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Beginning Math and Physics for Game Programmers

Book Description

Whether you're a hobbyist or a budding game design pro, your objective is probably the same: To create the coolest games possible using today's increasingly sophisticated technology. To do that, however, you need to understand some basic math and physics concepts. Not to worry: You don't need to go to night school if you get this handy guide! Through clear, step-by-step instructions, author Wendy Stahler covers the trigonometry snippets, vector operations, and 1D/2D/3D motion you need to improve your level of game development. Each chapter includes exercises to make the learning stick, and Visualization Experience sections are sprinkled throughout that walk you through a demo of the chapter's content. By the end of the volume, you'll have a thorough understanding of all of the math and physics concepts, principles, and formulas you need to control and enhance your user's gaming experience.

Table of Contents

  1. Copyright
  2. About the Author
  3. About the Technical Reviewers
  4. Acknowledgments
  5. Tell Us What You Think
  6. Introduction
  7. Points and Lines
    1. The Point Defined
    2. The Line Defined
    3. Properties of Lines
    4. Applications in Collision Detection
    5. Self-Assessment Solutions
  8. Geometry Snippets
    1. Distance Between Points
    2. Parabolas
    3. Circles and Spheres
    4. Applications in Collision Detection
    5. Visualization Experience: Collision Detection
    6. Self-Assessment Solutions
  9. Trigonometry Snippets
    1. Degrees Versus Radians
    2. Trigonometric Functions
    3. Trigonometric Identities
    4. Using Math Libraries in C++
    5. Self-Assessment Solutions
  10. Vector Operations
    1. Vector Versus Scalar
    2. Polar Coordinates Versus Cartesian Coordinates
    3. Vector Addition and Subtraction
    4. Scalar Multiplication
    5. Dot Product
    6. Cross Product
    7. Visualization Experience
    8. Self-Assessment Solutions
  11. Matrix Operations
    1. Equal Matrices
    2. Matrix Addition and Subtraction
    3. Scalar Multiplication
    4. Matrix Multiplication
    5. Transpose
    6. Visualization Experience
    7. Self-Assessment Solutions
  12. Transformations
    1. Translation
    2. Scaling
    3. Rotation
    4. Concatenation
    5. Visualization Experience
    6. Self-Assessment Solutions
  13. Unit Conversions
    1. The Metric System
    2. Converting Units Between Systems
    3. Computer Conversions
    4. Self-Assessment Solutions
  14. Motion in One Dimension
    1. Speed and Velocity
    2. Acceleration
    3. Equations of Motion
    4. Visualization Experience
    5. Self-Assessment Solutions
  15. Derivative Approach to Motion in One Dimension
    1. Visualizing Velocity and Derivative
    2. Visualizing Acceleration and Second Derivative
    3. Self-Assessment Solutions
  16. Motion in Two and Three Dimensions
    1. Using Vectors
    2. Projectiles
    3. Visualization Experience
    4. Self-Assessment Solutions
  17. Newton's Laws
    1. Forces
    2. Using Newton's Laws to Determine How Forces Affect an Object's Motion
    3. Self-Assessment Solutions
  18. Energy
    1. Work and Kinetic Energy
    2. Potential Energy and the Conservation Law
    3. Self-Assessment Solutions
  19. Momentum and Collisions
    1. Collision with a Stationary Object
    2. Momentum and Impulse Defined
    3. Modeling Collisions
    4. Visualization Experience
    5. Self-Assessment Solutions
  20. Rotational Motion
    1. Circular Motion
    2. Rotational Dynamics
    3. Self-Assessment Solutions
  21. List of Formulas
    1. Symbols
    2. Chapter 1, “Points and Lines”
    3. Chapter 2, “Geometry Snippets”
    4. Chapter 3, “Trigonometry Snippets”
    5. Chapter 4, “Vector Operations”
    6. Chapter 5, “Matrix Operations”
    7. Chapter 6, “Transformations”
    8. Chapter 7, “Unit Conversions”
    9. Chapter 8, “Motion in One Dimension”
    10. Chapter 9, “Derivative Approach to Motion in One Dimension”
    11. Chapter 10, “Motion in Two and Three Dimensions”
    12. Chapter 11, “Newton's Laws”
    13. Chapter 12, “Energy”
    14. Chapter 13, “Momentum and Collisions”
    15. Chapter 14, ”Rotational Motion”
  22. Suggested Reading
  23. What's on the CD-ROM
    1. Loading the CD Files
    2. Exercise Files
    3. Third-Party Programs
    4. Read This Before Opening the Software
  24. Glossary
  25. Index