Mathematics for Game Programming and Computer Graphics: Explore the essential mathematics for creating, rendering, and manipulating 3D virtual environments

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. Hello Graphics Window: You're on your way
2. Let's Start Drawing
3. Line Plotting Pixel by Pixel
4. Graphics and Game Engine Components
5. Let's Light it Up!
6. Updating and Drawing the Graphics Environment
7. Interactions with the Keyboard and Mouse for Dynamic Graphics Programs
8. Reviewing Our Knowledge of Triangles
9. Practicing Vector Essentials
10. Getting acquainted with Lines, Rays and Normals
11. Manipulating the Light and Texture of Triangles
12. Mastering Affine Transformations
13. Understanding the Importance of Matrices
14. Working with coordinate Spaces
15. Navigating the view space
16. Rotating with Quaternions
17. Vertex and fragment shading
18. Customizing the Render Pipeline
19. Rendering Visual Realism Like a Pro

Penny de Byl is a full stack developer with an honors in graphics and Ph.D. in artificial intelligence for games. She has a passion for teaching, teaching games development and computer graphics for over 25 years in universities in Australia and Europe. Her best-selling textbooks, including Holistic Game Development with Unity, are used in over 100 institutions. She has won numerous awards for teaching, including an Australian Government Excellence in Teaching Award and the Unity Mobile Game Curriculum Competition. Her approach to teaching computer science and related fields is project-based giving you hands-on workshops you can immediately get your teeth into. The full range of her teaching interests can be found at H3D Learn.