Computer Graphics: Theory and Practice, 1st Edition (Hardback) book cover

Computer Graphics

Theory and Practice, 1st Edition

By Jonas Gomes, Luiz Velho, Mario Costa Sousa

A K Peters/CRC Press

560 pages

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pub: 2012-04-24
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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.


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

Table of Contents


Data, Images, and Computer Graphics

Applications of Computer Graphics

The Four-Universe Paradigm

Example Models: Terrains and Two-Dimensional Images


A Practical Problem

Image Making: The Physical and Mathematical Universes

Comments and References



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



Affine Transformations and Coordinate Changes

Local and Global Transformations

Coordinates in Space

Curvilinear Coordinates

Comments and References


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


Converting between Representations

Comments and References



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



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 Algorithms

Quantization and Dithering

Image Coding

Comments and References


Planar Graphics Objects

Graphics Objects

Planar Graphics Objects

Polygonal Curves and Triangulation

Representation of Curves and Regions


Representation, Sampling, and Interpolation

Viewing Planar Graphic Objects

Two-Dimensional Clipping

Viewing Operations

Comments and References


Spatial Graphics Objects

Digital Geometry Processing

Spatial Curves


Volumetric Objects

Triangulations and Polyhedral Surfaces

Representation of Parametric Surfaces

Representation of Implicit Surfaces

Representation of Volumetric Objects

Comments and References



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


Geometric Modeling

Modeling and Representation

CSG Representation

Conversion between Representations

Generative Modeling

Modeling Systems

Operations with Models

Comments and References


Virtual Camera

A Basic Model

Viewing Coordinate Systems

Virtual Camera Parameters

Viewing Operations

Other Camera Models

Camera Specification

Comments and References



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



Visibility Foundations

(YXZ) Algorithms: Visibility with Rasterization

(XY)Z Algorithms: Visibility after Rasterization

Z(XY) Algorithms: Visibility before Rasterization

Comments and References




The Nature of Light

A Simple Illumination Model

Illumination Calculation

Ray Tracing

Ray Tracing Acceleration

Sampling and Ray Tracing

Comments and References




Point Sampling

Area Sampling

Comments and References


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



The Alpha Channel

Composition and Pixel Geometry

Composition Algebra

Composition of Images and Visibility

Comments and References


The Illumination Equation

Illumination Model

Ray Tracing Method

Radiosity Method

Comments and References

Appendix: Radiometry and Photometry


About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Computer Graphics