1st Edition
Computer Graphics Theory and Practice
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
The Four-Universe Paradigm
Example Models: Terrains and Two-Dimensional Images
Reconstruction
A Practical Problem
Image Making: The Physical and Mathematical Universes
Comments and References
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
Comments and References
Exercises
Coordinates
Affine Transformations and Coordinate Changes
Local and Global Transformations
Coordinates in Space
Curvilinear Coordinates
Comments and References
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
Comments and References
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
Comments and References
Exercises
Image
Image Abstraction Paradigms
Image Representation
Matrix Representation and Reconstruction
Elements of a Digital Image
Color and Image Quantization
Quantization and Cell Geometry
Adaptive Quantization Methods
Optimization and Quantization
Dithering
Dithering Algorithms
Quantization and Dithering
Image Coding
Comments and References
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
Comments and References
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
Comments and References
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
Comments and References
Exercises
Geometric Modeling
Modeling and Representation
CSG Representation
Conversion between Representations
Generative Modeling
Modeling Systems
Operations with Models
Comments and References
Exercises
Virtual Camera
A Basic Model
Viewing Coordinate Systems
Virtual Camera Parameters
Viewing Operations
Other Camera Models
Camera Specification
Comments and References
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
Comments and References
Exercises
Visibility
Visibility Foundations
(YXZ) Algorithms: Visibility with Rasterization
(XY)Z Algorithms: Visibility after Rasterization
Z(XY) Algorithms: Visibility before Rasterization
Comments and References
Exercises
Illumination
Foundations
The Nature of Light
A Simple Illumination Model
Illumination Calculation
Ray Tracing
Ray Tracing Acceleration
Sampling and Ray Tracing
Comments and References
Exercises
Rasterization
Sampling
Point Sampling
Area Sampling
Comments and References
Mappings
Mapping Graphics Objects
Two-Dimensional Mapping Methods
Calculating the Two-Dimensional Mapping
Some Two-Dimensional Mapping Applications
Noise Function
Scalar Noise
Gradient Noise
Comments and References
Exercises
Composition
The Alpha Channel
Composition and Pixel Geometry
Composition Algebra
Composition of Images and Visibility
Comments and References
Exercises
The Illumination Equation
Illumination Model
Ray Tracing Method
Radiosity Method
Comments and References
Appendix: Radiometry and Photometry
Bibliography
Biography
Jonas Gomes is a professor at the Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro. Gomes is also the head of the Department for Computer Activities at IMPA. He has published several books and research articles in the area of computer graphics.
Luiz Velho is a researcher and professor at IMPA - Instituto de Matematica Pura e Aplicada of CNPq and the leading scientist of VISGRAF Laboratory.His experience in computer graphics spans the fields of modeling, rendering, imaging, and animation. He is the author of several books and has taught many courses on graphics-related topics.
Mario Costa Sousa is an Associate Professor at the Department of Computer Science, University of Calgary, Canada. Sousa holds the AITF/ Foundation CMG Industrial Research Chair in Scalable Reservoir Visualization and leads the Interactive Reservoir Modeling and Visualization (iRMV) Research Group. His research interests focus on scientific/engineering visualization, computer graphics, non-photorealistic rendering / illustrative visualization, sketch-based interfaces and modeling, mutli-surface interaction, interactive simulations and real-time graphics. He is widely published and has taught many courses on graphics / visualization-related topics.
The strength of the book is that it emphasizes a mathematical approach and particularly mathematical models in teaching computer graphics. … An accompanying e-book provides complete working implementations and course-related material. … this novel, highly mathematical exploration of computer graphics is useful for advanced audiences. Recommended.
—C. Tappert, CHOICE, December 2012
