A comprehensive guide to learning fundamental 3D mathematical principles used in games and computer graphics by example

Key Features

  • Get acquainted with the essential mathematics needed to describe, simulate, and render 3D creations
  • Construct and manipulate 3D animated environments using Python, Pygame, and PyOpenGL
  • Develop vertex and fragment shaders in OpenGL shader language to speed up rendering

Book Description

Mathematics is an essential skill when it comes to graphics and game development, particularly if you want to understand the generation of real-time computer graphics and the manipulation of objects and environments in a detailed way. Python, together with Pygame and PyOpenGL, provides you with the opportunity to explore these features under the hood, revealing how computers generate and manipulate 3D environments.

Mathematics for Game Programming and Computer Graphics is an exhaustive guide to getting “back to the basics” of mathematics, using a series of problem-based, practical exercises to explore ideas around drawing graphic lines and shapes, applying vectors and vertices, constructing and rendering meshes, and working with vertex shaders. By leveraging Python, Pygame, and PyOpenGL, you'll be able to create your own mathematics-based engine and API that will be used throughout to build applications.

By the end of this graphics focussed book, you'll have gained a thorough understanding of how essential mathematics is for creating, rendering, and manipulating 3D virtual environments and know the secrets behind today's top graphics and game engines.

What you will learn

  • Get up and running with Python, Pycharm, Pygame, and PyOpenGL
  • Experiment with different graphics API drawing commands
  • Review basic trigonometry and how it's important in 3D environments
  • Apply vectors and matrices to move, orient, and scale 3D objects
  • Render 3D objects with textures, colors, shading, and lighting
  • Work with vertex shaders for faster GPU-based rendering

Who this book is for

This book is for programmers who want to enhance their 3D mathematics skills relating to computer graphics and computer games. Knowledge of high school–level mathematics and a working understanding in an object-orientated language is needed to grasp the contents present in this book.

Table of Contents

  1. Mathematics for Game Programming and Computer Graphics
  2. Contributors
  3. About the author
  4. About the reviewers
  5. Preface
  6. Part 1 – Essential Tools
  7. Chapter 1: Hello Graphics Window: You’re On Your Way
  8. Chapter 2: Let’s Start Drawing
  9. Chapter 3: Line Plotting Pixel by Pixel
  10. Chapter 4: Graphics and Game Engine Components
  11. Chapter 5: Let’s Light It Up!
  12. Chapter 6: Updating and Drawing the Graphics Environment
  13. Chapter 7: Interactions with the Keyboard and Mouse for Dynamic Graphics Programs
  14. Part 2 – Essential Trigonometry
  15. Chapter 8: Reviewing Our Knowledge of Triangles
  16. Chapter 9: Practicing Vector Essentials
  17. Chapter 10: Getting Acquainted with Lines, Rays, and Normals
  18. Chapter 11: Manipulating the Light and Texture of Triangles
  19. Part 3 – Essential Transformations
  20. Chapter 12: Mastering Affine Transformations
  21. Chapter 13: Understanding the Importance of Matrices
  22. Chapter 14: Working with Coordinate Spaces
  23. Chapter 15: Navigating the View Space
  24. Chapter 16: Rotating with Quaternions
  25. Part 4 – Essential Rendering Techniques
  26. Chapter 17: Vertex and Fragment Shading
  27. Chapter 18: Customizing the Render Pipeline
  28. Chapter 19: Rendering Visual Realism Like a Pro
  29. Index
  30. Other Books You May Enjoy