now has a remap node that does exactly what she described around 26:00.

  • Nevile Ruas
    Nevile Ruas 2 жыл бұрын

    That was AWESOME! Thank you!

  • josh gordon
    josh gordon  Жыл бұрын

    Wow amazing, I'm already thinking of ways I can use this in my programs

  • Andrew N
    Andrew N  Жыл бұрын +1

    If I only learn 50% of this math, I will know 100% more. interesting, even if I dont really understand everything :)

  • kummer45
    kummer45  Жыл бұрын +5

    The problem with Bernstein Polynomials and Bezier constructions that no one explains clearly how they where formed or derived in great detail.
    These are engineering drawing mechanical techniques that where rediscovered by computer scientists. It's amazing that forgotten techniques are being rediscovered again like the quaternions studied by Hamilton.

  • VMMI
    VMMI  Жыл бұрын

    This is amazing, i watched until the end 😭

  • Quinn Depatten
    Quinn Depatten  Жыл бұрын +5

    Holy shit, I can feel my brain expanding. This shit is awesome.

  • Kenbomp
    Kenbomp  Жыл бұрын

    Nice not too hard to make it plot angled polygons.

  • FairNut
    FairNut  Жыл бұрын +1

    30:57 literally the reason I don't attend a single math related class in my university, I either learn the things myself or you know... let them slide

  • Bissash 10
    Bissash 10 2 жыл бұрын +9

    Great Talk Freya

  • Rishikesh Jaiswal
    Rishikesh Jaiswal 2 жыл бұрын +4

    Bezier curves are literally what Pixar uses in their animation and modelling and shading!

  • vertenyi
    vertenyi  Жыл бұрын

    thank you, it was great

  • anhedonia
    anhedonia 5 ай бұрын

    I clicked on this video and didn't think I was actually going to be interested enough to watch the whole video. Its crazy how math can be used to emulate reality.

    EDISON PHOENIX  Жыл бұрын

    Absolutely Awesomeeee!

  • Prathvi Shetty
    Prathvi Shetty 2 жыл бұрын +5

    Wow that's visualisation was so cool

  • Thap Tam Studio
    Thap Tam Studio  Жыл бұрын

    This is awesome

  • levitycreations
    levitycreations  Жыл бұрын


  • Boba Squid
    Boba Squid  Жыл бұрын +3

    Math is a reason why so many people never finish their degrees. Non stem math requirements are needlessly too rigorous. It's a statistic.

    • qq qq
      qq qq 3 ай бұрын

      just skip the degree part and go work in a cafe or something

  • Gêm Đép 2
    Gêm Đép 2 2 жыл бұрын


  • William Zulu
    William Zulu 2 жыл бұрын

    Thanks Freya.

  • sp10sn
    sp10sn  Жыл бұрын +4

    I feel the editor was very rude to Freya. Despite her effort to call attention to slides, which she prefaced as critical, the edit is largely footage of her expressing an amazing narrative. But not in the way she wanted to.

    • big mistqke
      big mistqke  Жыл бұрын +1

      Mm, don't really understand what u mean. The graphics look clear and I can follow along easily.

  • Deplissee
    Deplissee  Жыл бұрын +2

    When copy&paste implementing: I think a Lerp with "(b-a) * t + a" would be faster (less operations).

    • Dev For Fun
      Dev For Fun 10 ай бұрын

      @jasmin UwU only if you use lerp whenever possible, which the talk is promoting

    • jasmin UwU
      jasmin UwU  Жыл бұрын +2

      Not that it matters much anyway. Most of your performance isn't being used on lerp

  • Kriss Loo
    Kriss Loo 2 жыл бұрын +5

    Haha, when she finally showed the lerp code I decided to test my understanding for what she was talking about and wrote my own code which is a step further from hers after simplifying stuff
    it goes like this:
    return a + t*(b - a);
    I wonder why didnt she notice that

    • Jules Wombat
      Jules Wombat  Жыл бұрын

      I am not sure the message was that lerp is anyway difficult, it was more about how such simple function can be applied and combined across vectors, images etc to create really impressive effects. Its the application of maths that makes is the beautiful here.

    • Kriss Loo
      Kriss Loo  Жыл бұрын +1

      @Freya Holmér My bad :) I got more knowledge about it now, you rock
      I'm a huge fan

    • Freya Holmér
      Freya Holmér  Жыл бұрын +6

      like Johannes said in the replies - I prefer the (1-t)a+bt lerp for numerical stability! I also like the way it reads like a weighted sum (while the other is more like a vector scale and add), and talking about the perf/accuracy differences between the two felt out of scope of this talk :)

    • Milan Stevic
      Milan Stevic 2 жыл бұрын

      btw youtube keeps swallowing my comment, I'll try to post it again :(
      also here's a step by step process of getting from basic lerp to something called a smoothstep (very ubiquitous in shaders)
      you start with a function A, that simply does t*t (basically t squared)
      then you make a t-inverse of that, called B, that does (1-t)*(1-t)
      however the result of this is upside down, so lets do 1-(1-t)*(1-t)
      now solve the square 1 - (1 - t)(1 - t) = 1 - (1 - 2t + t*t) = 2t - t*t
      we now know that A = t*t, and B = 2t - t*t
      these are the two ends of a smooth quadratic ramp, accelerating in and out
      now you can lerp between the two functions in time, knowing that A + t*(B - A)
      however these are functions, so A(t) + t*(B(t) - A(t))
      flatten this out, by substituting
      t*t + t((2t - t*t) - t*t)
      = t*t + t(2t - 2t*t)
      = t*t + 2t*t - 2t*t*t
      = t*t(1 + 2 - 2t)
      = t*t(3 - 2t)
      hence (as seen on wikipedia)
      float smoothstep(float a, float b, float x) {
      // Scale, bias and saturate x to 0..1 range (saturate means clamp in shader languages)
      float t = Mathf.Clamp01((x - a) / (b - a)); // notice that this is basically inverselerp from my previous comment
      // Evaluate polynomial
      return t * t * (3f - 2f * t);
      extrapolating from this basic process of merging polynomials let's you create any other smooth ramp

    • Milan Stevic
      Milan Stevic 2 жыл бұрын

      @Kriss Loo "we're performing less operations in the simpler method, aren't we?"
      don't pay too much attention to it. if you don't believe me, benchmark it, it's practically negligible in terms of performance.
      multiplication is VERY fast.

  • Donald Louis John
    Donald Louis John 2 ай бұрын

    Where was this event.? Seems like it was in the States, though she seems to work in Sweden. ……….( I’ll just add in my plea, which i expect to be well received in this company, to allow PHOTOS.! ………….In so many places, including here, photos are a no-no. Let’s open this up.! ) …………….[ Freya.: did U notice how i create space with periods.? Like right here. A period between the last word and the Question mark. Writing seems too crowded to me. ( I’m a painter. ) ]

  • josueurielquintana
    josueurielquintana Ай бұрын

    I woulda burned the whole house when you showed that sine cosine tang simulation graph

  • Alex Steed
    Alex Steed 2 жыл бұрын


  • Home Game Coder
    Home Game Coder  Жыл бұрын +3

    Thank you Freya!
    This is way easier... if the player goes faster, the camera opens to show more world... if it goes slower, it narrows to show more detail!
    playerVelocity = player.velocity.magnitude;
    float i = Mathf.InverseLerp(minVelocity, maxVelocity, playerVelocity);
    float o = Mathf.Lerp(minFieldOfView, maxFieldOfView, i);
    virtualCamera.m_Lens.FieldOfView = o;

    • Dev For Fun
      Dev For Fun 10 ай бұрын

      and if you wanna make a hardcore game do the opposite, since adrenalin causes tunnel vision, that could be used in a horror game

  • Dan
    Dan  Жыл бұрын

    I was thinking she may going to mention lerp. She did!

  • Nobody
    Nobody 2 ай бұрын +1

    I'm an old Electronics engineer, worked on TV sets (you know--REAL TVs with actual Cathode Ray Tubes as a viewing screen) in my younger years. I would LOVE for her to look at the old RCA color guns and explain them from input to light emission. I mean I understood it, probably better than most of my peers, I had no problems troubleshooting them... but I bet she could bring that antiquated circuit theory to life! (BTW--analog is always superior to digital in real life animation---brownie points for any body that can explain why below!)

  • Nobody
    Nobody 2 ай бұрын

    3:00 You couldn't have been more correct in that last statement... I LOVE math...and I always heard: "I'll never need to use this!" Yet people are confused about interest rate calculations and have no idea how to figure out their retirements??? MATH IS VERY IMPORTANT... PAY ATTENTION TO THIS PERSON!!!!!

  • Mads Horn
    Mads Horn 2 жыл бұрын +12

    Shouldn't inverse "Lerp" be "Prel"? ;-)

    RETSA PB  Жыл бұрын +1

    Thought i knew everything about lerps, was dead wrong

  • Pleyland
    Pleyland 3 ай бұрын

    as a user of blender, your exclamation that you can blender between anything doesn't impress me. In blender you can keyframe anything, and it will automatically "lerp" between them, and you have different lerp settings. You can do it with shaders, color, position, size, rotation, anything really

  • Joshua Stein
    Joshua Stein  Жыл бұрын

    she made Budget Cuts??? i almost broke my hand grabbing through the hole in the floor....

  • zett kusanagi
    zett kusanagi  Жыл бұрын +1

    im in love!!!!

  • Ph Pn
    Ph Pn Ай бұрын

    This is computer Graphics 101

  • Rodolfo Xavier Neto
    Rodolfo Xavier Neto  Жыл бұрын

    Thanks from Brazil

  • Kaus05
    Kaus05  Жыл бұрын

    She has a youtube channel if anyone wants

  • Martin Petersson
    Martin Petersson 5 ай бұрын

    Hah I knew it was a bezier as soon as I saw it!

  • Samuel Ferrer
    Samuel Ferrer 3 ай бұрын

    Lots of numbers... in programming? Those who state that are missing the whole point in programming... and math in general ...

  • Hot-Head Cringe
    Hot-Head Cringe Ай бұрын

    [sits on the floor]

  • RDT
    RDT  Жыл бұрын +9

    Man this girl is pretty cute and smart too! Best combo.

    • qq qq
      qq qq 3 ай бұрын +1

      @Infinitesimal Philip the correct term is degenerate

    • Olive
      Olive 10 ай бұрын +5

      @Double Bullet If you're gonna care about stuff like that at least be correct

    • Dev For Fun
      Dev For Fun 10 ай бұрын +4

      @Double Bullet at least be wrong correctly

    • King Bling
      King Bling  Жыл бұрын +1

      @Double Bullet yep

    • Double Bullet
      Double Bullet  Жыл бұрын +4

      @Infinitesimal Philip soo guy? 👍🏻

  • Nobody
    Nobody 2 ай бұрын

    3:42 Yeah... I understood it; but didn't know what it was either....

  • Corrie
    Corrie  Жыл бұрын


  • cup o stuff
    cup o stuff Ай бұрын

    1:03 ayo, who did these captions, she ain't named Franco Murray

  • Qubit
    Qubit 2 жыл бұрын +1


  • XR_XharpRazor Axtra
    XR_XharpRazor Axtra 3 ай бұрын

    my fav part OwO
    is it Lerp ? OwO

  • StickyLab
    StickyLab 2 жыл бұрын +1

    me ,dont understand at whole all ,

  • Fred Erik
    Fred Erik 7 ай бұрын

    that's just some math basics. Expected more from the title.

  • Negative Youtube
    Negative Youtube 2 ай бұрын

    right right right, right?

  • TaHaKa
    TaHaKa 2 жыл бұрын +6


  • k
    k  Жыл бұрын +2

    Why she is so.cute omg

    • lorem ispum
      lorem ispum 4 ай бұрын

      @Luce Quesbe i agree

    • Luce Quesbe
      Luce Quesbe  Жыл бұрын +10

      she uses shader on her skin

  • geddon436
    geddon436 7 ай бұрын +1

    simple math???? where?

  • Erik M
    Erik M 2 жыл бұрын +5

    Whut? i use these all the time. And every else seem to do that too. I dont understand...

    • Dani-Saur
      Dani-Saur 2 жыл бұрын +5

      @Erik M a LOT of game programmers learn through doing, either starting with visual scripting in gamemaker and moving up to stuff like unity, and they won't know the fundamentals

    • Erik M
      Erik M 2 жыл бұрын +2

      ​@Grey Fisher Unless the subject is how a quaternion is implemented i think most programmers also know whay say a lerp does internally.

    • Grey Fisher
      Grey Fisher 2 жыл бұрын +7

      Everyone DOES use these all the time, but the logic underpinning the techniques is seldom actually discussed. That's the point of the video, not to introduce lesser known techniques, but to explain the details of some commonly known techniques.

  • asscancer69 the third
    asscancer69 the third  Жыл бұрын

    Marry me

  • Rob Proctor
    Rob Proctor 2 жыл бұрын

    This is called regression, not progression

  • aa
    aa 2 ай бұрын +1

    Why did his parents call him Freya? It sounds like a girl's name.

  • Atef turki
    Atef turki 2 жыл бұрын +2

    nice slideshow Joachim.

  • qq qq
    qq qq 3 ай бұрын +1

    of course it is not a real one 🤮

  • 2PACBRB2014
    2PACBRB2014 2 ай бұрын +2

    Is that a man?

  • ukranaut
    ukranaut  Жыл бұрын +3

    Is that a dude?

  • constantinos schinas
    constantinos schinas 9 ай бұрын +1

    Sweet and locally smart guy, went to far, for no reason.

  • василий руков
    василий руков 2 жыл бұрын +10

    sound like man,

  • wxwf
    wxwf 5 ай бұрын +2

    disgusting to watch

    • qq qq
      qq qq 3 ай бұрын +2

      @lorem ispum "Patrick Bateman" calls someone an incel ahahahaahahaahahah 😄

    • wxwf
      wxwf 4 ай бұрын +3

      @lorem ispum you mean the guy in the video right?

  • Nohchi
    Nohchi 10 ай бұрын +2

    the hole video i was thinking: "her voice and looks are like of a man".
    I was not wrong, he is a man.

  • SRG Learn Code
    SRG Learn Code 4 ай бұрын

    I've discoverd you thanks to Joy Of Code (he does svelte things and recently he has done something with three.js) I owe him now because you are a great source of knowledge.