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

View More author details

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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Working with the Projection Matrix

The objective of the projection matrix is to take objects from view space into projection space. Basically, this takes coordinates inside the camera’s viewing volume (specified by the shape and size of the frustum or rectangular prism) and puts them in normalized device coordinates (NDCs). The calculations for a perspective view’s projection matrix were explained in Chapter 4, Graphics and Game Engine Components. The OpenGL documentation also specifies how it constructs the projection matrix with a call to gluPerspective() at registry.khronos.org/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml where the mathematics is revealed. The projection matrix is defined as follows:

Here, the values of a, b, c, and d are calculated from the parameters passed to gluPerspective(), which are the vertical field of view (fovy), the aspect ratio of the window, the near plane, and the far plane. These values are determined thus:

f = cotangent...