Half-title
Title
Copyright
Dedication
Contents
Preface
About This Book
How to Use This Book
Obtaining the Accompanying Software
Getting Started with OpenGL
Other Resources for Computer Graphics
For the Instructor
Acknowledgments
I Introduction
I.1 Display Models
I.1.1 Rectangular Arrays of Pixels
I.1.2 Vector Graphics
I.1.3 Polygonal Modeling
I.2 Coordinates, Points, Lines, and Polygons
I.2.1 Coordinate Systems
I.2.2 Geometric Shapes in OpenGL
Drawing Points in OpenGL
Drawing Lines in OpenGL
Drawing Polygons in OpenGL
Colors
Hidden Surfaces
Polygon Face Orientations
Toggling Wireframe Mode
I.3 Double Buffering for Animation
II Transformations and Viewing
II.1 Transformations in 2-Space
II.1.1 Basic Definitions
II.1.2 Matrix Representation of Linear Transformations
II.1.3 Rigid Transformations and Rotations
II.1.4 Homogeneous Coordinates
II.1.5 Matrix Representation of Affine Transformations
II.1.6 Two-Dimensional Transformations in OpenGL
II.1.7 Another Outlook on Composing Transformations
II.1.8 Two-Dimensional Projective Geometry
II.2 Transformations in 3-Space
II.2.1 Moving from 2-Space to 3-Space
II.2.2 Transformation Matrices in OpenGL
II.2.3 Derivation of the Rotation Matrix
II.2.4 Euler’s Theorem
II.2.5 Three-Dimensional Projective Geometry
II.3 Viewing Transformations and Perspective
II.3.1 Orthographic Viewing Transformations
II.3.2 Perspective Transformations
II.3.3 Mapping Lines to Lines
II.3.4 Another Use for Projection: Shadows
II.3.5 The OpenGL Perspective Transformations
II.4 Mapping to Pixels
II.4.1 Bresenham Algorithm
II.4.2 The Perils of Floating Point Roundoff
III Lighting, Illumination, and Shading
III.1 The Phong Lighting Model
III.1.1 Diffuse Reflection
III.1.2 Specular Reflection
III.1.3 Ambient Reflection and Emissivity
III.1.4 Putting It Together: Multiple Lights and Colors
III.1.5 Gouraud and Phong Shading
III.1.6 Computing Surface Normals
III.1.7 Affine Transformations and Normal Vectors
III.1.8 Light and Material Properties in OpenGL
III.2 The Cook–Torrance Lighting Model
III.2.1 Bidirectional Reflectivity
III.2.2 Overview of Cook–Torrance
III.2.3 The Microfacet Distribution Term
III.2.4 The Geometric Surface Occlusion Term
IV Averaging and Interpolation
IV.1 Linear Interpolation
IV.1.1 Interpolation between Two Points
IV.1.2 Weighted Averages and Affine Combinations
IV.1.3 Interpolation on Three Points: Barycentric Coordinates
Area Interpretation of Barycentric Coordinates
Calculating Barycentric Coordinates
IV.2 Bilinear and Trilinear Interpolation
IV.2.1 Bilinear Interpolation
IV.2.2 Inverting Bilinear Interpolation
IV.2.3 Trilinear Interpolation
IV.3 Convex Sets and Weighted Averages
IV.4 Interpolation and Homogeneous Coordinates
IV.5 Hyperbolic Interpolation
IV.6 Spherical Linear Interpolation
V Texture Mapping
V.1 Texture Mapping an Image
V.1.1 Interpolating a Texture to a Surface
V.1.2 Assigning Texture Coordinates
V.1.3 Mipmapping and Antialiasing
V.1.4 Stochastic Supersampling
V.2 Bump Mapping
V.3 Environment Mapping
V.4 Texture Mapping in OpenGL
V.4.1 Loading a Texture Map
V.4.2 Specifying Texture Coordinates
V.4.3 Modulating Color
V.4.4 Separate Specular Highlights
V.4.5 Managing Multiple Texture Maps
V.4.6 Environment Mapping in OpenGL
VI Color
VI.1 Color Perception
VI.2 Representation of Color Values
VI.2.1 Additive and Subtractive Colors
VI.2.2 Representation of RGB Colors
VI.2.3 Hue, Saturation, and Luminance
VII Bézier Curves
VII.1 Bézier Curves of Degree Three
VII.2 De Casteljau’s Method
VII.3 Recursive Subdivision
Applications of Recursive Subdivision
VII.4 Piecewise Bézier Curves
VII.5 Hermite Polynomials
VII.6 Bézier Curves of General Degree
VII.7 De Casteljau’s Method Revisited
VII.8 Recursive Subdivision Revisited
VII.9 Degree Elevation
VII.10 Bézier Surface Patches
VII.10.1 Basic Properties of Bézier Patches
VII.10.2 Joining Bézier Patches
Subdividing Bézier Patches
VII.11 Bézier Curves and Surfaces in OpenGL
VII.11.1 Bézier Curves
VII.11.2 Bézier Patches
VII.12 Rational Bézier Curves
VII.13 Conic Sections with Rational Bézier Curves
VII.14 Surface of Revolution Example
VII.15 Interpolating with Bézier Curves
VII.15.1 Catmull–Rom Splines
VII.15.2 Bessel–Overhauser Splines
VII.15.3 Tension–Continuity–Bias Splines
VII.16 Interpolating with Bézier Surfaces
VIII B-Splines
VIII.1 Uniform B-Splines of Degree Three
VIII.2 Nonuniform B-Splines
VIII.3 Examples of Nonuniform B-Splines
VIII.4 Properties of Nonuniform B-Splines
VIII.5 The de Boor Algorithm
VIII.6 Blossoms
VIII.7 Derivatives and Smoothness of B-Spline Curves
VIII.8 Knot Insertion
VIII.9 Bézier and B-Spline Curves
From Bézier Curves to B-Spline Curves
From B-Spline Curve to Piecewise Bézier Curve
VIII.10 Degree Elevation
VIII.11 Rational B-Splines and NURBS
VIII.12 B-Splines and NURBS Surfaces in OpenGL
VIII.13 Interpolating with B-Splines
IX Ray Tracing
IX.1 Basic Ray Tracing
Shadow Feelers
Reflection Rays
Transmission Rays
IX.1.1 Local Lighting and Reflection Rays
IX.1.2 Transmission Rays
IX.1.3 Putting It All Together
IX.2 Advanced Ray Tracing Techniques
IX.2.1 Distributed Ray Tracing
Antialiasing with Multiple Eye-to-Pixel Rays
Depth of Field with Jittered Eye Positions
Motion Blur
Soft Shadows with Extended Lights and Jittered Shadow Rays
Using Multiple Techniques at Once
Multiple Colors
Path Tracing. Tracing Diffuse Reflection and Transmission
IX.2.2 Backwards Ray Tracing
Further Reading
IX.3 Special Effects without Ray Tracing
Antialiasing Lines with Blending
Motion Blur and Depth of Field with the Accumulation Buffer
Depth of Field with z-Buffer–Based Blurring
Reflections with Environment Mapping
Mirror Reflections with Clones
Shadows
Transparency, Blending, and Fog
X Intersection Testing
X.1 Fast Intersections with Rays
X.1.1 Ray versus Sphere Intersections
X.1.2 Ray versus Plane Intersections
X.1.3 Ray versus Triangle Intersections
X.1.4 Ray versus Convex Polytope Intersections
X.1.5 Ray versus Cylinder Intersections
X.1.6 Ray versus Quadric Intersections
X.1.7 Ray versus Bézier Patch Intersections
X.2 Pruning Intersection Tests
XI Radiosity
XI.1 The Radiosity Equations
XI.1.1 Patches, Light Levels, and Form Factors
XI.1.2 High-Level Description of the Radiosity Algorithm
XI.2 Calculation of Form Factors
XI.2.1 The Ray Tracing Method
XI.2.2 The Hemicube Method
XI.3 Solving the Radiosity Equations
XI.3.1 Iterative Methods
XI.3.2 Jacobi Iteration
XI.3.3 Gauss–Seidel Iteration
XI.3.4 The Shooting Method
XII Animation and Kinematics
XII.1 Overview
XII.1.1 Techniques Evolved from Traditional Animation
XII.1.2 Computerized Animation
XII.2 Animation of Position
XII.2.1 Ease In: Fixed Target
XII.2.2 Ease In: Moving Target
XII.3 Representations of Orientations
XII.3.1 Rotation Matrices
XII.3.2 Yaw, Pitch, and Roll
XII.3.3 Quaternions
XII.3.4 Theoretical Development of Quaternions
XII.3.5 Representing Rotations with Quaternions
XII.3.6 Quaternion and Rotation Matrix Conversions
XII.3.7 Interpolation of Quaternions
XII.4 Kinematics
XII.4.1 Rigid Links and Joints
XII.4.2 Forward Kinematics
XII.4.3 Inverse Kinematics, Setting It Up
XII.4.4 Inverse Kinematics, Finding a Local Solution
APPENDIX A Mathematics Background
A.1 Preliminaries
A.2 Vectors and Vector Products
A.2.1 Vectors in R2
Dot Products in R2
Cross Products in R2
A.2.2 Vectors in R3
Dot Products in R3
Cross Products in R3
A.3 Matrices
A.3.1 Matrices and Vector Products in R3
A.3.2 Determinants, Inverses, and Adjoints
A.3.3 Linear Subspaces
A.4 Multivariable Calculus
A.4.1 Multivariable Functions
A.4.2 Vector-Valued Functions
A.4.3 Multivariable Vector-Valued Functions
APPENDIX B RayTrace Software Package
B.1 Introduction to the Ray Tracing Package
B.2 The High-Level Ray Tracing Routines
B.3 The RayTrace API
B.3.1 Specifying Lights
B.3.2 Defining the Viewport and Camera Positions
B.3.3 Working with the Pixel Array
B.3.4 Defining Materials
B.3.5 Defining Viewable Objects
B.3.6 Viewable Spheres
B.3.7 Viewable Triangles and Parallelograms
B.3.8 Viewable Ellipsoids
B.3.9 Viewable Cylinders
B.3.10 Viewable Cones
B.3.11 Viewable Parallelepipeds
B.3.12 Viewable Tori
B.3.13 Viewable Bézier Patches
B.3.14 Texture Maps
Bibliography
Index