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Basic Math for Game Development with Unity 3D.pdf

发布时间：2022-06-01 发布人：admin 分类：说明书 资料大小：6.83M 资料格式：pdf 举报 版权申诉
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    Table of Contents
    About the Authors
    About the Technical Reviewer
    Acknowledgments
    Introduction
    Chapter 1: Introduction and  Learning Environment
    Introduction
    Choice of Unity Engine
    Setting Up Your Development Environment
    Notes on Installing Unity
    Unity Editor Environment
    Opening the Intro to Unity Project
    Working with the Unity Editor
    Working with MyScript
    To Learn More About Working with Unity
    How to Use This Book
    Summary
    References
    Chapter 2: Intervals and Bounding Boxes
    Introduction
    Review of Cartesian Coordinate System
    Intervals: Min-Max Range
    Working with Examples in Unity
    The Interval Bounds In 1D Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Bounding Boxes: Intervals in Three Dimensions
    The Box Bounds Intervals in 3D Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Collision of Intervals
    The Interval Bound Intersections Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Collision of Bounding Boxes
    The Box Bound Intersections Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Placement of the Bounding Box over the Vehicles
    Bounding Box Collisions
    Void Space of a Bounding Box
    Details of MyScript
    Take Away from This Example
    Final Words on Bounding Boxes
    The Unity Bounds Class
    Summary
    Chapter 3: Distances and Bounding Spheres
    Introduction
    Distances Between Positions
    The Positions and Distances Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Sphere Colliders or Bounding Spheres
    The Sphere Bounds Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Collision of Bounding Spheres
    The Sphere Bound Intersections Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    The Unity BoundingSphere Class
    Summary
    Chapter 4: Vectors
    Introduction
    Vectors: Relating Two Points
    Position Vectors
    Following a Vector
    Following a Vector from Different Positions
    The Position Vectors Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Position Vector
    Vector Defined by Two Points
    Details of MyScript
    Region: Visualization On/Off
    Region: Position Vector
    Region: Vector from Two Points
    Take Away from This Example
    Vector Algebra: Scaling
    Normalization of Vectors
    Direction of Vectors
    The Vector Scaling and Normalization Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Scaled Vector
    Normalized or Unit Vector
    Position Vector from Direction and Magnitude
    Summary of Interaction
    Details of MyScript
    Visualization On/Off
    Vector Va
    DrawScaledVector
    DrawUnitVector
    DrawPositionVector
    Take Away from This Example
    Application of Vector: Velocity
    The Velocity and Aiming Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Process the Explorer
    Process the Agent
    Take Away from This Example
    Vector Algebra: Addition and Subtraction
    Rules of Vector Addition and Subtraction
    Addition and Subtraction with the Zero Vector
    Vectors in an Equation
    Geometric Interpretation of Vector Addition and Subtraction
    Vector Addition
    Commutative Property of Vector Addition
    Vector Subtraction
    The Vector Add and Sub Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Vector Addition and the Commutative Property
    Vector Subtraction
    Position Vector
    Details of MyScript
    Take Away from This Example
    Application of Vector Algebra
    The Windy Condition Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Summary
    Chapter 5: Vector Dot Products
    Introduction
    Vector Dot Product: Relating Two Vectors
    Definition of Vector Dot Product
    Properties of Vector Dot Product
    The Angle Between Two Vectors
    The Angle Between Vectors Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Vector Projections
    The Vector Projections Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Representation of a Line Segment
    Inside-Outside Test of a General 1D Interval
    The Line Interval Bound Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Line to Point Distance
    The Line to Point Distance Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Line to Line Distance
    The Line to Line Distance Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Summary
    Vector Dot Product Definition and Implications
    Interpreting the Dot Product Results
    Insights into the Subtended Angle
    The Line Equations
    Chapter 6: Vector Cross Products and 2D Planes
    Introduction
    3D Coordinate System Convention
    Unity Follows the Left-Handed Coordinate System
    Vector Cross Product: The Perpendicular Direction
    Definition of Vector Cross Product
    Geometric Interpretation of Vector Cross Products
    Properties of Vector Cross Product
    The Vector Cross Products Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    The Vector Plane Equation
    The Position Pn on a Plane
    Given a Position on a Plane
    Positions on 2D Planes
    The Vector Plane Equations Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Axis Frames and 2D Regions
    Bounds on a 2D Plane
    The Axis Frames and 2D Regions Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Projections onto 2D Planes
    The Point to Plane Projections Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Line to Plane Intersection
    The Line Plane Intersections Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Mirrored Reflection Across a Plane
    The Reflection Direction
    The Line Reflections Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Details of MyScript
    Take Away from This Example
    Summary
    Chapter 7: Conclusion
    The Final Comprehensive Example
    Examine the Scene
    Analyze MainCamera MyScript Component
    Interact with the Example
    Interact with the Aiming System
    Interact with the Agent
    Interact with the Plane
    Interact with the Shadow
    Interact with the Reflection
    Interact with the Colliding Treasure
    Summary of Interaction
    Details of MyScript
    Step 0: Initial Error Checking
    Step 1: The Aiming System
    Step 2: The Agent
    Step 3: The Plane
    Step 4: The Shadow
    Step 5: The Reflection
    Step 6: The Collision with Treasure
    Take Away from This Example
    What’s Next
    Index
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