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light7734 2025-05-18 21:30:29 +03:30
parent 42c9fbe971
commit d38341c9bc
Signed by: light7734
GPG key ID: 8C30176798F1A6BA
13 changed files with 1270 additions and 58 deletions
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5
src/routes/articles/Image.svelte
View file

@ -12,13 +12,8 @@
<style>
.container {
width: fit-content;
margin-left: auto;
margin-right: auto;
background-color: #1d2021;
padding: 1em;
border: 1px solid #928374;
border-radius: 2px;
display: flex; /* Arrange images horizontally */
/* Removed flex properties from here */
gap: 1em;
}

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

@ -33,10 +33,11 @@
min-width: 80ch;
max-width: 80ch;
text-wrap-mode: wrap;
text-wrap-style: pretty;
text-align: justify;
border-left: 1px solid #928374;
border-right: 1px solid #928374;
border-left: 1px solid #92837420;
border-right: 1px solid #92837420;
}
.padding {

17
src/routes/articles/Note.svelte
View file

@ -1,6 +1,6 @@
<script lang="ts">
import { Info, BookCopy, Eye, Network, Sigma } from '@lucide/svelte';
let { title, type = 'info' } = $props();
import { Info, BookCopy, Eye, Network, Sigma, Image } from '@lucide/svelte';
let { title = '', type = 'info' } = $props();
</script>
<div class="note">
@ -8,6 +8,8 @@
<div class="icon">
{#if type == 'info'}
<Info />
{:else if type == 'image'}
<Image />
{:else if type == 'diagram'}
<Network />
{:else if type == 'math'}
@ -23,6 +25,8 @@
<div class="horiz_line" style:background-color="#8ec07c"></div>
{:else if type == 'diagram'}
<div class="horiz_line" style:background-color="#d3869b"></div>
{:else if type == 'image'}
<div class="horiz_line" style:background-color="#d3869b"></div>
{:else if type == 'math'}
<div class="horiz_line" style:background-color="#fe8019"></div>
{:else if type == 'review'}
@ -37,6 +41,8 @@
<div class="line" style:background-color="#8ec07c"></div>
{:else if type == 'diagram'}
<div class="line" style:background-color="#d3869b"></div>
{:else if type == 'image'}
<div class="line" style:background-color="#d3869b"></div>
{:else if type == 'math'}
<div class="line" style:background-color="#fe8019"></div>
{:else if type == 'review'}
@ -46,7 +52,9 @@
{/if}
<div class="slot">
<p>{title}</p>
{#if title != ''}
<p class="title">{title}</p>
{/if}
<slot />
</div>
</div>
@ -55,6 +63,9 @@
<style>
@import url('https://fonts.googleapis.com/css2?family=IBM+Plex+Mono:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&display=swap');
.title {
}
.note {
display: block;
margin: 1em 0 1em 0;

4
src/routes/articles/Tip.svelte
View file

@ -15,7 +15,7 @@
font-weight: 600;
font-style: italic;
color: #fabd2f;
border-bottom: 1px solid #fe8019;
border-bottom: 1px dotted #fe8019;
}
/* Tooltip text */
@ -32,7 +32,7 @@
text-align: justify;
padding: 1em;
border-radius: 6px;
border: 1px dotted #fe8019;
border: 1px solid #fe8019;
top: 100%;
left: 50%;

5
src/routes/articles/article.css
View file

@ -50,3 +50,8 @@ a:hover {
width: max-content;
margin-left: 0;
}
.katex-display {
margin-top: 0;
}

143
src/routes/articles/the-graphics-pipeline/+page.svx
View file

@ -64,14 +64,18 @@ stage and have a recap afterwards!
Ever been jump-scared by this sight in an <Tip text="FPS">First Person (Shooter) perspective</Tip>? Why are (the inside of) things rendered like that?
<Note title="Boo!", type="image">
<Image
paths={["/images/boo.png"]}
/>
</Note>
In order to display a (murder) scene,
we need to have a way of **representing** the **surface** of its composing objects (like corpses) in computer memory.
We only care about the **surface** since we won't be seeing the insides anyway---Not with that attitude.
We only care about the **surface** since we won't be seeing the insides anyway---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 come at a much later stage once all the **geometry** has been processed.
@ -94,19 +98,27 @@ hundreds of thousands of objects (like a lot of corpses) in under a small fracti
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).
<Note title="A sphere made out of triangles", type="image">
<Image
paths={["/images/polygon_sphere.webp"]}
/>
</Note>
A **vertex** is simply a point in space.
Once we get enough of these **points**, we can connect them to form **primitives** such as **triangles**, **lines**, and **dots**.
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).
<Note title="Stanford bunny model in increasing level of detail (LoD)", type="image">
<Image
paths={["/images/bunny.jpg"]}
/>
</Note>
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 a variable number of edges?
@ -116,10 +128,14 @@ In <Tip text="Euclidean geometry"> Developed by **Euclid** around 300 BCE, is ba
any polygon composed of more than 3 points may break this rule, but why does polygons residing in one plane so important
to us?
<Note title="Planar vs Non-Planar polygons" type="image">
<Image
paths={["/images/planar.jpg", "/images/non_planar_1.jpg", "/images/non_planar_2.png"]}
/>
</Note>
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
@ -136,7 +152,7 @@ Also, it is a common practice in computer science to break down hard problems in
This will be a lot more convincing when we cover the **rasterization** stage :)
<Note title="Bonus point: evolution", type="info">
<Note title="Bonus point, evolution", type="info">
present-day **hardware** and **algorithms** have become **extremely efficient** at processing
triangles by doing operations such as sorting, rasterizing, etc, after eons of evolving around them.
@ -152,98 +168,133 @@ of the primitives to be generated from our set of vertices by
configuring the **primitive topology** of the **input assembler**.
We'll get into the **input assembler** bit in a second, but let's clarify the topology with some examples.
**Point list**:
When the topology is **point list**, each **consecutive vertex** (v) defines a **single point** primitive (p)
and the number of primitives (n_p) is equals to the number of vertices (n_v).
When the topology is point list, each **consecutive vertex** defines a **single point** primitive, according to the equation:
<Note title="equation", type="math">
<Note title="", type="image">
<Image
paths={["/images/primitive_topology_point_list.svg"]}
/>
</Note>
<Note type="math">
```math
p_i = \{ v_{i} \}
\begin{aligned}
&p_i = \{ v_{i} \} \\ &n_p = n_v
\end{aligned}
```
</Note>
**Line list**:
When the topology is **line list**, each **consecutive pair of vertices** defines a **single line**
When the primitive topology is line list, each **consecutive pair of vertices** defines a **single line**, according to the equation:
<Note title="", type="image">
<Note title="equation", type="math">
```math
p_i = \{ v_{2i},\ v_{2i+1} \}
```
<Image
paths={["/images/primitive_topology_line_list.svg"]}
/>
</Note>
The number of primitives generated is equal to ⌊vertex_count / 2⌋.
<Note type="math">
**Line Strip**:
```math
\begin{aligned}
&p_i = \{ v_{2i},\ v_{2i+1} \} \\ &n_p = ⌊ n_v / 2 ⌋
\end{aligned}
```
</Note>
When the primitive topology is line strip, **one line** is defined by each **vertex and the following vertex**, according to the equation:
<Note title="equation", type="math">
<Note title="", type="image">
```math
p_i = \{ v_i, v_{i+1} \}
```
<Image
paths={["/images/primitive_topology_line_strip.svg"]}
/>
</Note>
The number of primitives generated is equal to max(0, vertex_count - 1).
**Triangle list**:
<Note type="math">
```math
\begin{aligned}
&p_i = \{ v_i, v_{i+1} \} \\ &n_p = \text{max}(0, n_v - 1)
\end{aligned}
```
</Note>
When the primitive topology is triangle list, each **consecutive set of three vertices** defines a **single triangle**, according to the equation:
<Note title="equation", type="math">
```math
p_i = \{ v_{3i}, v_{3i+1}, v_{3i+2} \}
```
<Note title="", type="image">
<Image
paths={["/images/primitive_topology_triangle_list.svg"]}
/>
</Note>
<Note type="math">
The number of primitives generated is equal to ⌊vertex_count / 3⌋.
```math
\begin{aligned}
&p_i = \{ v_{3i}, v_{3i+1}, v_{3i+2} \} \\ &n_p = ⌊n_v / 3⌋
\end{aligned}
```
**Triangle strip**:
</Note>
When the primitive topology is triangle strip, **one triangle** is defined by each **vertex and the two vertices that follow it**, according to the equation:
<Note title="equation", type="math">
<Note title="", type="image">
<Image
paths={["/images/primitive_topology_triangle_strip.svg"]}
/>
</Note>
<Note type="math">
```math
p_i = \{ v_i,\ v_{i + (1 + i \bmod 2)},\ v_{i + (2 - i \bmod 2)} \}
\begin{aligned}
&p_i = \{ v_i,\ v_{i + (1 + i \bmod 2)},\ v_{i + (2 - i \bmod 2)} \} \\ &n_p = \text{max}(0, n_v- 2)
\end{aligned}
```
</Note>
The number of primitives generated is equal to max(0, vertex_count - 2).
**Triangle fan**:
When the primitive topology is trinagle fan, triangleas are defined **around a shared common vertex**, according to the equation:
<Note title="equation", type="math">
<Note title="", type="image">
<Image
paths={["/images/primitive_topology_triangle_fan.svg"]}
/>
</Note>
<Note type="math">
```math
p_i = \{ v_{i+1}, v_{i+2}, v_0 \}
\begin{aligned}
&p_i = \{ v_{i+1}, v_{i+2}, v_0 \} \\ &n_p = \text{max}(0, n_v - 2)
\end{aligned}
```
</Note>
The number of primitives generated is equal to max(0, vertex_count - 2).
There's also some topologies suffixed with the word **adjacency**, and a special type of primitive called **patch** primitive.
But for the sake of simplicity we won't get into them.
So what's next?
## Indices
Great, we got our vertices, we figured out how to connect them, but there's one last thing we need
to understand before we can **assemble** our input using the **input assembler**. The **indices**.
Indices are an array of integers that reference vertices in a vertex buffer.
They define the order in which vertices are used to form primitives (triangles, strips, etc.),
allowing vertex reuse and reducing memory usage. Instead of duplicating vertex data, indices let you build complex geometry efficiently.
## **Input Assembler**
Every section before this explained terminologies needed to grasp this,

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static/images/primitive_topology_line_list.svg Normal file
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After

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