Computer Graphics

Title Page
Copyright Page
Preface
Contents
Chapter 1 Introduction
1.1 A Mini-Survey
Image Processing
Computer-Human Interaction
1.2 What's Ahead
Chapter 2 Image Representation
2.1 The RGB Color Model
2.2 Direct Coding
2.3 Lookup Table
2.4 Display Monitor
Color Display
2.5 Printer
Halftoning
Halftone Approximation
Dithering
Error Diffusion
2.6 Image Files
2.7 Setting the Color Attribute of Pixels
2.8 Example: Visualizing the Mandelbrot Set
Julia Sets
Solved Problems
Supplementary Problems
Chapter 3 Scan Conversion
3.1 Scan-Converting a Point
3.2 Scan-Converting a Line
Direct Use of the Line Equation
DDA Algorithm
Bresenham's Line Algorithm
3.3 Scan-Converting a Circle
Defining a Circle
Bresenham's Circle Algorithm
Midpoint Circle Algorithm
Arbitrarily Centered Circles
3.4 Scan-Converting an Ellipse
Polynomial Method of Defining an Ellipse
Trigonometric Method of Defining an Ellipse
Ellipse Axis Rotation
Midpoint Ellipse Algorithm
3.5 Scan-Converting Arcs and Sectors
Arcs
Sectors
3.6 Scan-Converting a Rectangle
3.7 Region Filling
4-Connected vs. 8-Connected
A Boundary-fill Algorithm
A Flood-fill Algorithm
A Scan-line Algorithm
3.8 Scan-Converting a Character
Bitmap Font
Outline Font
3.9 Anti-Aliasing
Staircase
Unequal Brightness
The Picket Fence Problem
Anti-aliasing
Pre-flltering and Post-filtering
Area Sampling
Super Sampling
Lowpass Filtering
Pixel Phasing
3.10 Example: Recursively Defined Drawings
C Curve
The Koch Curve
The Sierpinski Gasket
Solved Problems
Supplementary Problems
Chapter 4 Two-Dimensional Transformations
4.1 Geometric Transformations
Translation
Rotation about the Origin
Scaling with Respect to the Origin
Mirror Reflection about an Axis
Inverse Geometric Transformations
4.2 Coordinate Transformations
Translation
Rotation about the Origin
Scaling with Respect to the Origin
Mirror Reflection about an Axis
Inverse Coordinate Transformations
4.3 Composite Transformations
Matrix Description of the Basic Transformations
Concatenation of Matrices
Caution on Matrix Notations
4.4 Instance Transformations
Nested Instances and Multilevel Structures
Solved Problems
Supplementary Problems
Chapter 5 Two-Dimensionsl Viewing and Clipping
5.1 Window-to-Viewport Mapping
5.2 Point Clipping
5.3 Line Clipping
The Cohen-Sutherland Algorithm
Midpoint Subdivision
The Liang-Barsky Algorithm
5.4 Polygon Clipping
Convex Polygonal Clipping Windows
The Sutherland-Hodgman Algorithm
The Weiler-Atherton Algorithm
5.5 Example: A 2D Graphics Pipeline
Panning and Zooming
Double Buffering
Lookup Table Animation
Solved Problems
Supplementary Problems
Chapter 6 Three-Dimensional Transformations
6.1 Geometric Transformations
Translation
Scaling
Rotation
6.2 Coordinate Transformations
6.3 Composite Transformations
6.4 Instance Transformations
Solved Problems
Supplementary Problems
Chapter 7 Mathematics of Projection
7.1 Taxonomy of Projection
7.2 Perspective Projection
Basic Principles
Mathematical Description of a Perspective Projection
Perspective Anomalies
7.3 Parallel Projection
Basic Principles
Mathematical Description of a Parallel Projection
Solved Problems
Supplementary Problems
Chapter 8 Three-Dimensional Viewing and Clipping
8.1 Three-Dimensional Viewing
Specifying the View Plane
View Plane Coordinates
Specifying the View Volume
8.2 Clipping
Clipping against a Finite View Volume
Clipping Strategies
Clipping Algorithms
8.3 Viewing Transformation
Normalized Viewing Coordinates
Screen Projection Plane
Constructing a Three-dimensional View
8.4 Example: A 3D Graphics Pipeline
Solved Problems
Supplementary Problems
Chapter 9 Geometric Representation
9.1 Simple Geometric Forms
Points and Lines
Polylines
Polygons
9.2 Wireframe Models
Representing a Polygonal Net Model
Polyhedron
Advantages and Disadvantages of Wireframe Models
9.3 Curved Surfaces
9.4 Curve Design
9.5 Polynomial Basis Functions
Lagrange Polynomials of Degree
Hermite Cubic Polynomials
B-Splines
Bernstein Polynomials
9.6 The Problem of Interpolation
Lagrange Polynomial Interpolation Solution
Hermitian Cubic Interpolation Solution
Spline Interpolation
9.7 The Problem of Approximation
Bezier-Bernstein Approximation
Properties of the Bezier-Bernstein Approximation
Bezier-B-Spline Approximation
Closed Curves
Properties of Bezier-B-Spline Approximation
9.8 Curved-Surface Design
Guiding Nets
Interpolating Surface Patches
9.9 Transforming Curves and Surfaces
9.10 Quadric Surfaces
Sphere
Ellipsoid
One-sheeted Hyperboloid
Two-sheeted Hyperboloid
Elliptic Cylinder
Elliptic Paraboloid
Hyperbolic Parboloid
Elliptic Cone
9.11 Example: Terrain Generation
Midpoint Displacement
Brownian Distribution of Disks
Solved Problems
Supplementary Problems
Chapter 10 Hidden Surfaces
10.1 Depth Comparisons
10.2 Z-Buffer Algorithm
10.3 Back-Face Removal
10.4 The Painter's Algorithm
Assigning Priorities
Testing Whether P Obscures Q
The Algorithm
10.5 Scan-Line Algorithm
y Scan
x Scan
Types of Coherence
A Scan-line Algorithm
10.6 Subdivision Algorithm
Removing Polygons Hidden by a Surrounding Polygon
Subdivision Algorithm
10.7 Hidden-Line Elimination
10.8 The Rendering of Mathematical Surfaces
The Perimeter Method for Rendering the Surface
The Visibility Test
The Wright Algorithm for Rendering Mathematical Surfaces
Solved Problems
Supplementary Problems
Chapter 11 Color and Shading Models
11.1 Light and Color
Basic Characteristics of Light
The Trichromatic Generalization Theory
CIE XYZ Color Model
CIE Chromaticity Diagram
Color Gamut Mapping
The NTSC YIQ Color Model
11.2 The Phong Model
11.3 Interpolative Shading Methods
Constant Shading
Gouraud Shading
Phong Shading
11.4 Texture
Projected Texture
Texture Mapping
Solid Texture
Solved Problems
Supplementary Problems
Chapter 12 Ray Tracing
12.1 The Pinhole Camera
12.2 A Recursive Ray-Tracer
12.3 Parametric Vector Representation of a Ray
12.4 Ray-Surface Intersection
Coordinate System Plane
Arbitrary Plane
Sphere
General Implicit Surface
12.5 Execution Efficiency
Adaptive Depth Control
Bounding Volume Extension
Hierarchy of Bounding Volumes
Spatial Coherence/Spatial Subdivision
12.6 Anti-Aliasing
Supersampling
Adaptive Supersampling
Stochastic Supersampling
12.7 Additional Visual Effects
Environment Mapping
Soft Shadow
Blurry Reflection
Translucency
Motion Blur
Solved Problems
Supplementary Problems
Appendix 1 Mathematics for Two-Dimensional Computer Graphics
A1.1 The Two-Dimensional Cartesian Coordinate System
Measuring Distances in Cartesian System
Measuring Angles in Cartesian System
Describing a Line in Cartesian System
Curves and Parametric Equations
A1.2 The Polar Coordinate System
Changing Coordinate Systems
A1.3 Vectors
Properties of Vectors
Coordinate Vectors and Components
The Dot Product
A1.4 Matrices
Arithmetic Properties of Matrices
Matrix Inversion and the Identity Matrix
A1.5 Functions and Transformations
Graphs of Functions
Composing Functions
The Inverse Function
Solved Problems
Appendix 2 Mathematics for Three-Dimensional Computer Graphics
A2.1 Three-Dimensional Cartesian Coordinates
Orientation
The Right-Hand Rule
Cartesian Coordinates of Points in Three-dimensional Space
Distance Formula
A2.2 Curves and Surfaces in Three Dimensions
Curves
Surfaces
A2.3 Vectors in Three Dimensions
The Dot and the Cross Product
The Vector Equation of a Line
The Vector Equation of a Plane
A2.4 Homogeneous Coordinates
The Two-dimensional Projective Plane
Homogeneous Coordinates of Points and Lines of the Projective Plane
Correlation between Homogeneous and Cartesian Coordinates
Three-dimensional Projective Plane and Homogeneous Coordinates
Solved Problems
Answers To Supplementary Problems
Index