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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

Anti-aliasing

In the previous sections, we worked on producing pixel-by-pixel lines where one pixel was chosen over another in order to create a continual line or circle. If you zoom in on these pixels, however, you will find that they are quite jagged in appearance, as illustrated by the zoomed-in section of a circle shown in Figure 3.10:

Figure 3.10: A zoomed-in section of the Bresenham circle pixels

This effect occurs because of the way that integer values are chosen to represent the drawing. However, when we looked at the actual equations for lines and circles in the The Naïve Way: Drawing a line with brute force and Drawing Circles the Bresenham way sections, it was clear they involved floating-point values and seemed to pass through more than one pixel. To improve the look of these kinds of drawings, a process called anti-aliasing is employed to blur the pixels that are neighbors of the line pixels to fade the edges of the line. Figure 3.11 shows...

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