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Foundations of Game Engine Development, Volume 1: Mathematics, by Eric Lengyel
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The first volume of Foundations of Game Engine Development discusses the mathematics needed by engineers who work on games or other types of virtual simulations. The book begins with conventional treatments of topics such as linear algebra, transforms, and geometry. Then, it introduces 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. Includes exercises.
- Chapter 1: Vectors and Matrices
- 1.1 Vector Fundamentals
- 1.2 Basic Vector Operations
- 1.2.1 Magnitude and Scalar Multiplication
- 1.2.2 Addition and Subtraction
- 1.3 Matrix Fundamentals
- 1.4 Basic Matrix Operations
- 1.4.1 Addition, Subtraction, and Scalar Multiplication
- 1.4.2 Matrix Multiplication
- 1.5 Vector Multiplication
- 1.5.1 Dot Product
- 1.5.2 Cross Product
- 1.5.3 Scalar Triple Product
- 1.6 Vector Projection
- 1.7 Matrix Inversion
- 1.7.1 Identity Matrices
- 1.7.2 Determinants
- 1.7.3 Elementary Matrices
- 1.7.4 Inverse Calculation
- 1.7.5 Inverses of Small Matrices
- Chapter 2: Transforms
- 2.1 Coordinate Spaces
- 2.1.1 Transformation Matrices
- 2.1.2 Orthogonal Transforms
- 2.1.3 Transform Composition
- 2.2 Rotations
- 2.2.1 Rotation About a Coordinate Axis
- 2.2.2 Rotation About an Arbitrary Axis
- 2.3 Reflections
- 2.4 Scales
- 2.5 Skews
- 2.6 Homogeneous Coordinates
- 2.7 Quaternions
- 2.7.1 Quaternion Fundamentals
- 2.7.2 Rotations With Quaternions
- Chapter 3: Geometry
- 3.1 Triangle Meshes
- 3.2 Normal Vectors
- 3.2.1 Calculating Normal Vectors
- 3.2.2 Transforming Normal Vectors
- 3.3 Lines and Rays
- 3.3.1 Parametric Lines
- 3.3.2 Distance Between a Point and a Line
- 3.3.3 Distance Between Two Lines
- 3.4 Planes
- 3.4.1 Implicit Planes
- 3.4.2 Distance Between a Point and a Plane
- 3.4.3 Reflection Through a Plane
- 3.4.4 Intersection of a Line and a Plane
- 3.4.5 Intersection of Three Planes
- 3.4.6 Intersection of Two Planes
- 3.4.7 Transforming Planes
- 3.5 Pl�cker Coordinates
- 3.5.1 Implicit Lines
- 3.5.2 Homogeneous Formulas
- 3.5.3 Transforming Lines
- Chapter 4: Advanced Algebra
- 4.1 Grassmann Algebra
- 4.1.1 Wedge Product
- 4.1.2 Bivectors
- 4.1.3 Trivectors
- 4.1.4 Algebraic Structure
- 4.1.5 Complements
- 4.1.6 Antivectors
- 4.1.7 Antiwedge Product
- 4.2 Projective Geometry
- 4.2.1 Lines
- 4.2.2 Planes
- 4.2.3 Join and Meet
- 4.2.4 Line Crossing
- 4.2.5 Plane Distance
- 4.2.6 Summary and Implementation
- 4.3 Matrix Inverses
- 4.4 Geometric Algebra
- 4.4.1 Geometric Product
- 4.4.2 Vector Division
- 4.4.3 Rotors
- 4.5 Conclusion
- Sales Rank: #327706 in Books
- Published on: 2016-09-11
- Original language: English
- Dimensions: 9.25" h x .47" w x 7.50" l,
- Binding: Paperback
- 200 pages
Most helpful customer reviews
0 of 0 people found the following review helpful.
Five Stars
By Nicholas LeFave
A well written reference for the mathematics required for application development using Graphics APIs
3 of 4 people found the following review helpful.
Excellent to revise 3D math concepts
By Amazon Customer
Excellent book! Unlike other books on similar topics, it doesn't just leave you on the basics, it takes you all the way through to the stuff that is actually used.
Looking forward to more volumes in this series.
1 of 2 people found the following review helpful.
Best game development mathematics book
By Amazon Customer
Excellent book on the basics of mathematics applied to computer graphics and game development.
Wonderful print with great images and well taken example. Love it !
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