Preface
1 A Survey of Computer Graphics
1-1 Graphs and Charts
1-2 Computer-Aided Design
1-3 Virtual-Reality Environments
1-4 Data Visualizations
1-5 Education and Training
1-6 Computer Art
1-7 Entertainment
1-8 Image Processing
1-9 Graphical User Interfaces
1-10 Summary
References
2 Overview of Graphics Systems
2-1 Video Display Devices
·Refresh Cathode-Ray Tubes
·Raster-Scan Displays
·Random-Scan Displays
·Color CRT Monitors
·Flat-Panel Displays
·Three-Dimensional Viewing Devices
·Stereoscopic and Virtual-Reality Systems
2-2 Raster-Scan Systems
·Video Controller
·Raster-Scan Display Processor
2-3 Graphics Workstations and Viewing Systems
2-4 Input Devices
·Keyboards,Button Boxes,and Dials
·Mouse Devices
·Trackballs and Spaceballs
·Joysticks
·Data Gloves
·Digitizers
·Image Scanners
·Touch Panels
·Light Pens
·Voice Systems
2-5 Hard-Copy Devices
2-6 Graphics Networks
2-7 Graphics on the Internet
2-8 Graphics Software
·Coordinate Representations
·Graphics Functions
·Software Standards
·Other Graphics Packages
2-9 Introduction to OpenGL
·Basic OpenGL Syntax
·Related Libraries
·Header Files
·Display-Window Management Using GLUT
·A Complete OpenGL Program
2-10 Summary
References
Exercises
3 Graphics Output Primitives
3-1 Corrdinate Reference Frames
·Screen Coordinates
·Absolute and Relative Coordinate Specifications
3-2 Specifying a Two-Dimensional World-Coordinate Reference Frame in OpenGL
3-3 OpenGL Point Functions
3-4 OpenGL Line Functions
3-5 Line-Drawing Algorithms
·Line Equations
·DDA Algorithm
·Bresenham's Line Algorithm
·Displaying Polylines
3-6 Parallel Line Algorithms
3-7 Setting Frame-Buffer Values
3-8 OpenGL Curve Functions
3-9 Circle-Generating Algorithms
·Properties of Circles
·Midpoint Circle Algorithms
3-10 Ellipse-Cenerating Algorithm
·Properties of Ellipses
·Midpoint Ellipse Algorithm
3-11 Other Curves
·Conic Sections
·Polynomials and Spline Curves
3-12 Parallel Curve Algorithms
3-13 Pixel Addressing and Object Geometry
·Screen Grid Coordinates
·Maintaining Geometric Properties of Displayed Objects
3-14 Fill-Area Primitives
3-15 Polygon Fill Areas
·Polygon Classifications
·Identifying Concave Polygons
·Splitting Concave Polygons
·Splitting a Convex Polygon into a Set of Triangles
·Inside-Outside Tests
·Polygon Tables
·Plane Equations
·Front and Back Polygon Faces
3-16 OpenGL Polygon Fill-Area Functions
3-17 OpenGL Vertex Arrays
3-18 Pixel-Array Primitives
3-19 OpenGL Pixel-Array Functions
·OpenGL Bitmap Function
·OpenGL Pixmap Function
·OpenGL Raster Operations
3-20 Character Primitives
3-21 OpenGL Character Functions
3-22 Picture Partitioning
3-23 OpenGL Display Lists
·Creating and Naming an OpenGL Display List
·Executing OpenGL Display Lists
·Deleting OpenGL Display Lists
3-24 OpenGL Display-Window Reshape Function
3-25 Summary
Example Programs
References
Exercises
4 Attributes of Graphics Primitives
4-1 OpenGL State Variables
4-2 Color and Gray Scale
·RGB Color Components
·Color Tables
·Gray Scale
·Other Color Parameters
4-3 OpenGL Color Functions
·The OpenGL RGB and RGBA Color Modes
·OpenGL Color-Index Mode
·OpenGL Color Blending
·OpenGL Color Arrays
·Other OpenGL Color Functions
4-4 Point Attributes
4-5 Line Attributes
·Line Width
·Line Style
·Pen and Brush Options
4-6 Curve Attributes
4-7 OpenGL Point-Attribute Functions
4-8 OpenGL Line-Attribute Functions
·OpenGL Line-Width Function
·OpenGL Line-Style Function
·Other OpenGL Line Effects
4-9 Fill-Area Attributes
·Fill Styles
·Color-Blended Fill Regions
4-10 General Scan-Line Polygon-Fill Algorithm
4-11 Scan-Line Fill of Convex Polygons
4-12 Scan-Line Fill for Regions with Curved Boundaries
4-13 Fill Methods for Areas with Irregular Boundaries
·Boundary-Fill Algorithm
·Flood-Fill Algorithm
4-14 OpenGL Fill-Area Attribute Functions
·OpenGL Fill-Pattern Function
·OpenGL Texture and Interpolation Patterns
·OpenGL Wire-Frame Methods
·OpenGL Front-Face Function
4-15 Character Attributes
4-16 OpenGL Character-Attribute Functions
4-17 Antialiasing
·Supersampling Straight-Line Segments
·Subpixel Weighting Masks
·Area Sampling Straight Line Segments
·Filtering Techniques
·Pixel Phasing
·Compensating for Line-Intensity Differences
·Antialiasing Area Boundaries
4-18 OpenGL Antialiasing Functions
4-19 OpenGL Query Functions
4-20 OpenGL Attribute Groups
4-21 Summary
References
Exercises
5 Geometric Transformations
5-1 Basic Two-Dimensional Geometric Transformations
·Two-Dimensional Translation
·Two-Dimensional Rotation
·Two-Dimensional Scaling
5-2 Matrix Representations and Homogeneous Coordinates
·Homogeneous Coordinates
·Two-Dimensional Translation Matrix
·Two-Dimensional Rotation Matrix
·Two-Dimensional Scaling Matrix
5-3 Inverse Transformations
5-4 Two-Dimensional Composite Transformations
·Composite Two-Dimensional Translations
·Composite Two-Dimensional Rotations
·Composite Two-Dimensional Scalings
·General Two-Dimensional Pivot-Point Rotation
·General Two-Dimensional Fixed-Point Scaling
·General Two-Dimensional Scaling Directions
·Matrix Concatenation Properties
·General Two-Dimensional Composite Transformations and Computational Efficiency
·Two-Dimensional Rigid-Body Transformation
·Constructing Two-Dimensional Rotation Matrices
·Two-Dimensional Composite-Matrix Programming Example
5-5 Other Two-Dimensional Transformations
·Reflection
·Shear
5-6 Raster Methods for Geometric Transformations
5-7 OpenGL Raster Transformations
5-8 Transformations Between Two-Dimensional Coordinate Systems
5-9 Geometric Transformations in Three-Dimensional Space
5-10 Three-Dimensional Translation
5-11 Three-Dimensional Rotation
·Three-Dimensional Coordinate-Axis Rotations
·General Three-Dimensional Rotations
·Quaternion Methods for Three-Dimensional Rotations
5-12 Three-Dimensional Scaling
5-13 Composite Three-Dimensional Transformations
5-14 Other Three-Dimensional Transformations
·Three-Dimensional Reflections
·Three-Dimensional Shears
5-15 Transformations Between Three-Dimensional Coordinate Systems
5-16 Affine Transformations
5-17 OpenGL Geometric-Transformation Functions
·Basic OpenGL Geometric Transformations
·OpenGL Matrix Operations
·OpenGL Matrix Stacks
·OpenGL Geometric-Transformation Programming Examples
5-18 Summary
References
Exercises
6 Two-Dimensional Viewing
6-1 The Two-Dimensional Viewing Pipeline
6-2 The Clipping Window
·Viewing-Coordinate Clipping Window
·World-Coordinate Clipping Window
6-3 Normalization and Viewport Transformation
·Mapping the Clipping Window into a Normalized Viewport
·Mapping the Clipping Window into a Normalized Square
·Display of Character Strings
·Split-Screen Effects and Multiple Output Devices
6-4 OpenGL Two-Dimensional Viewing Functions
·OpenGL Projection Mode
·GLU Clipping-Window Function
·OpenGL Viewport Function
·Creating a GLUT Display Window
·Setting the GLUT Display-Window Mode and Color
·GLUT Display-Window Identifier
·Deleting a GLUT Display Window
·Current GLUT Display Window
·Relocating and Resizing a GLUT Display Window
·Managing Multiple GLUT Display Windows
·GLUT Subwindows
·Selecting a Display-Window Screen Cursor Shape
·Viewing Graphics Objects in a GLUT Display Window
·Executing the Application Program
·Other GLUT Functions
·OpenGL Two-Dimensional Viewing Program Example
6-5 Clipping Algorithms
6-6 Two-Dimensional Point Clipping
6-7 Two-Dimensional Line Clipping
·Cohen-Sutherland Line Clipping
·Liang-Barsky Line Clipping
·Nichol-Lee-Nichol Line Clipping
·Line Clipping Using Nonrectangular Polygon Clip Windows
·Line Clipping Using Nonlinear Clipping-Window Boundaries
6-8 Polygon Fill-Area Clipping
·Sutherland-Hodgman Polygon Clipping
·Weiler-Atherton Polygon Clipping
·Polygon Clipping Using Nonrectangular Polygon Clip Windows
·Polygon Clipping Using Nonlinear Clipping-Window Boundaries
6-9 Curve Clipping
6-10 Text Clipping
6-11 Summary
References
Exercises
7 Three-Dimensional Viewing
7-1 Overview of Three-Dimensional Viewing Concepts
·Viewing a Three-Dimensional Scene
·Projections
·Depth Cueing
·Identifying Visible Lines and Surfaces
·Surface Rendering
·Exploded and Cutaway Views
·Three-Dimensional and Stereoscopic Viewing
7-2 The Three-Dimensional Viewing Pipeline
7-3 Three-Dimensional Viewing-Coordinate Parameters
·The View-Plane Normal Vector
·The View-Up Vecotr
·The uvn Viewing-Coordinate Reference Frame
·Generating Three-Dimensional Viewing Effects
7-4 Transformation from World to Viewing Coordinates
7-5 Projection transformations
7-6 Orthogonal Projections
·Axonometric and Isometric Orthogonal Projections
·Orthogonal Projections Corrdinates
·Clipping Window and Orthogonal-Projection View Volume
·Normalization Transformation for an Orthogonal Projections
7-7 Oblique Parallel Projections
·Oblique Parallel Projections in Drafting and Design
·Cavalier and Cabinet Oblique Parallel Projections
·Oblique Parallel-Projections Vector
·Clipping Window and Oblique Parallel-Projection View Volume
·Oblique Parallel-Projection Transformation Matrix
·Normalization Transformation for an Oblique Parallel Projection
7-8 Perspective Projections
·Perspective-Projection Transfromation Coordinates
·Perspective-Projection Equations:Special Cases
·Vanishing Points for Perspective Projections
·Perspective-Projection View Volume
·Perspective-Projection Transformation Matrix
·Symmetric Perspective Projection-Frustum
·Oblique Perspective-Projection Frustum
·Normalized Perspective-Projection Transformation Coordinates
7-9 The Viewport Transformation and Three-Dimensional Screen Coordinates
7-10 OpenGL Three-Dimensional Viewing Functions
·OpenGL Viewing-Transformation Function
·OpenGL Orthogonal-Projection Function
·OpenGL Symmetric Perspective-Projection Frustum
·OpenGL General Perspective-Projection Frustum
·OpenGL Viewports and Display Windows
·OpenGL Three-Dimensional Viewing Program Example
7-11Three-Dimensional Clipping Algorithms
·Clipping in Three-Dimensional Homogeneous Coordinates
·Three-Dimensional Region Codes
·Three-Dimensional Point and Line Clipping
·Three-Dimensional Polygon Clipping
·Three-Dimensional Curve Clipping
·Arbitary Clipping Planes
7-12 OpenGL Optional Clipping Planes
7-13 Summary
References
Exercises
8 Three-Dimensional Object Representations
8-1 Polyhedra
8-2 OpenGL Polyhedron Functions
·OpenGL Polyhedron Fill-Area Functions
·GLUT Regular-Polyhedron Functions
·Example GLUT Polyhedron Program
8-3 Curved Surfaces
8-4 Quadric Surfaces
·Sphere
·Ellipsoid
·Torus
8-5 Superquadrics
·Superellipse
·Superellipsoid
8-6 OpenGL Quadric-Surface and Cubic-Surface Functions
·GLUT Quadric-Surface Functions
·GLUT Cubic-Surface Teapot Function
·GLU Quadric-Surface Functions
·Example Program Using GLUT and GLU Quadric-Surface Functions
8-7 Blobby Objects
8-8 Spline Representations
·Interpolation and Approximation Splines
·Parametric Continuity Conditions
·Geometric Continuity Conditions
·Spline Specifications
·Spline Surfaces
·Trimming Spline Surfaces
8-9 Cubic-Spline Interpolation Methods
·Natural Cubic Splines
·Hermite Interpolation
·Cardinal Splines
·Kochaned-Bartels Splines
8-10 Bezier Spline Curves
·Bezier Curve Equations
·Example Bezier Curve-Generating Program
·Properties of Bezier Curves
·Design Techniques Using Bezier Curves
·Cubic Bezier Curves
8-11 Bezier Surfaces
8-12 B-Spline Curves
·B-Spline Curves Equations
·Uniform Periodic B-Spline Curves
·Cubic Periodic B-Spline Curves
·Open Uniform B-Spline Curves
·Nonuniform B-Spline Curves
8-13 B-Spline Surfaces
8-14 Beta Splines
·Beta-Spline Continuity Conditions
·Cubic Periodic Beta-Spline Matrix Representation
8-15 Rational Splines
8-16 Conversion Between Spline Representations
8-17 Displaying Spline Curves and Surfaces
·Horner's Rule
·Forward-Difference Calculations
·Subdivision Methods
8-18 OpenGL Approximation-Spline Functions
·OpenGL Bezier Spline Curve Functions
·OpenGL Bezier Spline Surface Functions
·GLU B-Spline Curve Functions
·GLU B-Spline Surface Functions
·GLU Surface-Trimming Functions
8-19 Sweep Representations
8-20 Constructive Solid-Geometry Methods
8-21 Octrees
8-22 BSP Trees
8-23 Fractal-Geometry Methods
·Fractal Generation Procedures
·Classification of Fractals
·Fractal Dimension
·Geometric Construction of Deterministic Self-Similar Fractals
·Geometric Construction of Statistically Self-Similar Fractals
·Affine Fractal-Construction Methods
·Random Midpoint-Displacement Methods
·Controlling Terrain Topography
·Self-Squaring Fractals
·Self-Inverse Fractals
8-24 Shape Grammars and Other Procedural Methods
8-25 Particle Systems
8-26 Physically Based Modeling
8-27 Visualization of Data Sets
·Visual Representations for Scalar Fields
·Visual Representations for Vector Fields
·Visual Representations for Tensor Fields
·Visual Representations for Multivariate Data Fields
8-28 Summary
References
Exercises
9 Visible-Surface Detection Methods
9-1 Classification of Visible-Surface Detection Algorithms
9-2 Back-Face Detection
9-3 Depth-Buffer Method
9-4 A-Buffer Method
9-5 Scan-Line Method
9-6 Depth-Sorting Method
9-7 BSP-Tree Method
9-8 Area-Subdivision Method
9-9 Octree Methods
9-10 Ray-Casting method
9-11 Comparision of Visibility-Detection Methods
9-12 Curved Surfaces
·Curved Surface Representations
·Surface Contour Plots
9-13 Wire-Frame Visibility Methods
·Wire-Frame Surface-Visibility Algorithms
·Wire-Frame Depth-Cueing Algorithms
9-14 OpenGL Visibility-Detection Functions
·OpenGL Polygon-Culling Functions
·OpentGL Depth-Buffer Functions
·OpenGL Wire-Frame Surface-Visibility Methods
·OpenGL Depth-Cueing Function
9-15 Summary
References
Exercises
10 Illumination Models and Surface-Rendering Methods
10-1 Light Sources
·Point Light Sources
·Infinitely Distant Light Sources
·Radial Intensity Attenuation
·Directional Light Sources and Spotlight Effects
·Angular Intensity Attenuation
·Extended LightSources and the Warn Model
10-2 Surface Lighting Effects
10-3 Basic Illumination Models
·Ambient Light
·Diffuse Reflection
·Specular Reflection and the Phong Model
·Combined Diffuse and Specular Reflections
·Diffuse and Specular Reflections form Multiple Light Sources
·Surface Light Emissions
·Basic Illumination Model with Intensity Attenuation and Spotlights
·RGB Color Considerations
·Other Color Representations
·Luminance
10-4 Transparent Surfaces
·Translucent Materials
·Light Refraction
·Basic Transparency Model
10-5 Atmospheric Effects
10-6 Shadows
10-7 Camera Parameters
10-8 Displaying Light Intensities
·Distributing System Intensity Levels
·Gamma Correction and Video Lookup Tables
·Displaying Continuous-Tone Images
10-9 Halftone Patterns and Dithering Techniques
·Halftone Approximations
·Dithering Techniques
10-10 Polygon-Rendering Methods
·Constant-Intensity Surface Rendering
·Gouraud Surface Rendering
·Phong Surface Rendering
·Fast Phong Surface Rendering
10-11 Ray-Tracing Methods
·Basic Ray-Tracing Algorithm
·Ray-Surface Intersection Calculations
·Ray-Sphere Intersections
·Ray-Polyhedron Intersections
·Reducing Object-Intersection Calculations
·Space-Subdivision Methods
·Simulating Camera Focusing Effects
·Antialiased Ray Tracing
·Distributed Ray Tracing
10-12 Radiosity Lighting Model
·Radiant-Energy Terms
·The Basic Radiosity Model
·Progressive Refinement Radiosity Method
10-13 Environment Mapping
10-14 Photon Mapping
10-15 Adding Surface Detail
10-16 Modeling Surface Detail with Polygons
10-17 Texture Mapping
·Linear Texture Patterns
·Surface Texture Patterns
·Volume Texture Patterns
·Texture Reduction Patterns
·Procedural Texturing Methods
10-18 Bump Mapping
10-19 Frame Mapping
10-20 OpenGL Illumination and Surface-Rendering Functions
·OpenGL Point Light-Source Functions
·Specifying an OpenGL Light-Source Position and Type
·Specifying OpenGL Light-Source Colors
·Specifying Radial-Intensity Attenuation Coefficients for an OpenGL Light Source
·OpenGL Directional Light Sources(Spotlights)
·OpenGL Global Lighting Parameters
·OpenGL Surface-Property Function
·OpenGL Illumination Model
·OpenGL Atmospheric Effects
·OpenGL Transparency Functions
·OpenGL Surface-Rendering Functions
·OpenGL Halftoning Operations
10-21 OpenGL Texture Functions
·OpenGL Line-Texture Functions
·OpenGL Surface-Texture Functions
·OpenGL Volume-Texture Functions
·OpenGL Color Options for Texture Patterns
·OpenGL Texture-Mapping Options
·OpenGL Texture Wrapping
·Copying OpenGL Texture Patterns from the Frame Buffer
·OpenGL Texture-Coordinate Arrays
·Naming OpenGL Texture Patterns
·OpenGL Texture Subpatterns
·OpenGL Texture Reduction Patterns
·OpenGL Texture Borders
·OpenGL Proxy Textures
·Automatic Texturing of Quadric Surfaces
·Homogeneous Texture Coordinates
·Additional OpenGL Texture Options
10-22 Summary
References
Exercises
11 Interactive Input Methods and Graphical User Interfaces
11-1 Graphical Input Data
11-2 Logical Classification of Input Devices
·Locator Devices
·Stroke Devices
·String Devices
·Valuator Devices
·Choice Devices
·Pick Devices
11-3 Input Functions for Graphical Data
·Input Modes
·Echo Feedback
·Callback Function
11-4 Interactive Picture-Construction Techniques
·Basic Positioning Methods
·Dragging
·Constraints
·Grids
·Rubber-Band Methods
·Gavity Field
·Interactive Painting and Drawing Methods
11-5 Virtual-Reality Environments
11-6 OpenGL Interactive Input-Device Functions
·GLUT Mouse Functions
·GLUT Keyboard Functions
·GLUT Tablet Functions
·GLUT Spaceball Functions
·GLUT Button-Box Functions
·GLUT Dials Functions
·OpenGL Picking Operations
11-7 OpenGL Menu Functions
·Creating a GLUT Menu
·Creating and Managing Multiple GLUT Menus
·Creating GLUT Submenus
·Modifying GLUT Menus
11-8 Designing a Graphical User Interface
·The User Dailogue
·Windows and Icons
·Accommodating Multiple Skill Levels
·Consistency
·Minimizing Memorization
·Backup and Error Handling
·Feedback
11-9 Summary
References
Exercises
12 Color Models and Color Applications
12-1 Properties of Light
·The Electromagnetic Spectrum
·Psychological Characteristics of Color
12-2 Color Models
·Primary Colors
·Intuitive Color Concepts
12-3 Standard Primaries and the Chromaticity Diagram
·The XYZ Color Model
·Normalized XYZ Values
·The CIE Chromaticity Diagram
·Color Gamuts
·Complementary Colors
·Dominant Wavelength
·Purity
12-4 The RGB Color Model
12-5 The YIQ and Related Color Models
·The YIQ Parameters
·Transformations Between RGB and YIQ Color Spaces
·The YUV YCrCb Systems
12-6 The CMY and CMYK Color Models
·The CMY Parameters
·Transformations Between CMY and RGB Color Spaces
12-7 The HSV Color Model
·The HSV Parameters
·Selecting Shades,Tints,and Tones
·Transformations Between HSV and RGB Color Spaces
12-8 The HLS Color Model
12-9 Color Selection and Application
12-10 Summary
References
Exercises
13 Computer Animation
13-1 Raster Methods for Computer Animation
·Double Buffering
·Generating Animations Using Raster Operations
13-2 Design of Animation Sequences
13-3 Traditional Animation Techniques
13-4 General Computer-Animation Functions
13-5 Computer-Animation Lanuages
13-6 Key-Frame Systems
·Morphing
·SimulatingAccelerations
13-7 Motion Specifications
·Direct Motion Specification
·Goal-Directed Systems
·Kinematics and Dynamics
13-8 Articulated Figure Animation
13-9 Periodic Motions
13-10 OpenGL Animation Procedures
13-11 Summary
References
Exercises
14 Hierarchical Modeling
14-1 Basic Modeling Concepts
·System Representations
·Symbol Hierarchies
14-2 Modeling Packages
14-3 General Hierarchical Modeling Methods
·Local Coordinates
·Modeling Transformations
·Creating Hierarchical Structures
14-4 Hierarchical Modeling Using OpenGL Display Lists
14-5 Summary
References
Exercises
15 Graphics File Formats
15-1 Image-File Configurations
15-2 Color-Reduction Methods
·Uniform Color Reduction
·Popularity Color Reduction
·Median-Cut Color Reduction
15-3 File-Compression Techniques
·Run-Length Encoding
·LZW Encoding
·Other Pattern-Recognition Compression Methods
·Huffman Encoding
·Arithmetic Encoding
·Discrete Cosine Transform
15-4 Composition of the Major File Formats
·JPEG:Joint Photographic Experts Group
·CGM:Computer-Graphics Metafile Format
·TIFF:Tag Image-File Format
·PNG:Portable Network-Graphics Format
·XBM:X Window System bitmap Format&XPM:X Windows System Pixmap Format
·Adobe Photoshop Format
·MacPaint:Macintosh Paint Format
·PICT:Picture Data Format
·BMP:Bitmap Format
·PCX:PC Paintbrush File Format
·TGA:Truevision Graphics-Adapter Format
·GIF:Graphics Interchange Format
15-5 Summary
References
Exercises
A Mathematics for Computer Graphics
A-1 Coordinate Reference Frames
·Two-Dimensional Cartesian Screen Coordinates
·Standard Two-Dimensional Cartesian Reference Frames
·Polar Coordinates in the xy Plane
·Standard Three-Dimensional Cartesian Reference Frames
·Three-Dimensional Cartesian Screen Coordinates
·Three-Dimensional Curvilinear-Coordinate Systems
·Solid Angle
A-2 Points and Vectors
·Point Properties
·Vector Properties
·Vector Addition and Scalar Multiplication
·Scalar Product of Two Vectors
·Vector Product of Two Vectors
A-3 Tensors
A-4 Basis Vectors and the Metric Tensor
·Determining Basis Vectors for a Coordinate Space
·Orthonormal Basis
·Metric Tensor
A-5 Matrices
·Scalar Multiplication and Matrix Addition
·Matrix Multiplication
·Matrix Transpose
·Determinant of a Matrix
·Matrix Inverse
A-6 Complex Numbers
·Basic Complex Arithmetic
·Imaginary Unit
·Complex Conjugate and Modulus of a Complex Number
·Complex Division
·Polar-Coordinate Representation for a Complex Number
A-7 Quaternions
A-8 Nonparametric Representations
A-9 Parametric Representations
A-10 Rate-of-Change Operators
·Gradient Operator
·Directional Derivative
·General Form of the Gradient Operator
·Laplace Operator
·Divergence Operator
·Curl Operator
A-11 Rate-of-Change Integral Transformation Theorems
·Stokes's theorem
·Green's Theorem for a Plane Surface
·divergence theorem
·Green's Transformation Equations
A-12 Area and Centroid of a Polygon
·Area of a Polygon
·Centroid of a Polygon
A-13 Calculating Properties of Polyhedra
A-14 Numerical Methods
·Solving Sets of Linear Equations
·Finding Roots of Nonlinear Equations
·Evaluating Integrals
·Solving Ordinary Differential Equations
·Solving Partial differential Equations
·Least-Squares Curve-Fitting Methods for Data Sets
Bibliography
Subject Index
OpenGL Function Index
·Core Library Functions
·GLU Functions
·GLUT Functions
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