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@ -40,7 +40,7 @@ towards executing a TON of **branch-less** or **branch-light** code in parallel-
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code for each pixel on your screen, there are a ton of pixels but they mostly do their own independent logic. </Tip>.
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The updated scene data is then prepped and fed to the **GPU** for **geometry processing**. Here
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we figure out where everything ends up on our screen by doing lots of fancy matrix math.
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we figure out where everything ends up on our screen by doing lots of fancy linear algebra.
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We'll cover this stage in depth very soon so don't panic (yet).
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Afterwards, the final geometric data are converted into <Tip text="pixels"> Pixel is the shorthand for **picture-element**, Voxel is the shorthand for **volumetric-element**. </Tip>
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@ -325,7 +325,7 @@ So far, all the examples show the geometry in NDC (Normalized Device Coordinates
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This is because the **rasterizer** expects the final vertex coordinates to be in the NDC range.
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Anything outside of this range is **clipped** henceforth not visible.
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Yet, as you'll understand after this section, doing everything in the **NDC** is inconvenient and very limiting.
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Yet, as you'll understand soon, doing everything in the **NDC** is inconvenient and very limiting.
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What we'd like to do is to transform these vertices through 5 different coordinate systems before ending up in NDC
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(or outside of if they're meant to be clipped).
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The purpose of each space will be explained shortly. But doing these **transformations** require
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@ -337,8 +337,9 @@ But if you feel extra savvy you may skip the following **linear algebra** sectio
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<Note title="Algebra Ahead!">
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The concepts in the following sections may be difficult to grasp at first. And **that's okay**, you don't
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need to pickup everything the first time you read them. If you feel passionate about these topics
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and want to have a better grasp, refer to the references at the bottom of this article.
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need to pickup everything the first time you read them (I didn't). If you feel passionate about these topics
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and want to have a better grasp, refer to the references at the bottom of this article and **take
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your time** :)
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</Note>
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@ -382,9 +383,15 @@ All **affine** transformations can be represented as matrix operations using **h
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**Scale**
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**Rotation**
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**Translation**
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**Rotation**
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<Note type="info", title="Homogeneous coordinates">
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Why are we using 4D matrixes for vertices that are three dimensional?
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</Note>
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**Embedding it all in one matrix**
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@ -460,8 +467,9 @@ baa
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</Note>
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But don't get over-confident yet, this is the **simple** part of the view matrix that handles only
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the **position**. But in any worthwhile game we need to **look around** too and orient ourselves.
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** Position **
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** Orientation **
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We can **rotate** the camera, or more accurately **reverse-rotate** the world, via 3 unit vectors snuggled
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inside a matrix, the **up** vector (U), the **target** or **direction** vector (D) and the **right**
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@ -495,16 +503,34 @@ to the **local space** vertices of our model:
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That's two down, one left to slay!
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## Coordinate system -- Clip Space
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This one is gonna get a little complicated so buckle up :)
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">>>>>" need to study more for the rest of the coordinates section, forgot every fucking thing I knew...
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**Overview***
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**Aspect Ratio***
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**Field of view***
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**Normalization***
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**Putting it all together**
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<Note tye="math", title="Model_View transformation">
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```math
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\text{model}_M * \text{view}_M * \text{projection}_M * \text{local}_V
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```
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</Note>
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## Coordinate system -- Screen Space
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** Viewport transform **
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## Coordinate system -- Recap
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<Note title="Coordinate System", type="diagram">
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</Note>
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## Vertex Shader
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@ -530,18 +556,15 @@ than only positions.
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<Note title="Reviewers", type="review">
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Mohammad-Reza Nemati
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MMZ ❤️
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</Note>
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<Note title="Books", type="resource">
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[Tomas Akenine Moller --- Real-Time Rendering 4th Edition (referenced multiple times)](https://www.realtimerendering.com/intro.html)
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[JoeyDeVriez --- LearnOpenGL - Hello Triangle](https://learnopengl.com/Getting-started/Hello-Triangle)
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[JoeyDeVriez --- LearnOpenGL - Face Culling](https://learnopengl.com/Advanced-OpenGL/Face-culling)
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[JoeyDeVriez --- LearnOpenGL - Coordinate Systems](https://learnopengl.com/Getting-started/Coordinate-Systems)
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[JoeyDeVriez --- LearnOpenGL - Transformations](https://learnopengl.com/Getting-started/Transformations)
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[JoeyDeVriez --- LearnOpenGL - Camera](https://learnopengl.com/Getting-started/Camera)
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[Tomas Akenine Moller --- Real-Time Rendering](https://www.realtimerendering.com/intro.html)
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[Gabriel Gambetta --- Computer Graphics from Scratch](https://gabrielgambetta.com/computer-graphics-from-scratch/)
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[JoeyDeVriez --- LearnOpenGL](https://learnopengl.com/)
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</Note>
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<Note title="Wikipedia", type="resource">
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@ -555,24 +578,26 @@ Mohammad-Reza Nemati
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<Note title="Youtube", type="resource">
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[Miolith --- Quick Understanding of Homogeneous Coordinates for Computer Graphics](https://www.youtube.com/watch?v=o-xwmTODTUI)
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[Leios Labs --- What are affine transformations?](https://www.youtube.com/watch?v=E3Phj6J287o)
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[3Blue1Brown --- Essence of linear algebra (highly recommended playlist)](https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)
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[3Blue1Brown --- Quaternions and 3d rotation, explained interactively](https://www.youtube.com/watch?v=zjMuIxRvygQ)
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[pikuma --- Math for Game Developers (playlist)](https://www.youtube.com/watch?v=Do_vEjd6gF0&list=PLYnrabpSIM-93QtJmGnQcJRdiqMBEwZ7_)
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[pikuma --- 3D Graphics (playlist)](https://www.youtube.com/watch?v=Do_vEjd6gF0&list=PLYnrabpSIM-97qGEeOWnxZBqvR_zwjWoo)
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[pikuma --- Perspective Projection Matrix](https://www.youtube.com/watch?v=EqNcqBdrNyI)
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[Cem Yuksel --- Introduction to Computer Graphics (playlist)](https://www.youtube.com/watch?v=vLSphLtKQ0o&list=PLplnkTzzqsZTfYh4UbhLGpI5kGd5oW_Hh)
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[javidx9 --- Essential Mathematics For Aspiring Game Developers](https://www.youtube.com/watch?v=DPfxjQ6sqrc)
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...
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</Note>
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<Note title="Stackoverflow", type="resource">
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<Note title="Articles", type="resource">
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[Why do 3D engines primarily use triangles to draw surfaces?](https://stackoverflow.com/questions/6100528/why-do-3d-engines-primarily-use-triangles-to-draw-surfaces)
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[Stackoverflow --- Why do 3D engines primarily use triangles to draw surfaces?](https://stackoverflow.com/questions/6100528/why-do-3d-engines-primarily-use-triangles-to-draw-surfaces)
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[The ryg blog --- The barycentric conspiracy](https://fgiesen.wordpress.com/2013/02/06/the-barycentric-conspirac/)
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[Juan Pineda --- A Parallel Algorithm for Polygon Rasterization](https://www.cs.drexel.edu/~deb39/Classes/Papers/comp175-06-pineda.pdf)
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[Kristoffer Dyrkorn --- A fast and precise triangle rasterizer](https://kristoffer-dyrkorn.github.io/triangle-rasterizer/)
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</Note>
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<Note title="Vulakn Docs", type="resource">
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<Note title="Documentations", type="resource">
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[Drawing](https://docs.vulkan.org/spec/latest/chapters/drawing.html)
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[Pipeline Diagram](https://docs.vulkan.org/spec/latest/_images/pipelinemesh.svg)
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[Vulkan Docs --- Drawing](https://docs.vulkan.org/spec/latest/chapters/drawing.html)
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[Vulkan Docs --- Pipeline Diagram](https://docs.vulkan.org/spec/latest/_images/pipelinemesh.svg)
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</Note>
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