**Gustavo Pezzi – 3D Computer Graphics Programming**

**Description Of 3D Computer Graphics Programming**

**This is one of my favorites!**

This course is a complete immersion into the fundamentals of computer graphics! You’ll learn how a software 3D engine works under the hood, and use the C programming language to write a complete software rasterizer from scratch; including textures, camera, clipping, and loading complex OBJ files. Pixel per pixel, triangle per triangle, mesh per mesh.

We’ll review all the beautiful math that makes 3D computer graphics possible as we tackle all concepts from first principles. We’ll also write a comprehensive software renderer that can display complex 3D objects on the screen without the help of any graphics API. No GPU, no OpenGL, no DirectX! Just a C compiler and a little bit of linear algebra is all we need to create a final project that is nothing short of amazing!

**The tools you’ll need**

We’ll simply use the command-line, a code editor, and a C compiler. All these tools are multi-platform, so you’ll be able to code along on either Windows, macOS, or Linux!

Also, make sure you have pen and paper ready for the lectures. This course will probably be a little bit different than other programming courses you took before. We will take our sweet time and make sure we understand every formula we find along the way!

**What you’ll learn in 3D Computer Graphics Programming**

**Course content**

**1. Introduction**

- Motivations & Learning Outcomes
- How to Take This Course

**2. Compiling our C Project**

- Configuring Dependencies
- Project Folder Structure
- Configuring a Makfile
- Compiling on Linux
- Compiling on macOS
- Configuring Visual Studio on Windows

**3. SDL Window & Color Buffer**

- Creating an SDL Window
- Declaring a Color Buffer
- Allocating and Freeing Memory
- Quiz: Memory Allocation
- SDL Texture
- Fullscreen Window
- Exercise: Drawing a Background
- Drawing Rectangles
- Quiz: Color Buffer

**4. Header Files**

- Defining Header Files
- Quiz: Header Files

**5. Vectors and Points**

- A Function to Draw Pixels
- Vectors
- Declaring a Vector Type
- Declaring Structs
- Array of Vector Points
- Quiz: Vectors and Points

**6. Projecting Points**

- Orthographic Projection
- Isometric Projection
- Perspective Projection
- Implementing the Perspective Divide
- Coordinate System Handedness
- Quiz: Perspective Projection

**7. Vector Transformations**

- Transforming Vectors
- Review of Sine, Cosine, and Tangent
- Quiz: Trigonometric Functions
- Rotating Vectors
- Proof of Angle Sine Addition
- Proof of Angle Cosine Addition
- Quiz: Rotating Vectors

**8. Fixed Framerate**

- Fixing our Game Loop Timestep
- Using a Delay Function
- Constant Framerate and Variable Delta Time

**9. Triangles and Vertices**

- 3D Triangles and Meshes
- Vertices and Triangle Faces
- Triangle Edges
- Quiz: Joystick Input

**10. Drawing Lines**

- Line Equation
- DDA Line Drawing Algorithm
- Do We Need Bresenham Lines?
- Coding a Function to Draw Lines

**11. Dynamic Arrays**

- Dynamic Arrays in C
- Dynamic Mesh Vertices and Faces
- Defining the Project Playfield Graphics

**12. OBJ Files**

- OBJ File Vertices and Faces
- Exercise: Loading OBJ File Content
- OBJ File Triangles and Quads

**13. Vector Operations**

- Introduction to Back-face Culling
- Vector Magnitude
- Vector Addition
- Vector Subtraction
- Vector Scaling
- Vector Cross Product
- Finding the Triangle Normal Vector
- Dot Product
- Implementing the Back-face Algorithm
- Vector Normalization
- Quiz: Vector Operations

**14. Triangle Rasterization**

- Triangle Fill
- Flat-Top & Flat-Bottom Technique
- Flat-Top Triangle Code
- Flat-Bottom Triangle Code
- Avoiding Division by Zero
- Exercise: Different Rendering Methods
- Solid Color Triangle Faces

**15. Sorting Faces by Depth**

- Painter’s Algorithm
- Exercise: Sorting Faces by Depth
- A Simple Sorting Function

**16. Matrices**

- Matrices Review
- Matrix Operations
- Matrix Multiplication
- Exercise: Matrix Multiplication
- 2D Rotation Matrix

**17. 3D Matrix Transformations**

- 3D Scale Matrix
- 3D Translation Matrix
- 3D Rotation Matrices
- The World Matrix
- Order of Matrix Transformations
- Quiz: Matrix Transformations
- Translation is Not a Linear Transformation

**18. Projection Matrix**

- Defining a Projetion Matrix
- Populating the Perspective Projection Matrix
- Exercise: Projecting Negative Z Values
- Projection in OpenGL & DirectX
- Row-Major and Column-Major Order

**19. Light and Shading**

- Flat Shaded Triangles
- Coding Flat Shading and Light
- Smooth Shading
- Gouraud Shading & Phong Shading

**20. Texture Mapping**

- Representing Textures in Memory
- Textured Triangles
- Textured Flat-Top Triangle
- Textured Flat-Bottom Triangle
- Barycentric Coordinates
- Barycentric Weights (α, β, γ)
- Coding Textured Triangles
- Quiz: Texture Mapping

**21. Perspective Correct Interpolation**

- Perspective Correct Interpolation
- What Does “Affine” Mean?
- 3D UV Coordinates

**22. Decoding PNG Files**

- Decoding PNG Files
- Loading PNG File Content
- Freeing PNG Textures from Memory
- Quiz: PNG Files

**23. Textured OBJ Files**

- Loading OBJ Textures Attributes
- Preventing Texture Buffer Overflow
- Rasterization Rules
- Visualizing Textured OBJ Files

**24. Z-Buffer**

- Implementing a Z-Buffer
- Exercise: Z-Buffer for Flat-Shaded Triangles
- Z-Buffer for Flat-Shaded Triangles
- Reviewing Dynamic Memory Allocation

**25. Camera**

- Camera Space
- LookAt Camera Model
- LookAt Camera Transformations
- Implementing a Variable Delta Time
- Coding a Simple FPS Camera Movement
- Quiz: Camera Transformations

**26. 3D Clipping**

- Frustum Clipping
- Frustum Planes
- Exercise: Frustum Planes and Normals
- Computing Points Inside and Outside Planes
- Intersection Between Lines and Planes
- Clipping Polygon Against a Plane
- Coding the Function to Clip Polygons Against Planes
- Visualizing Clipped Triangles
- Horizontal and Vertical FOV
- Clipping Texture UV Coordinates
- Clipping Space
- Quiz: 3D Clipping
- Deciding What Not to Render

**27. Code Refactoring**

- Working with Static Variables
- Refactoring SDL Global Variables
- Refactoring Light Code
- Simulating Low-Resolution Display with SDL
- Exercise: Camera Pitch Rotation
- Implementing Camera Pitch Rotation

**28. Rendering Multiple Meshes**

- Declaring Multiple Meshes
- Coding Multiple Meshes
- Coding Multiple Textures

**29. Conclusion & Next Steps**

**Is this 3D Computer Graphics Programming course for you?**

This is a self-contained course with no prerequisites. However, you will probably get the most out of it if you already know the basics of coding (if-else, loops, functions).

If you never programmed in C before, don’t worry! Many successful students come from different languages like Java, Python, JavaScript, Swift, and others. We’ll learn to work with the C language together.

**How is this 3D Computer Graphics Programming course different?**

This 3D Computer Graphics Programming course is not just a simple tutorial on how to use an existing graphics library or how to glue OpenGL or Vulkan code together. This course focus on the foundation of 3D graphics and provides a careful review of the math that underpins these concepts.

If you want to understand how computers display 3D objects on the screen and also learn some of the techniques used in the development of retro 3D games, then buckle up! This is going to be a 35-hour journey of pure nerd fun!

**About Gustavo Pezzi**

Gustavo Pezzi is a university lecturer in London, UK. He has won multiple education awards as a teacher and is also the founder of pikuma.com.

Gustavo Pezzi teaches fundamentals of computer science and mathematics; his academic path includes institutions such as Pittsburg State University, City University of London, and University of Oxford.

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