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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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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

Getting Acquainted with Lines, Rays, and Normals

Since we covered vectors in the previous chapter, it’s time to jump into exploring the mathematics of lines, rays, and normals. All three can be defined by vectors and on the surface, all appear to be the same and yet they have very specific and differing uses in graphics. Fortunately, their similarities concerning geometric structure allow them to be defined and manipulated by the same equations, as you will discover in this chapter.

The one thing lines, rays, and normals have in common is that they are all straight. This makes them very useful in graphics for defining space, direction, the edges of meshes, distance, collisions, reflections, and much more. The line construct is one of the fundamental drawing operations in graphics, as we covered in Chapter 1, Hello Graphics Window: You're On Your Way, and Chapter 2, Let’s Start Drawing.

In this chapter, we will cover the essential knowledge you need to define...

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