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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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Author (1):
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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

Line Plotting Pixel by Pixel

It’s difficult to appreciate what goes on mathematically behind the scenes of high-level drawing methods, such as those used by Pygame methods, unless you’ve written a program to plot objects pixel by pixel – because when it comes down to it, this is how the methods produce their rendered results. To that end, we are going to explore a little deeper the techniques involved in drawing a line pixel by pixel onto the screen. At first, you might assume this is quite a simple thing to do, but you’ll soon discover that it’s quite complex.

As we progress through the content, it will become clear why special algorithms are required to draw mathematical constructs such as lines on a pixel display. The algorithm we are going to explore is also a key technique that can be used for various other graphics and game-related functions wherever straight-line calculations are needed.

Once you’ve completed this chapter, you...

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