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

An understanding of triangles is essential for those who want to program in the graphics and games domains. They are the foundation of the data structures used to store meshes, as well as the basic drawing components of them. When it comes to mathematics in these realms, they are equally as important. Their trigonometric properties, as you will see in the next chapter, form the basis of vector mathematics.

In this chapter, you explored the fundamental properties of triangles and learned how to calculate the length of a triangle’s sides and angles using the relationships between similar triangles and the trigonometric rules found in right-angled triangles. Following the theory, we applied our knowledge of triangles to load a triangulated mesh into OpenGL and display it.

Now that you have explored the mathematics of triangles, we can start examining vectors.