Mathematics for and Computer Graphics

Mathematics for 3D Game Programming and Computer Graphics

Third Edition

Eric Lengyel

Course Technology PTR

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Mathematics for 3D Game Programming and Computer Graphics, Third Edition By Eric Lengyel

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Contents

Preface What's New in the Third Edition Contents Overview Website and Code Listings Notational Conventions

Chapter 1 The Rendering Pipeline 1.1 Graphics Processors 1.2 Vertex Transformation 1.3 Rasterization and Fragment Operations

Chapter 2 Vectors 2.1 Vector Properties 2.2 The Dot Product 2.3 The Cross Product 2.4 Vector Spaces Chapter 2 Summary Exercises for Chapter 2

Chapter 3 Matrices 3.1 Matrix Properties 3.2 Linear Systems 3.3 Matrix Inverses 3.4 Determinants 3.5 Eigenvalues and Eigenvectors 3.6 Diagonalization

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Chapter 3 Summary Exercises for Chapter 3

Chapter 4 Transforms

4.1 Linear Transformations 4.1.1 Orthogonal Matrices 4.1.2 Handedness

4.2 Scaling Transforms 4.3 Rotation Transforms

4.3.1 Rotation About an Arbitrary Axis 4.4 Homogeneous Coordinates

4.4.1 Four-Dimensional Transforms 4.4.2 Points and Directions 4.4.3 Geometrical Interpretation of the w Coordinate 4.5 Transforming Normal Vectors 4.6 Quaternions 4.6.1 Quaternion Mathematics 4.6.2 Rotations with Quaternions 4.6.3 Spherical Linear Interpolation Chapter 4 Summary Exercises for Chapter 4

Chapter 5 Geometry for 3D Engines

5.1 Lines in 3D Space 5.1.1 Distance Between a Point and a Line 5.1.2 Distance Between Two Lines

5.2 Planes in 3D Space 5.2.1 Intersection of a Line and a Plane 5.2.2 Intersection of Three Planes 5.2.3 Transforming Planes

5.3 The View Frustum 5.3.1 Field of View 5.3.2 Frustum Planes

5.4 Perspective-Correct Interpolation 5.4.1 Depth Interpolation 5.4.2 Vertex Attribute Interpolation

5.5 Projections 5.5.1 Perspective Projections 5.5.2 Orthographic Projections

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