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light7734 2025-05-05 16:54:00 +03:30
parent edde7d66cc
commit 4c6b0983dd
Signed by: light7734
GPG key ID: B76EEFFAED52D359
11 changed files with 371 additions and 441 deletions
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47
mdsvex.config.js
View file

@ -1,9 +1,38 @@
import { defineMDSveXConfig as defineConfig } from 'mdsvex';
import remarkMath from 'remark-math';
import rehypeKatex from 'rehype-katex-svelte';
import rehypeMermaid from 'rehype-mermaid'; // Import rehype-mermaid
import math from 'remark-math';
import rehype_katex from 'rehype-katex';
import katex from 'katex';
import visit from 'unist-util-visit';
const config = defineConfig({
const correct_hast_tree = () => (tree) => {
visit(tree, 'text', (node) => {
if (node.value.trim().startsWith('<')) {
node.type = 'raw';
}
});
};
const katex_blocks = () => (tree) => {
visit(tree, 'code', (node) => {
if (node.lang === 'math') {
const str = katex.renderToString(node.value, {
displayMode: true,
leqno: false,
fleqn: false,
throwOnError: true,
errorColor: '#cc0000',
strict: 'warn',
output: 'htmlAndMathml',
trust: false,
macros: { '\\f': '#1f(#2)' }
});
node.type = 'raw';
node.value = '{@html `' + str + '`}';
}
});
};
export const mdsvex_config = {
extensions: ['.md', '.svx'],
layout: "./src/routes/articles/Layout.svelte",
@ -11,8 +40,6 @@ const config = defineConfig({
dashes: 'oldschool'
},
remarkPlugins: [remarkMath],
rehypePlugins: [rehypeKatex, rehypeMermaid]
});
export default config;
remarkPlugins: [math, katex_blocks],
rehypePlugins: [correct_hast_tree, rehype_katex]
};

5
package.json
View file

@ -53,9 +53,12 @@
]
},
"dependencies": {
"katex": "^0.16.22",
"mermaid": "^11.6.0",
"playwright": "^1.52.0",
"rehype-katex": "^5.0.0",
"rehype-katex-svelte": "^1.2.0",
"remark-math": "^6.0.0"
"remark-math": "2",
"unist-util-visit": "^2.0.3"
}
}

523
pnpm-lock.yaml generated
View file

@ -8,18 +8,27 @@ importers:
.:
dependencies:
katex:
specifier: ^0.16.22
version: 0.16.22
mermaid:
specifier: ^11.6.0
version: 11.6.0
playwright:
specifier: ^1.52.0
version: 1.52.0
rehype-katex:
specifier: ^5.0.0
version: 5.0.0
rehype-katex-svelte:
specifier: ^1.2.0
version: 1.2.0
remark-math:
specifier: ^6.0.0
version: 6.0.0
specifier: '2'
version: 2.0.1
unist-util-visit:
specifier: ^2.0.3
version: 2.0.3
devDependencies:
'@eslint/compat':
specifier: ^1.2.8
@ -873,15 +882,15 @@ packages:
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engines: {node: '>= 16'}
@ -1089,6 +1098,9 @@ packages:
color-name@1.1.4:
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@ -1316,9 +1328,6 @@ packages:
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engines: {node: '>=6'}
@ -1579,6 +1588,9 @@ packages:
hast-util-from-html@2.0.3:
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hast-util-from-parse5@8.0.3:
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@ -1588,9 +1600,15 @@ packages:
hast-util-has-property@2.0.1:
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hast-util-is-element@1.1.0:
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hast-util-is-element@3.0.0:
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hast-util-parse-selector@2.2.5:
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hast-util-parse-selector@4.0.0:
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@ -1600,12 +1618,18 @@ packages:
hast-util-to-string@2.0.0:
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hast-util-to-text@2.0.1:
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hast-util-to-text@4.0.2:
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hast-util-whitespace@2.0.1:
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hastscript@9.0.1:
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@ -1651,6 +1675,10 @@ packages:
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is-buffer@2.0.5:
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engines: {node: '>= 0.4'}
@ -1670,6 +1698,10 @@ packages:
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engines: {node: '>=0.12.0'}
is-plain-obj@2.1.0:
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is-plain-obj@4.1.0:
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engines: {node: '>=12'}
@ -1715,6 +1747,10 @@ packages:
json-stable-stringify-without-jsonify@1.0.1:
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katex@0.13.24:
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hasBin: true
katex@0.16.22:
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hasBin: true
@ -1843,9 +1879,6 @@ packages:
lodash@4.17.21:
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@ -1864,21 +1897,6 @@ packages:
engines: {node: '>= 18'}
hasBin: true
mdast-util-from-markdown@2.0.2:
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peerDependencies:
@ -1899,72 +1917,6 @@ packages:
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micromark-util-encode: 2.0.1
micromark-util-normalize-identifier: 2.0.1
micromark-util-resolve-all: 2.0.1
micromark-util-sanitize-uri: 2.0.1
micromark-util-subtokenize: 2.1.0
micromark-util-symbol: 2.0.1
micromark-util-types: 2.0.2
transitivePeerDependencies:
- supports-color
micromatch@4.0.8:
dependencies:
braces: 3.0.3
@ -4725,6 +4565,8 @@ snapshots:
dependencies:
callsites: 3.1.0
parse5@6.0.1: {}
parse5@7.3.0:
dependencies:
entities: 6.0.0
@ -4834,6 +4676,10 @@ snapshots:
prismjs@1.30.0: {}
property-information@5.6.0:
dependencies:
xtend: 4.0.2
property-information@6.5.0: {}
property-information@7.0.0: {}
@ -4862,6 +4708,15 @@ snapshots:
hast-util-to-string: 2.0.0
katex: 0.16.22
rehype-katex@5.0.0:
dependencies:
'@types/katex': 0.11.1
hast-util-to-text: 2.0.1
katex: 0.13.24
rehype-parse: 7.0.1
unified: 9.2.2
unist-util-visit: 2.0.3
rehype-mermaid@3.0.0(playwright@1.52.0):
dependencies:
'@types/hast': 3.0.4
@ -4878,14 +4733,14 @@ snapshots:
transitivePeerDependencies:
- supports-color
remark-math@6.0.0:
rehype-parse@7.0.1:
dependencies:
'@types/mdast': 4.0.4
mdast-util-math: 3.0.0
micromark-extension-math: 3.1.0
unified: 11.0.5
transitivePeerDependencies:
- supports-color
hast-util-from-parse5: 6.0.1
parse5: 6.0.1
remark-math@2.0.1: {}
repeat-string@1.6.1: {}
resolve-from@4.0.0: {}
@ -4970,6 +4825,8 @@ snapshots:
source-map-js@1.2.1: {}
space-separated-tokens@1.1.5: {}
space-separated-tokens@2.0.2: {}
stackback@0.0.2: {}
@ -5076,6 +4933,8 @@ snapshots:
dependencies:
punycode: 2.3.1
trough@1.0.5: {}
trough@2.2.0: {}
ts-api-utils@2.1.0(typescript@5.8.3):
@ -5114,11 +4973,27 @@ snapshots:
trough: 2.2.0
vfile: 6.0.3
unified@9.2.2:
dependencies:
'@types/unist': 2.0.11
bail: 1.0.5
extend: 3.0.2
is-buffer: 2.0.5
is-plain-obj: 2.1.0
trough: 1.0.5
vfile: 4.2.1
unist-util-find-after@3.0.0:
dependencies:
unist-util-is: 4.1.0
unist-util-find-after@5.0.0:
dependencies:
'@types/unist': 3.0.3
unist-util-is: 6.0.0
unist-util-is@4.1.0: {}
unist-util-is@5.2.1:
dependencies:
'@types/unist': 2.0.11
@ -5140,6 +5015,11 @@ snapshots:
dependencies:
'@types/unist': 3.0.3
unist-util-visit-parents@3.1.1:
dependencies:
'@types/unist': 2.0.11
unist-util-is: 4.1.0
unist-util-visit-parents@5.1.3:
dependencies:
'@types/unist': 2.0.11
@ -5150,6 +5030,12 @@ snapshots:
'@types/unist': 3.0.3
unist-util-is: 6.0.0
unist-util-visit@2.0.3:
dependencies:
'@types/unist': 2.0.11
unist-util-is: 4.1.0
unist-util-visit-parents: 3.1.1
unist-util-visit@4.1.2:
dependencies:
'@types/unist': 2.0.11
@ -5170,6 +5056,8 @@ snapshots:
uuid@11.1.0: {}
vfile-location@3.2.0: {}
vfile-location@5.0.3:
dependencies:
'@types/unist': 3.0.3
@ -5185,6 +5073,13 @@ snapshots:
'@types/unist': 3.0.3
unist-util-stringify-position: 4.0.0
vfile@4.2.1:
dependencies:
'@types/unist': 2.0.11
is-buffer: 2.0.5
unist-util-stringify-position: 2.0.3
vfile-message: 2.0.4
vfile@6.0.3:
dependencies:
'@types/unist': 3.0.3
@ -5289,6 +5184,8 @@ snapshots:
dependencies:
xml-name-validator: 5.0.0
web-namespaces@1.1.4: {}
web-namespaces@2.0.1: {}
webidl-conversions@7.0.0: {}
@ -5321,6 +5218,8 @@ snapshots:
xmlchars@2.2.0: {}
xtend@4.0.2: {}
yaml@1.10.2: {}
yocto-queue@0.1.0: {}

10
src/routes/articles/Heading.svelte
View file

@ -1,25 +1,27 @@
<script lang="ts">
import './article.css';
import HorizontalBreak from './HorizontalBreak.svelte';
export let title;
export let date;
</script>
<div>
<div class="heading">
<h1>{title}</h1>
<p>{date}</p>
</div>
<HorizontalBreak />
<style>
div {
.heading {
width: 100%;
}
h1 {
.heading > h1 {
display: inline-block;
}
p {
.heading > p {
float: right;
padding-left: auto;
padding-right: auto;

5
src/routes/articles/HorizontalBreak.svelte
View file

@ -1,11 +1,10 @@
<script lang="ts">
</script>
<div>
</div>
<div class="horizontal_break"></div>
<style>
div {
.horizontal_break {
margin-top: 1em;
background-color: #928374;
height: 1px;

3
src/routes/articles/Layout.svelte
View file

@ -4,7 +4,6 @@
export let title;
export let date;
</script>
<div class="container">
@ -39,11 +38,9 @@
border-right: 1px solid #928374;
text-align: justify;
}
.padding {
flex: 1;
}
</style>

13
src/routes/articles/Paragraph.svelte
View file

@ -1,13 +0,0 @@
<script lang="ts">
let { children } = $props();
</script>
<div>
{@render children()}
</div>
<style>
div {
margin-top: 1em;
}
</style>

10
src/routes/articles/article.css
View file

@ -31,3 +31,13 @@ h2 {
margin-right: 0;
font-weight: bold;
}
.katex {
background-color: #1d2021;
padding: 1em;
border: 1px solid #928374;
border-radius: 2px;
width: max-content;
margin-left: auto;
margin-right: auto;
}

118
src/routes/articles/the-graphics-pipeline/+page.svx
View file

@ -3,100 +3,104 @@ title: The Graphics Pipeline
date: "April 20 - 2025"
---
<script>
import Paragraph from '../Paragraph.svelte';
import HorizontalBreak from '../HorizontalBreak.svelte';
</script>
Ever wondered how games put all that gore on your display? All that beauty is brought into life by
a process called **rendering**, and at the heart of it, is the **graphics pipeline**.
In this article we'll dive deep into the intricate details of this beast.
<HorizontalBreak/>
<Paragraph>
Ever wondered how games put all that gore on your display? Well you're about to find out :)
At the heart of rendering, is the **Graphics Pipeline**. And like any pipeline, it's comprised
Like any pipeline, the **graphics pipeline** is comprised
of several **stages**, each of which can be a pipeline in itself or even parallelized.
Each stage takes some input data (and configuration), to generate some output for the next stage.
</Paragraph>
Each stage takes some input (data and configuration) to generate some output data for the next stage.
We can coarsely divide the pipeline into **4 stages**:
<Paragraph>
```math
\texttt{Application} \rightarrow \color{#fabd2f}{\texttt{GeometryProcessing}}\color{none} \rightarrow \texttt{Rasterization} \rightarrow \texttt{PixelProcessing}
```
We can coarsely divide the **Graphics Pipeline** into 4 stages:
**Application -> Geometry Processing -> Rasterization -> Pixel Processing**
The pipeline will then serve the output of the **Pixel Processing** stage, which is a **rendered image**,
The pipeline will then serve the output of the **pixel processing** stage, which is a **rendered image**,
to your pretty eyes using your display.
</Paragraph>
<Paragraph>
But to avoid drowning you in overviews, let's jump right into the details of the "Geometry Processing"
But to avoid drowning you in overviews, let's jump right into the gory details of the **geometry processing**
stage and have a recap afterwards to demystify this 4-stage division.
</Paragraph>
<Paragraph>
## Surfaces
In order to display a murder scene, we need to have a way of **representing** the deceased in computer memory.
Ever been jump-scared by this sight in an FPS? Why are things rendered like that?
In order to display a scene (like a murder scene),
we need to have a way of **representing** the **surface** of the composing objects (like corpses) in computer-memory.
We only care about the **surface** since we won't be seeing the insides anyways---Not that we want to.
At this stage, we only care about the **shape** or the **geometry** of the **surface**.
Texturing, lighting and all the sweet gory details comes at a much later stage once all the **geometry** has been processed.
Texturing, lighting and all the sweet gory details comes at a much later stage once all the **geometry** have been processed.
But how should we represent surfaces in memory?
</Paragraph>
But how do we represent surfaces in computer-memory?
## Vertices
<Paragraph>
There are several ways to **represent 3d objects** for a computer to understand.
There are several ways to **represent** the surfaces of 3d objects for a computer to understand.
For instance, **NURB surfaces** are great for representing **curves**
and it's all about the **high-precision** needed to do **CAD**.
We could also do **ray-tracing** using fancy equations for rendering **photo-realistic** images.
</Paragraph>
<Paragraph>
These are all great--ignoring the fact that they would take "an eternity" to process.
But what we need is a **hardware-friendly** approach that can do this for an entire scene with
hundereds of thousands of objects for at least **60 times undr a second**. What we need is **polygonal modeling**.
</Paragraph>
These are all great--ignoring the fact that they would take an eternity to process...
But what we need is a **performant** approach that can do this for an entire scene with
hundereds of thousands of objects (like a lot of corpses) in under a small fraction of a second. What we need is **polygonal modeling**.
<Paragraph>
**Polygonal modeling** allows us to do **real-time rendering**. The idea is that we only need an
**Polygonal modeling** enables us to do an exciting thing called **real-time rendering**. The idea is that we only need an
**approximation** of a surface to render it **realisticly-enough** for us to have some fun killing time!
We can achieve this approximation using a collection of **triangles**, **lines** and **dots** (primitives),
which themselves are composed of a series of **vertices** (points in space).
</Paragraph>
<Paragraph>
A **vertex** is simply a point in space.
Once we get enough of these **points**, we can conncet them to form **primitives** such as **triangles**, **lines** and **dots**.
And once we have enough **primitives** together, they form a **model** or a **mesh** (that we need for our corpse).
With some interesting models, we can compose a **scene**.
</Paragraph>
And once we connect enough of these **primitives** together, they form a **model** or a **mesh** (that we need for our corpse).
With some interesting models put together, we can compose a **scene** (like a murder scene :D).
<Paragraph>
But let's not get ahead of ourselves. The primary type of **primitive** we care about during **polygonal modeling**
But let's not get ahead of ourselves. The primary type of **primitive** that we care about during **polygonal modeling**
is a **triangle**. But why not squares or polygons with variable number of edges?
</Paragraph>
## Why Triangles?
"Always Planar":
<Paragraph>
Triangles can never be __non-planar__(reside in more than 1 plane)! In Euclidean geometry, any
</Paragraph>
In **Euclidean geometry**, triangles are always **planar** (they exist only in one plane),
any polygon composed of more than 3 points may break this rule, but why does polygons residing in one plane so important
to us?
"Normal surface:"
Being non-planar makes it rather difficult to determine
"Algorithm Simplicity:"
"Predictable Winding Order:"
When a polygon exists only in one plane, we can safely imply that **only one face** of it can be visible
at any one time, this enables us to utilize a huge optimization technique called **back-face culling**.
Which means we avoid wasting a ton of **precious processing time** on the polygons that
we know won't be visible to us. We can safely **cull** the **back-faces** since we won't
be seeing the **back** of a polygon when it's in the context of a closed off model.
We figure this by simply using the **winding-order** of the triangle to determine whether we're looking at the
back of the triangle or the front of it.
Normal surface
Triangles also have very small **memory footprint**, for instance when using the **triangle-strip** topology (more on this very soon), for each additional triangle after the first one, only **one extra vertex** is needed.
The most important attribute however (in my opinion) is the **algorithmic simplicity**.
Any polygon or shape can be composed from a **set of triangle**, for instance a rectangle is
simply **two co-planar triangles**.
It is becoming an increasingly more common practice in computer science to break down
hard problems into simpler, smaller problems. This will be more convincing when we cover the **rasterization** stage :)
Bonus point: present day **hardwares** and **algorithms** have become **extremely efficient** at processing
triangles (sorting, rendering, etc) after eons of evolving around them.
## Primitive Topology
So, we got our set of triangles, but how do we make a model out of them?
## Primitive Topologies
## Indices
@ -116,6 +120,8 @@ Triangles can never be __non-planar__(reside in more than 1 plane)! In Euclidean
## Tessellation & Geometry Shaders
## Let's Recap!
## Rasterizer
## Pixel Shader

18
svelte.config.js
View file

@ -1,18 +1,11 @@
import { mdsvex } from 'mdsvex';
import mdsvexConfig from './mdsvex.config.js';
import { mdsvex_config } from './mdsvex.config.js';
import adapter from '@sveltejs/adapter-static';
import { vitePreprocess } from '@sveltejs/vite-plugin-svelte';
/** @type {import('@sveltejs/kit').Config} */
const config = {
// Consult https://svelte.dev/docs/kit/integrations
// for more information about preprocessors
preprocess: [
vitePreprocess(),
mdsvex(mdsvexConfig)
],
kit: {
// adapter-auto only supports some environments, see https://svelte.dev/docs/kit/adapter-auto for a list.
// If your environment is not supported, or you settled on a specific environment, switch out the adapter.
@ -20,7 +13,14 @@ const config = {
adapter: adapter()
},
extensions: ['.svelte', '.svx', '.md']
extensions: ['.svelte', '.svx', '.md'],
// Consult https://svelte.dev/docs/kit/integrations
// for more information about preprocessors
preprocess: [
vitePreprocess(),
mdsvex(mdsvex_config)
],
};
export default config;