Games101 on Feynman's Blog

06 | Geometry (Basic Representations & Curves and Surfaces & Mesh Processing) and Shadow Mapping

Wed, 09 Sep 2026 18:00:00 +0800

Instructor: Lingqi Yan | UCSB Bilibili: https://www.bilibili.com/video/BV1X7411F744 Lectures covered: Lecture 10 (Geometry 1: Introduction), Lecture 11 (Geometry 2: Curves and Surfaces), Lecture 12 (Geometry 3)

Geometry is an extremely important yet difficult topic in computer graphics. This post covers various ways to represent geometry (implicit and explicit), curves and surfaces (Bezier curves, B-splines, Bezier surfaces), mesh processing (subdivision, simplification, regularization) as well as the shadow mapping technique.

05 | Shading (Illumination Models and Texture Mapping)

Sun, 30 Aug 2026 18:00:00 +0800

Instructor: Lingqi Yan | UCSB Bilibili: https://www.bilibili.com/video/BV1X7411F744 Lectures covered: Lecture 7 (Illumination, Shading and Graphics Pipeline), Lecture 8 (Shading, Pipeline and Texture Mapping), Lecture 9 (Texture Mapping cont.)

Note: In the official condensed slides, texture applications (environment maps, bump/normal/displacement maps, 3D textures) appear in Lecture 10 and shadow mapping in Lecture 12; following the full Bilibili course structure, they are grouped under the shading topic here.

Shading is the process of applying material properties to objects, which determines their color and appearance under different lighting conditions. This post covers the depth buffer (visibility/occlusion), the Blinn-Phong reflectance model, shading frequencies, the graphics pipeline, texture mapping and related techniques.

04 | Rasterization (Triangle Discretization and Anti-Aliasing)

Sun, 16 Aug 2026 12:00:00 +0800

Instructor: Lingqi Yan | UCSB Bilibili: https://www.bilibili.com/video/BV1X7411F744

Rasterization is the process of converting vector graphics (geometric descriptions) into pixel images (raster images).

Rasterization = drawing continuous geometry as discrete pixels. It is the foundational technique of real-time rendering.

This chapter corresponds to lectures 5-6 (the depth buffer part corresponds to the start of lecture 7).

Lecture 05 slides (PDF)

Lecture 06 slides (PDF)

Bilibili video

1 Perspective Projection Wrap-Up: fovY and Aspect Ratio

In the MVP transform, the perspective projection frustum is defined by $l, r, b, t$ (left, right, bottom, top bounds of the near clip plane), but in practice developers prefer vertical field of view (fovY) and aspect ratio (assuming symmetry, i.e. $l = -r$, $b = -t$):

03 | Transformations (2D and 3D)

Sun, 09 Aug 2026 12:00:00 +0800

Instructor: Lingqi Yan | UCSB Bilibili: https://www.bilibili.com/video/BV1X7411F744

1 Why Study Transformations

Transformations have two core applications in graphics:

Application	Description	Example
Modeling	Place objects in a scene	Translate, rotate, scale objects
Viewing	Project 3D scene onto a 2D image	Camera transform, projection transform

2 2D Transformations

Scale

Uniform scale (all directions scaled equally):

$x' = sx \qquad y' = sy$

$$ \begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} s & 0 \\ 0 & s \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} $$

For example: $x = 2, \; y = 2, \; s = 0.5$

02 | Vectors and Linear Algebra

Tue, 21 Jul 2026 12:00:00 +0800

Instructor: Lingqi Yan | UCSB Bilibili: https://www.bilibili.com/video/BV1X7411F744

1 Vector Basics

Definition of Vectors

Vectors have direction and length, but no absolute starting position
Commonly denoted as $\vec{a}$ or bold a
Represented by start and end points: $\overrightarrow{AB} = B - A$

Vector Normalization

Magnitude (length) of a vector: $||\vec{a}||$
Unit vector: A vector with magnitude 1, used to represent direction
Normalization: $\hat{a} = \frac{\vec{a}}{||\vec{a}||}$

Vector Addition

Geometric representation: Parallelogram law & triangle law
Algebraic calculation: Add corresponding coordinates

$$ \vec{a} + \vec{b} = \begin{pmatrix} x_a + x_b \\ y_a + y_b \end{pmatrix} $$

Geometric representation of vector addition:

01 | Overview & Rasterization

Mon, 20 Jul 2026 12:00:00 +0800

Instructor: Lingqi Yan | UCSB Course Link: https://www.bilibili.com/video/BV1X7411F744

1 What is Computer Graphics

Computer Graphics: The use of computers to synthesize and manipulate visual information.

The core task of computer graphics is to represent, process, render, and display graphics and images in computers.

Application Areas

Area	Examples
Video Games	Real-time rendering, 3D scenes
Film VFX	Offline rendering, visual effects
Animation	CG animation like Frozen, Zootopia
Design & CAD	Industrial design, architectural visualization
Data Visualization	Scientific, engineering, medical data
Virtual Reality	Immersive virtual environments
Augmented Reality	Real-virtual fusion (AR navigation)
Simulation	Physics, weather, black hole visualization

2 Four Core Topics

GAMES101 covers four core topics in modern computer graphics: