Foundations

of

Game Engine Development

Foundations of Game Engine Development, Volume 1: Mathematics Foundations of Game Engine Development, Volume 2: Graphics Foundations of Game Engine Development, Volume 3: Animation Foundations of Game Engine Development, Volume 4: Physics

Foundations of Game Engine Development is a new book series currently being written by Eric Lengyel. Its four volumes cover the essentials of game engine development in the broad areas of mathematics, graphics, animation, and physics.

Foundations of Game Engine Development, Volume 1: Mathametics

Volume 1: Mathematics
Release date: August 2016
ISBN: 978-0-9858117-4-7
Full color · Soft cover
Approximately 200 pages

Volume 1 book will begin with conventional treatments of topics such as linear algebra, geometry, and transforms. Then, it will introduce Grassmann algebra and geometric algebra to provide a much deeper understanding of the subject matter and highlight the places where traditional arithmetic with vectors, matrices, quaternions, etc., isn't quite correct.

Below is a tentative table of contents listing most of the important topics that will be covered in the book. Each chapter will go into great detail and include extensive problem sets.

Chapter 1: Vectors and Matrices

  • Basic vector operations
  • Basic matrix operations
  • Dot product, cross product
  • Scalar triple product
  • Vector projection, rejection
  • Orthogonalization
  • Matrix inversion
  • Determinants

Chapter 2: Transforms

  • Transformation matrices
  • Orthogonal transforms
  • Rotation, reflection, scale, skew
  • Homogeneous coordinates
  • Quaternions

Chapter 3: Geometry

  • Triangle meshes
  • Normal vectors
  • Lines and rays
  • Planes
  • Plücker coordinates

Chapter 4: Advanced Algebra

  • Grassmann algebra
  • Wedge product, antiwedge product
  • Bivectors, trivectors, antivectors
  • Dual numbers
  • 4D geometry, lines, planes
  • Meet and join operations
  • Geometric product
  • Vector division
  • Rotors
Foundations of Game Engine Development, Volume 2: Graphics

Volume 2: Graphics
ISBN: 978-0-9858117-5-4
Full color · Soft cover
Length to be determined

Below is a list of topics that are planned to be covered in the second volume.

  • View frustums
  • Projection matrices
  • Object culling
  • Light sources
  • Shadow mapping
  • Conventional shading
  • Physically-based shading
  • Volume rendering
  • Marching cubes
  • Scene organization
  • Zones and portals
Foundations of Game Engine Development, Volume 3: Animation

Volume 3: Animation
ISBN: 978-0-9858117-6-1
Full color · Soft cover
Length to be determined

Below is a list of topics that are planned to be covered in the third volume.

  • Bézier curves
  • B-splines
  • Hierarchical models
  • Morphing
  • Skinning
  • Forward kinematics
  • Inverse kinematics
  • Dual quaternions
  • Animation trees
  • Projectiles
  • Particle systems
  • Special effects
Foundations of Game Engine Development, Volume 4: Physics

Volume 4: Physics
ISBN: 978-0-9858117-7-8
Full color · Soft cover
Length to be determined

Below is a list of topics that are planned to be covered in the fourth volume.

  • Linear velocity, angular velocity
  • Forces, acceleration
  • Center of mass
  • Moment of inertia
  • Collision detection
  • GJK algorithm
  • Conservative advancement
  • Velocity constraints, position constraints
  • Lagrange multipliers
  • Jacobians
  • Split impulses
  • Joints (e.g., spherical, cylindrical, revolute)
  • Restitution
  • Friction
  • Rolling resistance
  • Buoyancy