3D Math Primer For Graphics and Game Development 1st Edition by Fletcher Dunn, Ian Parberry ISBN 9781284096200 1284096203

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Product details:
ISBN 10: 1284096203
ISBN 13: 9781284096200
Author: Fletcher Dunn, Ian Parberry

3D Math Primer For Graphics and Game Development 1st Edition Table of contents:

Chapter 1: Vectors and Vectors in 3D Space

• Introduction to Vectors and Their Properties
• Vector Operations: Addition, Subtraction, Scalar Multiplication
• Dot Product and Cross Product
• Unit Vectors and Normalization
• Vectors in 3D Space
• Applications of Vectors in Game Development

Chapter 2: Matrices and Transformations

• What Are Matrices and Why Are They Important?
• Matrix Operations: Addition, Subtraction, Multiplication
• Identity Matrix and Inverse Matrix
• Transformation Matrices: Scaling, Translation, Rotation
• Homogeneous Coordinates
• 3D Transformations: Modeling, Viewing, and Projection
• Combining Multiple Transformations
• Coordinate Systems and Changing Frames of Reference

Chapter 3: Geometry and 3D Shapes

• Points, Lines, and Planes in 3D
• Representing 3D Objects: Meshes and Polygons
• The Geometry of Solids: Spheres, Cubes, and Prisms
• Parametric Equations for Curves and Surfaces
• Computational Geometry Basics for Game Development
• Collision Detection Using Geometry
• Using Geometry in 3D Rendering

Chapter 4: Rotation and Orientation

• Basic Rotations in 2D and 3D
• Understanding Euler Angles and Gimbal Lock
• Quaternion Representation of Rotation
• Rotating Vectors and Matrices
• Understanding Rotation in Game Engines
• Using Quaternions for Smooth Rotations and Interpolation
• Implementing Rotation in 3D Game Engines

Chapter 5: 3D Camera Systems

• The Role of the Camera in 3D Graphics
• Coordinate Systems for Cameras
• Viewing and Projection Matrices
• The Camera Transformation: Moving, Rotating, Zooming
• Implementing First-Person and Third-Person Cameras
• Understanding the LookAt Matrix
• Field of View, Aspect Ratio, and Near/Far Planes

Chapter 6: Lighting and Shading

• Introduction to Light Sources and Their Properties
• Types of Lights: Ambient, Directional, Point, and Spotlights
• The Dot Product and Its Role in Lighting Calculations
• Phong Shading Model: Ambient, Diffuse, and Specular Components
• Calculating Lighting for 3D Models
• Shadows and Shadow Mapping
• Implementing Lighting Models in Game Engines

Chapter 7: 3D Rendering and Projection

• Perspective Projection vs. Orthographic Projection
• Creating a Projection Matrix
• The Camera-World Relationship
• Field of View and Aspect Ratio
• The Role of Clipping in 3D Graphics
• Pipeline for Rendering a 3D Object
• Rendering Techniques in Real-Time Graphics

Chapter 8: Physics and Motion in 3D

• Introduction to Physics for Games
• Kinematics: Position, Velocity, and Acceleration
• Understanding Newtonian Physics in 3D
• Gravity and Forces in 3D Space
• Rigid Body Motion: Translational and Rotational Motion
• Integrating Physics into a Game Engine
• Simulating Realistic Motion for Game Objects

Chapter 9: Collision Detection and Response

• The Basics of Collision Detection
• Bounding Volumes: Spheres, Boxes, and Capsules
• Axis-Aligned Bounding Boxes (AABB) and Oriented Bounding Boxes (OBB)
• Separating Axis Theorem for Collision Detection
• Collision Response: Elastic and Inelastic Collisions
• Handling Collisions in 3D Game Engines
• Optimizing Collision Detection for Performance

Chapter 10: Advanced Topics in 3D Math

• Curve and Surface Representation: Bezier Curves, NURBS
• Spline Interpolation for Animation
• Rigid Body Dynamics and Constraints
• Fluid Simulations and Particle Systems
• Advanced Lighting Models: Radiosity and Global Illumination
• Real-Time Ray Tracing Basics
• Implementing Advanced Mathematics in Game Development

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