---
title: The Graphics Pipeline --- Rasterization
date: "April 20 - 2025"
---

<script>
import Image from "../../Image.svelte"
import Note from "../../Note.svelte"
import Tip from "../../Tip.svelte"
</script>

## Rasterization

**Bounding Box**

**Winding order**

**P needs to be on the "RIGHT" side of a->b**

**Cross Product**

**Interpolation**

Remember the god forsaken **input assembler**? Let's expand our understanding of it
since-- for simplicity's sake, we skipped over the fact that **vertices** can hold much, much more data
than only positions.

**Barycentric Interpolation** NOTE NOT linear interpolation

**Some Optimizations**

<Note title="Software Rasterization">

What we've implemented is a simple toy rasterizer written to be run on the CPU for educational
purposes only. It is inefficient, has shit precision (integer precision) thus it is choppy when moving things around, and has many problems.
However, GPUs have dedicated hardwares that run incredibly optimized algorithms to do this
sort of thing; hence what we made is called a **software** rasterizer ---as opposed to the usual
**hardware** rasterizer.

It's nice to be aware of and appreciate the simplicity of triangles. If our polygons had variable
number of edges then it would be really difficult to come up with efficient algorithms for doing this.

</Note>

## Sources

<Note title="Reviewers", type="review">

MMZ ❤️

Grammarly

Some LLMs

</Note>

<Note title="Books", type="resource">

[Joey De Vriez --- LearnOpenGL](https://learnopengl.com/)
[Tomas Akenine Moller --- Real-Time Rendering (4th ed)](https://www.realtimerendering.com/intro.html)
[Gabriel Gambetta --- Computer Graphics from Scratch](https://gabrielgambetta.com/computer-graphics-from-scratch/)
</Note>

<Note title="Wikipedia", type="resource">

[Polygonal Modeling](https://en.wikipedia.org/wiki/Polygonal_modeling)
[Non-uniform Rational B-spline Surfaces](https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline)
[Computer Aided Design (CAD)](https://en.wikipedia.org/wiki/Computer-aided_design)
[Rasterization](https://en.wikipedia.org/wiki/Rasterisation)
[Euclidean geometry](https://en.wikipedia.org/wiki/Euclidean_geometry)
</Note>

<Note title="Youtube", type="resource">

[Miolith --- Quick Understanding of Homogeneous Coordinates for Computer Graphics](https://www.youtube.com/watch?v=o-xwmTODTUI)
[Leios Labs ---  What are affine transformations?](https://www.youtube.com/watch?v=E3Phj6J287o)
[3Blue1Brown --- Essence of linear algebra (highly recommended playlist)](https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)
[3Blue1Brown --- Quaternions and 3d rotation, explained interactively](https://www.youtube.com/watch?v=zjMuIxRvygQ)
[pikuma --- Math for Game Developers (playlist)](https://www.youtube.com/watch?v=Do_vEjd6gF0&list=PLYnrabpSIM-93QtJmGnQcJRdiqMBEwZ7_)
[pikuma --- 3D Graphics (playlist)](https://www.youtube.com/watch?v=Do_vEjd6gF0&list=PLYnrabpSIM-97qGEeOWnxZBqvR_zwjWoo)
[Cem Yuksel --- Introduction to Computer Graphics (playlist)](https://www.youtube.com/watch?v=vLSphLtKQ0o&list=PLplnkTzzqsZTfYh4UbhLGpI5kGd5oW_Hh)
[Cem Yuksel --- Interactive Computer Graphics (playlist)](https://www.youtube.com/watch?v=UVCuWQV_-Es&list=PLplnkTzzqsZS3R5DjmCQsqupu43oS9CFN&pp=0gcJCV8EOCosWNin)
[javidx9 --- Essential Mathematics For Aspiring Game Developers](https://www.youtube.com/watch?v=DPfxjQ6sqrc)
</Note>

<Note title="Articles", type="resource">

[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)
[The ryg blog --- The barycentric conspiracy](https://fgiesen.wordpress.com/2013/02/06/the-barycentric-conspirac/)
[Juan Pineda --- A Parallel Algorithm for Polygon Rasterization](https://www.cs.drexel.edu/~deb39/Classes/Papers/comp175-06-pineda.pdf)
[Kristoffer Dyrkorn --- A fast and precise triangle rasterizer](https://kristoffer-dyrkorn.github.io/triangle-rasterizer/)
[Microsoft --- Rasterization Rules](https://learn.microsoft.com/en-us/windows/win32/direct3d11/d3d10-graphics-programming-guide-rasterizer-stage-rules)
</Note>

<Note title="Documentations", type="resource">

[Vulkan Docs --- Drawing](https://docs.vulkan.org/spec/latest/chapters/drawing.html)
[Vulkan Docs --- Pipeline Diagram](https://docs.vulkan.org/spec/latest/_images/pipelinemesh.svg)
</Note>