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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

Viewing the Scene with Cameras

The camera is responsible for taking the coordinates of objects (specifically, all their vertices and other properties) and transforming them in the modelview of Figure 4.2. If you consider the vertices of the square mesh we looked at in the previous section, its coordinates are not going to retain those values as it will be moved around in the graphics/game world. The modelview takes the world location of the mesh and the location of the camera, as well as some additional properties, and determines the new coordinates of the mesh so that it can be rendered correctly. Note that I am being purposefully abstract in describing this process right now as there’s a lot of mathematics involved, and I don’t want to complicate the discussion at this point!

The camera is a virtual object through which the world is visualized. It is the eye of the viewer and can be moved around the environment to provide different points of view. As illustrated...

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