3D math primer for graphics and game development
By: Fletcher Dunn, Ian Parberry
Contributors: Parberry, Ian
Edition: 2nd ed.
Publisher: A K Peters; A K Peters/CRC Press
Published: 2011
Place of publication: Natick, MA
Language: eng
Number of pages: 846
ISBN-13: 9781568817231
Subjects: Computer games; Computer graphics; COMPUTERS / Programming / Games; Computer science; Mathematics; Programming
Other titles: Three-D math primer for graphics and game development
Description: "This book presents the essential math needed to describe, simulate, and render a 3D world. It provides an introduction to mathematics for game designers, including fundamentals of coordinate spaces, vectors, and matrices, orientation in three dimensions, introduction to calculus and dynamics, graphics, and parametric curves"--
Notes: Includes bibliographical references and index.
Table of contents: title: Acknowledgments
pagenum: xiii; title: Introduction
pagenum: xv; label: 1
title: Cartesian Coordinate Systems
pagenum: 1; label: 1.1
title: 1D Mathematics
pagenum: 2; label: 1.2
title: 2D Cartesian Space
pagenum: 5; label: 1.3
title: 3D Cartesian Space
pagenum: 12; label: 1.4
title: Odds and Ends
pagenum: 19; label: 1.5
title: Exercises
pagenum: 27; label: 2
title: Vectors
pagenum: 31; label: 2.1
title: Mathematical Definition of Vector, and Other Boring Stuff
pagenum: 32; label: 2.2
title: Geometric Definition of Vector
pagenum: 34; label: 2.3
title: Specifying Vectors with Cartesian Coordinates
pagenum: 36; label: 2.4
title: Vectors versus Points
pagenum: 39; label: 2.5
title: Negating a Vector
pagenum: 43; label: 2.6
title: Vector Multiplication by a Scalar
pagenum: 45; label: 2.7
title: Vector Addition and Subtraction
pagenum: 47; label: 2.8
title: Vector Magnitude (Length)
pagenum: 51; label: 2.9
title: Unit Vectors
pagenum: 53; label: 2.10
title: The Distance Formula
pagenum: 55; label: 2.11
title: Vector Dot Product
pagenum: 56; label: 2.12
title: Vector Cross Product
pagenum: 66; label: 2.13
title: Linear Algebra Identities
pagenum: 70; label: 2.14
title: Exercises
pagenum: 71; label: 3
title: Multiple Coordinate Spaces
pagenum: 79; label: 3.1
title: Why Bother with Multiple Coordinate Spaces?
pagenum: 80; label: 3.2
title: Some Useful Coordinate Spaces
pagenum: 81; label: 3.3
title: Basis Vectors and Coordinate Space Transformations
pagenum: 86; label: 3.4
title: Nested Coordinate Spaces
pagenum: 106; label: 3.5
title: In Defense of Upright Space
pagenum: 108; label: 3.6
title: Exercises
pagenum: 109; label: 4
title: Introduction to Matrices
pagenum: 113; label: 4.1
title: Mathematical Definition of Matrix
pagenum: 113; label: 4.2
title: Geometric Interpretation of Matrix
pagenum: 124; label: 4.3
title: The Bigger Picture of Linear Algebra
pagenum: 130; label: 4.4
title: Exercises
pagenum: 132; label: 5
title: Matrices and Linear Transformations
pagenum: 137; label: 5.1
title: Rotation
pagenum: 138; label: 5.2
title: Scale
pagenum: 144; label: 5.3
title: Orthographic Projection
pagenum: 148; label: 5.4
title: Reflection
pagenum: 151; label: 5.5
title: Shearing
pagenum: 152; label: 5.6
title: Combining Transformations
pagenum: 153; label: 5.7
title: Classes of Transformations
pagenum: 154; label: 5.8
title: Exercises
pagenum: 159; label: 6
title: More on Matrices
pagenum: 161; label: 6.1
title: Determinant of a Matrix
pagenum: 161; label: 6.2
title: Inverse of a Matrix
pagenum: 168; label: 6.3
title: Orthogonal Matrices
pagenum: 171; label: 6.4
title: 4 × 4 Homogeneous Matrices
pagenum: 176; label: 6.5
title: 4 × 4 Matrices and Perspective Projection
pagenum: 183; label: 6.6
title: Exercises
pagenum: 189; label: 7
title: Polar Coordinate Systems
pagenum: 191; label: 7.1
title: 2D Polar Space
pagenum: 191; label: 7.2
title: Why Would Anybody Use Polar Coordinates?
pagenum: 201; label: 7.3
title: 3D Polar Space
pagenum: 203; label: 7.4
title: Using Polar Coordinates to Specify Vectors
pagenum: 213; label: 7.5
title: Exercises
pagenum: 214; label: 8
title: Rotation in Three Dimensions
pagenum: 217; label: 8.1
title: What Exactly is "Orientation"?
pagenum: 218; label: 8.2
title: Matrix Form
pagenum: 220; label: 8.3
title: Euler Angles
pagenum: 229; label: 8.4
title: Axis-Angle and Exponential Map Representations
pagenum: 244; label: 8.5
title: Quaternions
pagenum: 246; label: 8.6
title: Comparison of Methods
pagenum: 273; label: 8.7
title: Converting between Representations
pagenum: 275; label: 8.8
title: Exercises
pagenum: 291; label: 9
title: Geometric Primitives
pagenum: 295; label: 9.1
title: Representation Techniques
pagenum: 295; label: 9.2
title: Lines and Rays
pagenum: 297; label: 9.3
title: Spheres and Circles
pagenum: 303; label: 9.4
title: Bounding Boxes
pagenum: 304; label: 9.5
title: Planes
pagenum: 311; label: 9.6
title: Triangles
pagenum: 317; label: 9.7
title: Polygons
pagenum: 332; label: 9.8
title: Exercises
pagenum: 339; label: 10
title: Mathematical Topics from 3D Graphics
pagenum: 343; label: 10.1
title: How Graphics Works
pagenum: 345; label: 10.2
title: Viewing in 3D
pagenum: 362; label: 10.3
title: Coordinate Spaces
pagenum: 369; label: 10.4
title: Polygon Meshes
pagenum: 381; label: 10.5
title: Texture Mapping
pagenum: 393; label: 10.6
title: The Standard Local Lighting Model
pagenum: 396; label: 10.7
title: Light Sources
pagenum: 414; label: 10.8
title: Skeletal Animation
pagenum: 424; label: 10.9
title: Bump Mapping
pagenum: 431; label: 10.10
title: The Real-Time Graphics Pipeline
pagenum: 438; label: 10.11
title: Some HLSL Examples
pagenum: 457; label: 10.12
title: Further Reading
pagenum: 475; label: 10.13
title: Exercises
pagenum: 476; label: 11
title: Mechanics 1: Linear Kinematics and Calculus
pagenum: 479; label: 11.1
title: Overview and Other Expectation-Reducing Remarks
pagenum: 479; label: 11.2
title: Basic Quantities and Units
pagenum: 483; label: 11.3
title: Average Velocity
pagenum: 486; label: 11.4
title: Instantaneous Velocity and the Derivative
pagenum: 490; label: 11.5
title: Acceleration
pagenum: 513; label: 11.6
title: Motion under Constant Acceleration
pagenum: 516; label: 11.7
title: The Integral
pagenum: 530; label: 11.8
title: Uniform Circular Motion
pagenum: 542; label: 11.9
title: Exercises
pagenum: 549; label: 12
title: Mechanics 2: Linear and Rotational Dynamics
pagenum: 553; label: 12.1
title: Newton's Three Laws
pagenum: 554; label: 12.2
title: Some Simple Force Laws
pagenum: 562; label: 12.3
title: Momentum
pagenum: 581; label: 12.4
title: Impulsive Forces and Collisions
pagenum: 590; label: 12.5
title: Rotational Dynamics
pagenum: 603; label: 12.6
title: Real-Time Rigid Body Simulators
pagenum: 621; label: 12.7
title: Suggested Reading
pagenum: 639; label: 12.8
title: Exercises
pagenum: 640; label: 13
title: Curves in 3D
pagenum: 645; label: 13.1
title: Parametric Polynomial Curves
pagenum: 646; label: 13.2
title: Polynomial Interpolation
pagenum: 653; label: 13.3
title: Hermite Curves
pagenum: 665; label: 13.4
title: Bézier Curves
pagenum: 670; label: 13.5
title: Subdivision
pagenum: 685; label: 13.6
title: Splines
pagenum: 690; label: 13.7
title: Hermite and Bézier Splines
pagenum: 694; label: 13.8
title: Continuity
pagenum: 697; label: 13.9
title: Automatic Tangent Control
pagenum: 702; label: 13.10
title: Exercises
pagenum: 711; label: 14
title: Afterword
pagenum: 715; label: 14.1
title: What Next?
pagenum: 715; label: 14.2
title: Exercises
pagenum: 715; label: A
title: Geometric Tests
pagenum: 717; label: A.1
title: Closest Point on 2D Implicit Line
pagenum: 717; label: A.2
title: Closest Point on a Parametric Ray
pagenum: 718; label: A.3
title: Closest Point on a Plane
pagenum: 719; label: A.4
title: Closest Point on a Circle or Sphere
pagenum: 719; label: A.5
title: Closest Point in an AABB
pagenum: 720; label: A.6
title: Intersection Tests
pagenum: 720; label: A.7
title: Intersection of Two Implicit Lines in 2D
pagenum: 721; label: A.8
title: Intersection of Two Rays in 3D
pagenum: 722; label: A.9
title: Intersection of a Ray and a Plane
pagenum: 724; label: A.10
title: Intersection of an AABB and a Plane
pagenum: 725; label: A.11
title: Intersection of Three Planes
pagenum: 726; label: A.12
title: Intersection of a Ray and a Circle or Sphere
pagenum: 727; label: A.13
title: Intersection of Two Circles or Spheres
pagenum: 729; label: A.14
title: Intersection of a Sphere and an AABB
pagenum: 731; label: A.15
title: Intersection of a Sphere and a Plane
pagenum: 732; label: A.16
title: Intersection of a Ray and a Triangle
pagenum: 734; label: A.17
title: Intersection of Two AABBs
pagenum: 737; label: A.18
title: Intersection of a Ray and an AABB
pagenum: 740; label: B
title: Answers to the Exercises
pagenum: 745; label: B.1
title: Chapter 1
pagenum: 745; label: B.2
title: Chapter 2
pagenum: 746; label: B.3
title: Chapter 3
pagenum: 758; label: B.4
title: Chapter 4
pagenum: 759; label: B.5
title: Chapter 5
pagenum: 763; label: B.6
title: Chapter 6
pagenum: 765; label: B.7
title: Chapter 7
pagenum: 767; label: B.8
title: Chapter 8
pagenum: 772; label: B.9
title: Chapter 9
pagenum: 774; label: B.10
title: Chapter 10
pagenum: 779; label: B.11
title: Chapter 11
pagenum: 781; label: B.12
title: Chapter 12
pagenum: 784; label: B.13
title: Chapter 13
pagenum: 792; label: B.14
title: Chapter 14
pagenum: 799; title: Bibliography
pagenum: 800; title: Index
pagenum: 807