1st Edition

Computer Graphics Theory and Practice

    576 Pages
    by A K Peters/CRC Press

    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.

    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



    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