Graphics on Feynman's Blog

11 | Light Fields, Color and Perception

Sat, 03 Oct 2026 15:00:00 +0800

Instructor: Lingqi Yan | UCSB
Bilibili: https://www.bilibili.com/video/BV1X7411F744
Lectures covered: Lecture 20 (Light Field / Lumigraph, Color and Perception)

Note: these are two topics that step outside geometry. The light field asks how much information a scene actually carries visually; colour asks why that information turns into colour once it enters the human eye. They look unrelated but point at the same conclusion: the “image” and the “colour” we perceive are only low-dimensional projections of the physical world onto human senses — the light field squeezes the 7D plenoptic function down to 4D, and colour squeezes an infinite-dimensional spectrum down to 3D. It is precisely because this compression exists that image capture and colour reproduction are possible at all.

12 | Animation and Simulation

Sat, 03 Oct 2026 15:00:00 +0800

Instructor: Lingqi Yan | UCSB
Bilibili: https://www.bilibili.com/video/BV1X7411F744
Lectures covered: Lecture 21 (Animation 1: Basic Concepts, Mass-Spring Systems, Kinematics, Rigging / Blend Shapes / Motion Capture), Lecture 22 (Animation Cont.: Solving ODEs, Rigid Body and Fluids)

Note: the previous eleven posts all dealt with the “static” problem — a scene sits there, and we care about how to compute and draw it. This one changes the dimension: making the scene move over time. Animation and simulation both look like they “generate motion”, but they take two fundamentally different routes: animation describes motion (a human supplies keyframes or joint angles and the computer interpolates), while simulation derives motion (a human supplies the laws of physics and the computer integrates). In practice the two roads meet in the same place — both end up solving differential equations numerically, and both can blow up because of discretisation.

10 | Cameras and Lenses

Sat, 03 Oct 2026 14:00:00 +0800

Instructor: Lingqi Yan | UCSB
Bilibili: https://www.bilibili.com/video/BV1X7411F744
Lectures covered: Lecture 19 (Cameras, Lenses and Light Fields)

Note: the previous nine posts kept answering “how do we draw a model into an image” — that is synthesis. This one turns around and asks how an image gets captured. Nearly every part of a camera — lens, aperture, shutter, sensor — maps onto a parameter in a renderer, and effects like depth of field, defocus blur and exposure finally get a physical model.

07 | Ray Tracing (Whitted-Style, Radiometry and Path Tracing)

Thu, 01 Oct 2026 18:00:00 +0800

Instructor: Lingqi Yan | UCSB
Bilibili: https://www.bilibili.com/video/BV1X7411F744
Lectures covered: Lecture 13 (Ray Tracing 1: Whitted-Style Ray Tracing), Lecture 14 (Ray Tracing 2: Acceleration & Radiometry), Lecture 15 (Light Transport & Global Illumination), Lecture 16 (Ray Tracing 4: Monte Carlo, Path Tracing)

Note: ray tracing is the longest block in GAMES101, spanning lectures 13-18. This post covers lectures 13-16 — from Whitted-style ray tracing, intersection tests and acceleration structures, through radiometry and the rendering equation, to path tracing. Materials and appearances (Lecture 17) and advanced rendering topics (Lecture 18) get their own posts.

08 | Materials and Appearances

Thu, 01 Oct 2026 18:00:00 +0800

Instructor: Lingqi Yan | UCSB
Bilibili: https://www.bilibili.com/video/BV1X7411F744
Lectures covered: Lecture 17 (Materials and Appearances)

Note: the previous post (#7) drove all the way to path tracing and solved the rendering equation. This one turns around and stares at the one term in that equation that is “known” yet endlessly complicated — $f_r$, the BRDF. Materials, appearances, glossiness, Fresnel, microfacets: they all answer the same question. When light hits this surface, how much energy goes where? The advanced rendering topics of Lecture 18 (BDPT, MLT, photon mapping, VCM, plus non-surface models such as participating media and hair) get their own post.

09 | Advanced Light Transport and Complex Appearance Modeling

Thu, 01 Oct 2026 18:00:00 +0800

Instructor: Lingqi Yan | UCSB
Bilibili: https://www.bilibili.com/video/BV1X7411F744
Lectures covered: Lecture 18 (Advanced Topics in Rendering)

Note: this closes out the rendering block. We walked from the rendering equation all the way to path tracing and got the basic framework standing. This post derives no new equation — it spreads out sideways instead. First, what other light transport algorithms exist (BDPT, MLT, photon mapping, VCM, instant radiosity); then, what to do when the “surface + BRDF” assumption stops being enough, and we have to model participating media, hair, skin and cloth.

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: