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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

Understanding OpenGL’s Matrix Stack

In graphics, the current transformation applied to a point or object is determined by the current model-view-projection (MVP) matrix. This is a culmination of the model matrix, the view matrix, and the projection matrix. We first discussed these matrices as coordinate spaces in Chapter 4, Graphics and Game Engine Components. Each one has a specific use in the graphics pipeline, as is shown in Figure 14.1 (this diagram has been reinserted here from Chapter 4, Graphics and Game Engine Components, for your convenience):

Figure 14.1: The graphics pipeline

The coordinates or points that define a graphics object are stored in a model’s local coordinate system. They define the geometry of the object independently of where it is situated in world space. As we saw in Chapter 4, Graphics and Game Engine Components, a cube can be defined by six points, one for each of the vertices, thus:

cube.vertices = [(0.5, -0.5...
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