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Foundations of game engine development, volume 1: mathematics, eric lengyel

1250 грн

Описание

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 Matrices1.1 Vector Fundamentals1.2 Basic
Vector Operations1.2.1 Magnitude and Scalar Multiplication1.2.2 Addition and
Subtraction1.3 Matrix Fundamentals1.4 Basic Matrix Operations1.4.1 Addition,
Subtraction, and Scalar Multiplication1.4.2 Matrix Multiplication1.5 Vector
Multiplication1.5.1 Dot Product1.5.2 Cross Product1.5.3 Scalar Triple
Product1.6 Vector Projection1.7 Matrix Inversion1.7.1 Identity Matrices1.7.2
Determinants1.7.3 Elementary Matrices1.7.4 Inverse Calculation1.7.5 Inverses
of Small MatricesChapter 2: Transforms2.1 Coordinate Spaces2.1.1
Transformation Matrices2.1.2 Orthogonal Transforms2.1.3 Transform
Composition2.2 Rotations2.2.1 Rotation About a Coordinate Axis2.2.2 Rotation
About an Arbitrary Axis2.3 Reflections2.4 Scales2.5 Skews2.6 Homogeneous
Coordinates2.7 Quaternions2.7.1 Quaternion Fundamentals2.7.2 Rotations With
QuaternionsChapter 3: Geometry3.1 Triangle Meshes3.2 Normal Vectors3.2.1
Calculating Normal Vectors3.2.2 Transforming Normal Vectors3.3 Lines and
Rays3.3.1 Parametric Lines3.3.2 Distance Between a Point and a Line3.3.3
Distance Between Two Lines3.4 Planes3.4.1 Implicit Planes3.4.2 Distance
Between a Point and a Plane3.4.3 Reflection Through a Plane3.4.4 Intersection
of a Line and a Plane3.4.5 Intersection of Three Planes3.4.6 Intersection of
Two Planes3.4.7 Transforming Planes3.5 Plücker Coordinates3.5.1 Implicit
Lines3.5.2 Homogeneous Formulas3.5.3 Transforming LinesChapter 4: Advanced
Algebra4.1 Grassmann Algebra4.1.1 Wedge Product4.1.2 Bivectors4.1.3
Trivectors4.1.4 Algebraic Structure4.1.5 Complements4.1.6 Antivectors4.1.7
Antiwedge Product4.2 Projective Geometry4.2.1 Lines4.2.2 Planes4.2.3 Join and
Meet4.2.4 Line Crossing4.2.5 Plane Distance4.2.6 Summary and Implementation4.3
Matrix Inverses4.4 Geometric Algebra4.4.1 Geometric Product4.4.2 Vector
Division4.4.3 Rotors4.5 Conclusion

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