Beginning Math and Physics for Game Programmers

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