Basic Math for Game Development with Unity 3D: A Beginner's Guide to Mathematical Foundations (Paperback)

Chapter 1: Introduction and Learning Environment

Chapter Goal: Sets the context, describes prerequisite knowledge, discusses learning philosophy, guides to install, and presents a very brief tutorial on working with Unity.

Sub-topics

1.       Philosophy, Background, and What You Will Learn

2.       The Platform of Learning: Unity

3.       C# Scripting: Modifying Behaviors in Unity

Chapter 2: Points and Bounds

Chapter Goal: Begins coverage with something very simple. Presents points, distances, and applications of these simple concepts

Sub-topics

1.       Points and Distances

2.       Colliders: Spheres

4.       Colliders: Axis Aligned Boxes

5.       Inside/Outside Tests

6.       Limitations of the Colliders

Chapter 3: Vectors

Chapter Goal: Introduces vectors and applications of vectors.

Sub-topic

1.       Vectors: Size and Direction

2.       Velocity

3.       Lines and Rays

4.       Applications: Following Way Points, Patrolling, Proximity-Based Behavior

Chapter 4: Vector Dot Products

Chapter Goal: Introduces dot products and its applications.

Sub-topics

1.       Dot Product Definition

2.       Interpretation of Results: Direction and Projection

3.       Point to Line Distance: Application in Proximity Tests

4.       Line to Sphere Intersection: Application in Ray Casting

Chapter 5: Planes

Chapter Goal: Acquaints readers to plane equation and applications involving planes.

Sub-topics

1.       Interpreting the Plane Equation

2.       Plane Normal Vectors

3.       Point to Plane Distance

4.       Line to Plane Intersection: Application in Dropping Shadows

5.       Reflecting a Vector: Application in Bouncing an Object

6.       Applications: Projections, Direction Aware Behaviors

Chapter 6: Vector Cross Products

Chapter Goal: Defines cross products and its applications

Sub-topics

1.       Cross Product Definition

2.       Interpretation of Results: Area and Direction

3.       Spanning of a Plane

4.       Identifying Directions

5.       Following and Chasing Behaviors

Chapter 7: Conclusion

Chapter Goal: Summarizes the book and learnings

Sub-topics

1.       Summary and Context of Knowledge

2.       What’s Next and Why

3.       Further Readings and References