You're reading from Mathematics for Game Programming and Computer Graphics Explore the essential mathematics for creating, rendering, and manipulating 3D virtual environments

Product type Paperback

Published in Nov 2022

Publisher Packt

ISBN-13 9781801077330

Length 444 pages

Edition 1st Edition

Languages

Python

Tools

OpenGL

Concepts

Game Optimization

Author (1):

Penny de Byl

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Table of Contents (26) Chapters

Preface

1. Part 1 – Essential Tools

2. Chapter 1: Hello Graphics Window: You’re On Your Way FREE CHAPTER

3. Chapter 2: Let’s Start Drawing

4. Chapter 3: Line Plotting Pixel by Pixel

5. Chapter 4: Graphics and Game Engine Components

6. Chapter 5: Let’s Light It Up!

7. Chapter 6: Updating and Drawing the Graphics Environment

8. Chapter 7: Interactions with the Keyboard and Mouse for Dynamic Graphics Programs

9. Part 2 – Essential Trigonometry

10. Chapter 8: Reviewing Our Knowledge of Triangles

11. Chapter 9: Practicing Vector Essentials

12. Chapter 10: Getting Acquainted with Lines, Rays, and Normals

13. Chapter 11: Manipulating the Light and Texture of Triangles

14. Part 3 – Essential Transformations

15. Chapter 12: Mastering Affine Transformations

16. Chapter 13: Understanding the Importance of Matrices

17. Chapter 14: Working with Coordinate Spaces

18. Chapter 15: Navigating the View Space

19. Chapter 16: Rotating with Quaternions

20. Part 4 – Essential Rendering Techniques

21. Chapter 17: Vertex and Fragment Shading

22. Chapter 18: Customizing the Render Pipeline

23. Chapter 19: Rendering Visual Realism Like a Pro

24. Index

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Summary

A lot of mathematical concepts were covered in this chapter that focused on matrices. Besides understanding vectors, a solid knowledge of matrices (especially 4 x 4) is an essential skill to have as a graphics programmer since they underpin the majority of the mathematics found in graphics and game engines. Once you appreciate the beauty of their simplicity and power, you’ll become more and more comfortable with their use.

In this chapter, we have only scratched the surface of using matrices in graphics. After learning how the addition operation that’s used in translations can be transformed into a 4 x 4 matrix, and integrated with scaling and rotation to perform compound transformations in 3D, we took a brief look at the ModelView Matrix in OpenGL using the project code created thus far. However, the way we currently perform the transformations is restricted to the same order as how glTranslate(), glRotate(), and glScale() are used in the existing code.

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