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Perspective Projection Matrix (Math for Game Developers)

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  • čas přidán 17. 08. 2024
  • In this video you'll learn what a projection matrix is, and how we can use a matrix to represent perspective projection in 3D game programming.
    You'll understand the derivation of a perspective projection matrix in 3D computer graphics. The matrix I'll derive is as used by left-handed coordinate systems like DirectX (OpenGL uses a right-handed system).
    In perspective projection, objects that are far away appear smaller, and objects that are close to us appear bigger. We will learn how to perform this type of 3D projection using a projection matrix.
    This is a very useful tool for 3D programmers, game developers, and other computer graphics professionals. Understanding the math behind how projection is achieved is important, and I want you to own this knowledge at the end of this video!
    For comprehensive courses on computer science, programming, and mathematics, visit: www.Pikuma.com.
    Don't forget to subscribe to receive updates and news about new courses and tutorials:
    / @pikuma
    Enjoy!

Komentáře • 122

  • @3rdGen-Media
    @3rdGen-Media Před rokem +17

    To those still scratching their heads after watching the end of this video and putting the perspective divide in your [vertex] shader here is the conclusion he left out:
    The output of the vertex shader is expected to be in Clip Space -- not NDC space (that is, with the projection matrix applied to the camera space vec4 but without perspective divide). Then, AFTER the fragment shader has run and the depth of each fragment has been determined the perspective divide is handled implicitly by the shader pipeline by dividing the values in the depth buffer by the w value stored in the output of the vertex stage.
    Also, contrary to his statements, both modern OpenGL and DirectX assume Clip Space to be a left-handed coordinate system. Vulkan assumes Clip Space to be right handed (with the positive Y axis facing down). Rather, OpenGL's Clip Space expects the near and far plane to be mapped into the -1, 1 range whereas DirectX and Vulkan expect the near and far plane to be mapped into the 0, 1 range.

  • @Password_1234
    @Password_1234 Před rokem +24

    This was *exactly* what I was looking for! Most tutorials are either way too simplistic, are focused on using specific game engines, or are so incredibly advanced that you need a PhD level to understand them. Your tutorial hit that exact sweet spot in the middle, where you get complete, detailed info, but can still understand it without already having ten years of experience. This vid made me subscribe.

  • @andreypopov6166
    @andreypopov6166 Před rokem +1

    I was super lucky to find this channel. After picking up some C/C++ and Linear algebra basics will definitively proceed a paid course about CG, Game engine and Raycasting to finally start my computer graphics journey after 20 years of procrastination :)

  • @florimonpoisson4718
    @florimonpoisson4718 Před rokem +4

    That feeling when you find that one video that answers all of your questions👍👌👌👌 thanks for the amazing explanation

  • @yusuf3728
    @yusuf3728 Před 2 lety +25

    Is this a joke, I just started learning rendering stuff and you just posted about the subject I was searching for. Your channel is a gem keep up the good work and thank you soo much for this quality content!

  • @starc0w
    @starc0w Před 2 lety +12

    Thank you for the great video! By the way, congratulations for completing the new physics tutorial. Another one that I really want to do!
    I can imagine that the last few weeks have been tough. It is often like that on the last mile of a project, right?
    Do you already have an idea of what topic you will do next?

  • @rigbyb
    @rigbyb Před 10 měsíci +2

    This is the best video I've seen explaining how this perspective projection matrix works. Thank you so much! 😊

  • @Seewolf1971
    @Seewolf1971 Před 10 měsíci +3

    Thats the best video i have seen in the last months i subscribed to your channel and liked the video keep it up you did a great job

  • @alastairtheduke
    @alastairtheduke Před 8 měsíci

    Took me weeks of learning this in school and it's summarized into one short video. Great job

  • @kellybmackenzie
    @kellybmackenzie Před rokem +9

    Your channel is amazing, muito obrigada!!

  • @flwi
    @flwi Před rokem +3

    Excellent explanation! Very well done and paced. I learned a lot!

  • @deinemama6303
    @deinemama6303 Před 2 lety +3

    Very nice and detailed explanation. Thank you very much!

  • @grtgoalsgrtgoal1247
    @grtgoalsgrtgoal1247 Před 7 měsíci

    All I can say after watching this video is awesome. You are the best by far compared to other videos on this topic.

  • @arielpajares4199
    @arielpajares4199 Před 8 měsíci +3

    this video is just something else, it explains so well a really complex thing.

  • @deathTurgenev
    @deathTurgenev Před 10 měsíci

    Wonderfully explained. Clear and thorough

  • @matheusreidopedaco
    @matheusreidopedaco Před 7 měsíci +1

    You deserve 1 trillion views.

  • @benwinstanleymusic
    @benwinstanleymusic Před měsícem

    Great video, thank you so much

  • @Metacious
    @Metacious Před 2 lety +3

    I'm already saving for the 2D Physics game course :)
    Just saying, I'm enjoying the Raycasting course while at it

    • @pikuma
      @pikuma  Před 2 lety +1

      No rush. 🙂 Enjoy every minute of it!

  • @ooichu_
    @ooichu_ Před 2 lety +3

    Thank you!

  • @wwaya
    @wwaya Před rokem +1

    this is the best video for beginner

  • @charliethreesome8407
    @charliethreesome8407 Před 7 měsíci

    I think you dropped this man 👑

  • @NonTwinBrothers
    @NonTwinBrothers Před 2 lety +3

    Fuck yesss, I have yet to watch but I'm glad to see this!

  • @somesome1315
    @somesome1315 Před 9 měsíci

    great explanation. I was learning shader stuff and it helped a lot

  • @shahroozleon9098
    @shahroozleon9098 Před 2 lety +1

    thanks so much, this was very useful and handy for me

  • @GodbornNoven
    @GodbornNoven Před rokem +5

    Why do we multiply x by the aspect ratio but not y?

    • @neuralworknet
      @neuralworknet Před 11 měsíci

      this is exactly what i wonder

    • @ohanime5755
      @ohanime5755 Před 7 měsíci +2

      Because it is a ratio between the x and y axis, specifically the width and the height which means one of the them is the base which always will be 1.0 or 100% whereas the other will have a percentage that based on the aforementioned base. For instance, a screen with 500 pixels height and 1000 pixels width will have an aspect ratio of 0.5:1. The reason why you only multiply x and not y is because once again it is a ratio, if you multiply both of them means nothing has change and this is not we wanted. Assuming that an object originally comes from a space that is considered square, the distribution of the values across x-axis and y-axis are equal but that is not the case in the screen space because its width and height are not equal. For example, a square with one of its vector as 0.5x, 0.5y if converted onto the screen space without multiplying the aspect ratio, what will happens? 0.5y = 50% of the height and 0.5x = 50% of the width and 50% of 500pixels and 50% of 1000pixels are clearly not the same. However if you now multiply x with 0.5 (the aspect ratio that we just calculated), 0.5x0.5 = 0.25, and 25% of 1000 pixels is indeed equal to 50% of 500pixels thus the square is now rendered correctly on the screen space

  • @nihits
    @nihits Před 7 měsíci +1

    It seems the calculation you have done for perspective projection martix assumes Z from 0 to 1 (to get Zf/(Zf-Zn) and -ZfZn/(Zf-Zn)) and not -1 to 1. for -1 to 1 the values would calculate to be (Zf+Zn)/(Zf-Zn) and -2ZfZn/(Zf-Zn).

  • @spgaming6089
    @spgaming6089 Před měsícem

    Hi Sir, I have on question - So, Extra added fourth column and row in our matrix is it for translation or perspective view?? or there is two separate matrix for projection and translation? can you please give me more information about this. And thank you so much for lecture I found your content best among all the available content related to graphics

  • @serhiybutz
    @serhiybutz Před 8 měsíci

    An amazing explanation!

  • @brunorafael6497
    @brunorafael6497 Před rokem +1

    Please correct if i am wrong: the normalization of z to 0 and 1 considering that what we are seing is between znear and zfar should be z' = (z-znear)/(zfar-znear), is not that?

  • @alexfrozen
    @alexfrozen Před měsícem +2

    1 / tan is cotan, isn't it? Divisions are evil in fast computations.

    • @pikuma
      @pikuma  Před měsícem

      @@alexfrozen Yes, that's correct. 🙂

  • @krystof7059
    @krystof7059 Před 2 lety +3

    I still don't understand why do we need zfar and znear.. what would happen if we didn't use them?

    • @pikuma
      @pikuma  Před 2 lety +1

      Hi krystof. They define what is visible in terms of depth. What is the closest and the furthest z value we will consider for the projection in the screen? Everything outside znear and zfar we won't consider.
      Another goal of the near and far planes is when we clip (see my video about the stages of the graphics pipeline), so we don't try to project verrices that are too close to the eye-point. If we try to project and divide by zero (division by z in the perspective divide) that would be a problem.

  • @Smash_ter
    @Smash_ter Před rokem +1

    I wonder how I could apply this with regards to VR and canted or non-parallel displays, as those view matrices are completely different both from a flat screen and each eye. Like for instance, in the left eye m20 is the inverse of m02 and m00 is the same value as m22. This is extremely hard to figure out

    • @pikuma
      @pikuma  Před rokem

      Hm, are you sure it's not simply a different handiness or system (like OpenGL) that achieves something similar but using different matrix entries?
      Can you kindly point out the resource you're using? 🙂

  • @kekt536
    @kekt536 Před měsícem

    I understood alot but ultimately confused. What to do when the camera is not point towards z? How does it work if the camera is pointing towards an object with z = 0?

  • @bizarrapmusic
    @bizarrapmusic Před rokem +1

    I understand this, however i still don't get how you pass from 3d coordenates to 2d, since the screen is actually a 2d raster, once you have the 3d coordenates, how do you represent the points in 2d? i'm stuck with this. Great videos btw, by far the best ones i've seen about computer graphics.

    • @pikuma
      @pikuma  Před rokem +2

      After the perspective-divide (where we divide both x's and y's by z), we simply plot a pixel at point (x,y) on the screen. It's almost likecwe forget there was a z, and we draw the x & y on the 2D screen.

    • @bizarrapmusic
      @bizarrapmusic Před rokem

      @@pikuma Thanks for the response! this actually clarified a lot for me.

  •  Před 2 lety +1

    Thank you so much!

  • @LuskyMJ
    @LuskyMJ Před rokem +2

    14:27 In this part you keep switching between whether the range is 0 to 1 or the range -1 to 1

    • @pikuma
      @pikuma  Před rokem +1

      Hi. I think I meant "0 to 1" for values that are in front of us.

    • @LuskyMJ
      @LuskyMJ Před rokem +1

      @@pikuma Hello. Thanks for answering back. I'm having a bit of an issue that I can't really solve though. Normally the camera in view space is oriented to face towards the -Z direction. I have a near clipping plane of 1 and a far clipping plane of 100. This would mean that all the points that should fit inside the clip box should have a z value between -1 and -100 since I'm facing the -Z direction. For some reason tho it's reversed so only the values between 1 and 100 are inside the clipping box (have a final z value between 0 and 1).
      I just figured out how to fix this while typing the comment but I'm going to post it anyway because it might help someone in the future. I fixed it by using negative values for my near and far z planes. So instead of Znear being 1 it's equal to -1 and likewise Zfar is equal to -100 instead of 100. I have no idea whether it's normal to use negative values for clipping planes but that's what I've done to fix my issue.
      Edit: DON'T DO THIS. The x and y components are going to flip sign (negative becomes positive and vise verca)

  • @DH-oj2ru
    @DH-oj2ru Před měsícem +1

    Could anyone explain where he got the scaling factors for normalizing z from? Totally lost me when it got to zfar/zfar-znear and -zfar*znear/zfar-znear.
    Great video, its just that I eould like to actually understand where the math comes from and not just copy and paste formulas.

    • @deroll_sweet
      @deroll_sweet Před měsícem

      It's essentially a unit conversion. The first term is a scaling factor that will squeeze the numbers between Znear and Zfar to the space between 0 and 1 with an offset. It's offset because the 0's don't line up in the two unit systems. Since Znear will become 0 after normalization we subtract it (after converting it with the scaling factor) from the scaled z. This will shift all the values to between 0 and 1, no offset.
      An alternative method would be to subtract Znear from z (line up the 0's). Then divide it by Zfar - Znear (scale between 0 and 1, no offset). This method breaks the matrix step though.

    • @laskdjf3880
      @laskdjf3880 Před měsícem

      @@deroll_sweet What do you mean exactly by it's offset 'because the 0s don't line up with the two unit systems'? I'm trying to figure out how to derive this scale factor but I can't :(

    • @hodayfa000h
      @hodayfa000h Před měsícem

      How the fuck did i understand this?​@@deroll_sweet

  • @simonvandenbroek6384
    @simonvandenbroek6384 Před rokem

    This is really well explained. do you go into more depth in your course "3D computer graphics?"

    • @pikuma
      @pikuma  Před rokem

      Sure. We cover a simplified (but complete) pipeline.

  • @Tobis0x00
    @Tobis0x00 Před rokem

    @pikuma looking at your equation, if z = znear, it looks like the outputted z value is going to be 0. From your explanation of NDC, shouldn't it equal -znear?

  • @amarelswtor5446
    @amarelswtor5446 Před 2 lety

    @Pikuma Please correct me if I'm wrong, but if you define aspect as height / width, then you don't need to inverse fov formula. I.e. when aspect = h /w, then fov = tan (angle / 2). Inversion is needed if aspect = width / height.

    • @pikuma
      @pikuma  Před 2 lety +1

      Hi @AmarelSWTOR. That's a good question. I thought the inversion was needed to correctly set the FOV angle as "inversely proportional" to how we scale the screen x and y. The FOV I'm using in the code is the vertical FOV (= h/w).

    • @Dannnneh
      @Dannnneh Před rokem

      Is this true?

    • @igz
      @igz Před rokem

      @@Dannnneh it's true

  • @solomonchild5
    @solomonchild5 Před 4 měsíci

    Is there any logic/intuition behind the lambda expression? I'm looking everywhere for derivation of that, but can't find any info.

    • @laskdjf3880
      @laskdjf3880 Před měsícem

      Did you ever figure it out? I need it too lol

  • @theman7050
    @theman7050 Před 5 měsíci

    Brilliant. Thanks

  • @joaquimjesus6134
    @joaquimjesus6134 Před rokem +1

    i need understand somethings:
    1 - after the projection, i can use the X and Y normaly without Z?
    2 - seen the matrix projection function, the parameters, the 'aspect' is the H/W... understand.... but what is the best for 'fov', ZNear and ZFar values?

    • @pikuma
      @pikuma  Před rokem +2

      Hi Joaquim. After the projection we usually render points (x,y) on the screen.
      That works ok, but in reality GPUs store the old z (depth) value with the projected point because it is useful for certain computations later (like texture mapping our polygons on the screen considering perspective). We need the z (actually 1/z) for that!
      Znear and Zfar you can manually choose for your game as you want. Some games use a very big Zfar, while others use a very small Zfar (and we can see less objects at the distance).
      Back in the day of slow machines we used small Zfar values (clipping objects to improve CPU performance). Sometimes we even added a *fog* effevt to mask that visible/aggressive far clipping.

    • @joaquimjesus6134
      @joaquimjesus6134 Před rokem

      @@pikuma thank so much for all. Do you have a video that uses a projection and dots/lines? I need learn more things ;)

    • @pikuma
      @pikuma  Před rokem +1

      @@joaquimjesus6134 Sure. I have the lectures on 3D graphics at pikuma.com that cover a complete software renderer.

    • @joaquimjesus6134
      @joaquimjesus6134 Před rokem

      @@pikuma thank you so much. Correct me anotherthing what is the best 'fov'?

    • @pikuma
      @pikuma  Před rokem +1

      @@joaquimjesus6134 Same thing, some games like 60 degrees, other games use 90 degrees... it depends on what's the angle of opening you want and how many objects you want to see inside your 'field of view' in your game.
      There's no correct answer. 🙂
      Abraços!

  • @Error-pb6ee
    @Error-pb6ee Před rokem

    great work and great explanation! thank you very much!

    • @Error-pb6ee
      @Error-pb6ee Před rokem

      i have a question, how can i determine de angle of a normal inside the projection matrix? i mean, how can i determine if a side of a cube is currently visible to the projection matrix?

    • @pikuma
      @pikuma  Před rokem

      Glad it was helpful! 🙂

  • @gavinkistnerus3895
    @gavinkistnerus3895 Před 11 měsíci

    Why would you divide `result.z / result.w` at the very end? What is the point of "perspective shrinking" the distance factor? Seems an unnecessary step, particularly if z was already normalized.

    • @pikuma
      @pikuma  Před 11 měsíci

      The normalization of the z values (value between 0 and 1) happens *after* the perspective divide.

  • @redfoxartist7548
    @redfoxartist7548 Před 3 měsíci +1

    dude, your brazilian is pretty strong, i can tell it by the tone

    • @pikuma
      @pikuma  Před 3 měsíci

      I'm glad. 🙂

  • @MrNickolay1986
    @MrNickolay1986 Před 2 měsíci

    I don't understand how just dividing by w you can normalize everything.
    If I have this vertex { -2.0, 0.0, 0.5 } and my projection parameters are fov = 60, aspect = 1.0, Znear = 0.1 and ZFar = 1000, I get w = 0.5. Projected X will be -3.46 and obviously, if you divide -3.46 by 0.5 it's the same as doubling it.

  • @ajinkyasanas2256
    @ajinkyasanas2256 Před 2 lety +1

    Great Tutorial I understood a lot but still my tiny brain can't handle some things.

  • @AmaanHasanDilawar
    @AmaanHasanDilawar Před rokem

    Awesome ♥♥

  • @ProGamer1115
    @ProGamer1115 Před 7 měsíci +1

    15:36 is what I don't get. How is λ derived? I've spent 3 days over this and still don't get it. Everything else is pretty easy

    • @rozt107
      @rozt107 Před 3 měsíci +1

      can relate lol

    • @laskdjf3880
      @laskdjf3880 Před měsícem

      Did you ever figure it out lol (I can't figure it out either)

    • @rozt107
      @rozt107 Před měsícem +1

      @@laskdjf3880 i ended up just copying math (or even using math library). Its easy to encapsulate and forget about it

  • @losertrader4925
    @losertrader4925 Před 2 měsíci

    I get it now. The bigger the field of view, the bigger the objects 😂

    • @pikuma
      @pikuma  Před 2 měsíci

      😱 Oh no! Hahaha.

  • @jonpritzker9709
    @jonpritzker9709 Před 5 měsíci

    I’m embarrassed, but why do we multiply the x component by the whole aspect ratio, instead of multiplying x by screen width and y by screen height? The unadjusted screen is a unit square, and we’re just stretching the square to fit the (rectangular) monitor. What am I missing?

    • @neoncyber2001
      @neoncyber2001 Před 3 měsíci +1

      Because it's a ratio. Like 1.5 to 1 The y is always multiplied by 1 and the x by 1.5. Because it's always a something to one we drop the 'to one' part.

    • @jonpritzker9709
      @jonpritzker9709 Před 3 měsíci

      @@neoncyber2001 so like y = 1 and x = 1(x/y). Where y is 1?

  • @stevenriofrio7963
    @stevenriofrio7963 Před rokem

    I need to understand something. The projection matrix receives the vertices of the world objects already normalized, or the matrix takes care of normalizing them in ranges from one to minus -1.

    • @pikuma
      @pikuma  Před rokem

      The projection matrix receives the values as they are in world space (not normalized), and the normalization of x's, y's, and z's (between -1 and 1) happens as we multiply the proj.matrix and also after the perspective divide (which i
      performs the division by w).

    • @stevenriofrio7963
      @stevenriofrio7963 Před rokem +1

      @@pikuma When it refers to world values, it refers to values ​​that are outside the range -1 and 1 for example I can put an arbitrary value for a vertize, maybe (5.0,2.0,3.0), then the matrix will take care of normalizing it so that are within that range (1 -1).

    • @pikuma
      @pikuma  Před rokem

      @@stevenriofrio7963 Yes, world space is basically any value in the 3D world... (0,0,-3.6), or (-4.5, 5.8, 47.0), etc.

    • @stevenriofrio7963
      @stevenriofrio7963 Před rokem

      @@pikuma The last question. If I provide one of my vertices with a z coordinate of (60.0) and my "zfar" is 20.0, will it not be seen on the screen? . Thank you very much for responding.

    • @pikuma
      @pikuma  Před rokem

      @@stevenriofrio7963 There's a little more to it, and it involves something called clipping. There is a stage where we clip all the triangles to only have objects inside the view frustum. The clipping happens at the top, bottom, left, right, and also the near and far planes. That's why vertices outside znear and zfar get discarded (clipped out of our final view) and we only render objects inside the view (between -1 and 1).

  • @marcosbarceloperez1039
    @marcosbarceloperez1039 Před rokem +6

    I don't understand anything about normalizing z.

    • @dijik123
      @dijik123 Před 2 měsíci

      Maybe I m wrong, Ur eyes or not on top of the screen Ur eyes are behind the screen and there is some distance between U and the screen as well, what I believe is that we R trying to place the objects as if Ur eyes are on the screen rather than u sitting on a chair, it would be not same like for example in an first person shooter games the player is u and what Ur seeing in the world is as if Ur seeing in that world and not behind the screen is what is done is what I believe, zfar is in terms of zfar from the perspective as if Ur eyes is on the screen not zfar Ur from the chair, and place the objects as if Ur eyes R on the screen not when ur sitting on the chair n looking at it, it's more realistic if ur eyes are on the screen rather than from u sitting on a chair

  • @joaquimjesus6134
    @joaquimjesus6134 Před rokem

    have have seen these video sometimes and i will see it more. theres 1 thing that you don't speak: do i need convert Degrees to Radiians? the computer don't use Radians instead Degrees?

    • @pikuma
      @pikuma  Před rokem +1

      Most graphics frameworks expect values to be in radians. Degreesxare only used to display or input angles from the user via UI. In programming, it's usually all done in radians.

    • @joaquimjesus6134
      @joaquimjesus6134 Před rokem

      @@pikuma thank you so much for all

  • @SkrovnoCZ
    @SkrovnoCZ Před rokem

    19:40 I'm not sure why but I don't understand the yellow part with the minus sign. Is it multiplied by w aswell or is it just incremented without multiplication?
    (the negative value to the z when doing x*0+y*0+z*(far/(dist))+(-(far/(dist))) or is it x*0+y*0+z*(far/(dist))+W*(-(far/(dist)))?)

    • @pikuma
      @pikuma  Před rokem +1

      Good question. So, the element [3,3] of the matrix multiplies Z, and the element [3,4] of the matrix multiplies by 1 but subtracts from the previous value of [3,3]*Z.
      It is:
      (zfar/(zfar-znear)) * Z - (znear*(zfar/(zfar-znear))) * 1
      All this will be stored in the final vector Z component.

    • @SkrovnoCZ
      @SkrovnoCZ Před rokem

      @@pikuma Oh thanks for explanation. I'm learning this because I'm trying to render things without OpenGL or anything.
      I'm still having problems with transforming Vector in 3D space to normalized Vector of the screen.

    • @pikuma
      @pikuma  Před rokem +1

      @@SkrovnoCZ Hm, I see. I believe OpenGL uses a different perapective projection matrix than the one I mentioned. All the same tasks are still basically the same, but the handedness and the final normalization is a bit different.
      For a breakdown of OpenGL "way of doing projectio ", this website is great:
      www.songho.ca/opengl/gl_projectionmatrix.html

    • @SkrovnoCZ
      @SkrovnoCZ Před rokem

      @@pikuma Thanks. I'm not using OpenGL because I don't understand it. I'm just doing printf() of a prepared string which will output 3D shapes.
      You are explainig it great btw.
      Do you also have a video about "Clipping" in image space? (when a triangle is on the borders of the image space then 3 points of that triangle become 4 which will result in cutting the remainig part out of bounds so the triangle will become a rectangle?)

    • @pikuma
      @pikuma  Před rokem

      @@SkrovnoCZ Sure. All the pipeline is covered in our lectures at pikuma.com, including clipping. Although we do frustum clipping in world space in our code.

  • @jingseng2129
    @jingseng2129 Před 17 dny

    pretty sure aspect ratio is w/h. or am i mistaken?

    • @pikuma
      @pikuma  Před 16 dny

      Hi there. Did I make a mistake? So, for example, if we have a resolution of 800x600, the factor that we are looking for to multiply our x component is 0.75. That is h/w, no?

  • @lanchanoinguyen2914
    @lanchanoinguyen2914 Před rokem

    I don't understand lambda much,why don't we divide zfar÷znear = ratio? But zfar÷(zfar-znear)????

  • @Felipekimst
    @Felipekimst Před 7 měsíci +1

    Eyes on the prize! This guy is a national pride haushs
    I was wondering, isn't the following matrix correct?
    projectionMatrix = [
    [aspectRatio * FOV, 0, 0, 0],
    [0, FOV, 0, 0],
    [0, 0, lambda, 1 ],
    [0, 0, -lambdaOffset, 0],

    ]
    since we have to subtract the lambdaOffset for the Z component, wouldnt it be better if it was in the 3rd column? (, '-')a

    • @Felipekimst
      @Felipekimst Před 7 měsíci +1

      I just spotted the difference!
      i was doing the vector[1x4] . [4x4]matrix
      you're doing the matrix[4x4] .[4x1] vector

    • @Felipekimst
      @Felipekimst Před 7 měsíci

      but unfortunately, my rendering is still all messed up

  • @claudiocampofelice4507
    @claudiocampofelice4507 Před 2 lety +1

    What are the values of fov, znear and far? How can I get them?

    • @pikuma
      @pikuma  Před 2 lety +1

      You can pick them yoursef. Some games use a FOV of 60°, others 50°, etc.
      Znear and Zfar the same thing. Some games have a znear of 100, others 1000.
      It's up to you, the programmer.

    • @claudiocampofelice4507
      @claudiocampofelice4507 Před 2 lety

      @@pikuma okk got you! Thank u!

  • @pietrononame4945
    @pietrononame4945 Před 13 dny

    First, we do not need matrices to calculate Xp and Yp. Matrices will not do much if you do not understand how to manipulate the 3d vertices without them :) Aspect ratio is not needed at all, because you do not change the aspect ratio of displayed objects. In real life cameras eye and lense does not care about aspect ratios - the fov angle is always the same. zfar is not needed at all. People stop complicating easy things.

  • @alexfish7792
    @alexfish7792 Před rokem

    (zFar / zFar-zNear) will never be between 0 and 1... Think about it. (10/10-1) or (100/100-20).

    • @pikuma
      @pikuma  Před rokem +1

      My understanding is that this z "normalization" will happen after the perspective divide, placing the z values between 0 and 1 (in front of us in a left-handed system). Or simply -1 and 1 in most APIs.

    • @alexfish7792
      @alexfish7792 Před 6 měsíci

      @@aprile1710 I was able to build an engine without this part. I use the following matrix below, then I perform perspective division. Works just fine without this step. (See link below)
      // Perspective Projection Matrix
      float persp[4][4] = {
      {aspect * 1/tan(fov/2), 0, 0, 0},
      {0, 1/tan(fov/2), 0, 0},
      {0, 0, 1, 0},
      {0, 0, -1, 0}
      };
      czcams.com/video/IO9sT3t2fSc/video.html&ab_channel=AlexFish

  • @AntoineVanGeyseghem
    @AntoineVanGeyseghem Před rokem

    :D

  • @adrok8644
    @adrok8644 Před 5 měsíci

    its a shame he ruined the video by flashing his satan hands all the way through it.