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Mathematics for Game Programming and Computer Graphics

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

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Product type Paperback
Published in Nov 2022
Publisher Packt
ISBN-13 9781801077330
Length 444 pages
Edition 1st Edition
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Penny de Byl Penny de Byl
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Table of Contents (26) Chapters Close

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 25. Other Books You May Enjoy

Defining matrices

A matrix is an array of numbers. It is defined by the number of rows and columns that define its size. For example, this is a matrix with three rows and two columns:

Each value in the matrix is associated with its location. The value of 3 in the preceding matrix is located in row 0, column 0. More formally, we write the following:

The values specified in the square brackets are in the order [row, column], like so:

Here, the value in row 2, column 1 is 1, and the value in row 1, column 0 is 4.

In pure theoretical mathematics, the row and column values start at 1. We are starting our count at 0 because, in programming, when storing arrays and matrices, the index values start at 0.

Now, let’s take a look at the mathematical operations that can be achieved with two matrices.

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