1st Edition

# Computer Graphics Theory and Practice

576 Pages
by A K Peters/CRC Press

544 Pages
by A K Peters/CRC Press

Also available as eBook on:

Computer Graphics: Theory and Practice provides a complete and integrated introduction to this area. The book only requires basic knowledge of calculus and linear algebra, making it an accessible introductory text for students. It focuses on conceptual aspects of computer graphics, covering fundamental mathematical theories and models and the inherent problems in implementing them. In so doing, the book introduces readers to the core challenges of the field and provides suggestions for further reading and studying on various topics. For each conceptual problem described, solution strategies are compared and presented in algorithmic form. This book, along with its companion Design and Implementation of 3D Graphics Systems, gives readers a full understanding of the principles and practices of implementing 3D graphics systems.

Introduction
Data, Images, and Computer Graphics
Applications of Computer Graphics
Example Models: Terrains and Two-Dimensional Images
Reconstruction
A Practical Problem
Image Making: The Physical and Mathematical Universes
Exercises

Geometry
What Is a Geometry?
Transformations and Computer Graphics
Euclidean Geometry
Affine Geometry
The Geometry of Computer Graphics
The Projective Space
Projective Transformations
The Fundamental Theorem of Projective Geometry
Projections and Projective Geometry
Exercises

Coordinates
Affine Transformations and Coordinate Changes
Local and Global Transformations
Coordinates in Space
Curvilinear Coordinates
Exercises

The Space of Rotations
Plane Rotations
Introduction to Rotations in Space
Axis and Angle of Rotation
Parameterization by Three Rotation Angles
Interpolation of Rotations
Pause for Commercials
Quaternions
Converting between Representations
Exercises

Color
Color in the Physical Universe
Spectral Color Space
Color Representation and Reconstruction
Physical Color Systems
TristimulusValues and Metameric Reconstruction
The Standard CIE-RGB System
The Geometry of Color Space
The CIE-XYZ Color System
Dominant Wavelength and Complementary Colors
Color Systems and Computer Graphics
Exercises

Image
Image Representation
Matrix Representation and Reconstruction
Elements of a Digital Image
Color and Image Quantization
Quantization and Cell Geometry
Optimization and Quantization
Dithering
Dithering Algorithms
Quantization and Dithering
Image Coding
Exercises

Planar Graphics Objects
Graphics Objects
Planar Graphics Objects
Polygonal Curves and Triangulation
Representation of Curves and Regions
Rasterization
Representation, Sampling, and Interpolation
Viewing Planar Graphic Objects
Two-Dimensional Clipping
Viewing Operations
Exercises

Spatial Graphics Objects
Digital Geometry Processing
Spatial Curves
Surfaces
Volumetric Objects
Triangulations and Polyhedral Surfaces
Representation of Parametric Surfaces
Representation of Implicit Surfaces
Representation of Volumetric Objects
Exercises

Hierarchies
Objects with Hierarchy
Hierarchy of Articulated Objects
Hierarchy of the Human Body
Current Transformation and Data Structure
Hierarchies of Composed Objects
Partitioning Trees (BSP-Trees)
Classification and Search using BSP-Trees
Exercises

Geometric Modeling
Modeling and Representation
CSG Representation
Conversion between Representations
Generative Modeling
Modeling Systems
Operations with Models
Exercises

Virtual Camera
A Basic Model
Viewing Coordinate Systems
Virtual Camera Parameters
Viewing Operations
Other Camera Models
Camera Specification
Exercises

Clipping
Classification, Partitioning, and Clipping
Clipping Applications
Clipping Acceleration
Clipping Methodology
Two-Dimensional Clipping
Clipping a Segment against the Virtual Screen
Polygon Clipping
Three-Dimensional Clipping
Clipping and Viewing
Exercises

Visibility
Visibility Foundations
(YXZ) Algorithms: Visibility with Rasterization
(XY)Z Algorithms: Visibility after Rasterization
Z(XY) Algorithms: Visibility before Rasterization
Exercises

Illumination
Foundations
The Nature of Light
A Simple Illumination Model
Illumination Calculation
Ray Tracing
Ray Tracing Acceleration
Sampling and Ray Tracing
Exercises

Rasterization
Sampling
Point Sampling
Area Sampling

Mappings
Mapping Graphics Objects
Two-Dimensional Mapping Methods
Calculating the Two-Dimensional Mapping
Some Two-Dimensional Mapping Applications
Noise Function
Scalar Noise
Exercises

Composition
The Alpha Channel
Composition and Pixel Geometry
Composition Algebra
Composition of Images and Visibility
Exercises

The Illumination Equation
Illumination Model
Ray Tracing Method