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 inher IntroductionData, Images, and Computer GraphicsApplications of Computer Graphics The Four-Universe Paradigm Example Models: Terrains and Two-Dimensional ImagesReconstruction A Practical Problem Image Making: The Physical and Mathematical Universes Comments and ReferencesExercisesGeometryWhat Is a Geometry? Transformations and Computer Graphics Euclidean GeometryAffine GeometryThe Geometry of Computer GraphicsThe Projective Space Projective Transformations The Fundamental Theorem of Projective Geometry Projections and Projective GeometryComments and ReferencesExercises CoordinatesAffine Transformations and Coordinate ChangesLocal and Global TransformationsCoordinates in SpaceCurvilinear Coordinates Comments and ReferencesExercises The Space of RotationsPlane Rotations Introduction to Rotations in SpaceAxis and Angle of Rotation Parameterization by Three Rotation Angles Interpolation of RotationsPause for Commercials QuaternionsConverting between RepresentationsComments and ReferencesExercisesColorColor in the Physical Universe Spectral Color Space Color Representation and ReconstructionPhysical Color Systems TristimulusValues and Metameric ReconstructionThe Standard CIE-RGB System The Geometry of Color SpaceThe CIE-XYZ Color System Dominant Wavelength and Complementary ColorsColor Systems and Computer Graphics Comments and ReferencesExercises ImageImage Abstraction Paradigms Image Representation Matrix Representation and ReconstructionElements of a Digital ImageColor and Image QuantizationQuantization and Cell GeometryAdaptive Quantization Methods Optimization and QuantizationDithering Dithering Algorithms Quantization and DitheringImage Coding Comments and ReferencesExercises Planar Graphics ObjectsGraphics Objects Planar Graphics Objects Polygonal Curves and TriangulationRepresentation of Curves and RegionsRasterizationRepresentation, Sampling And InterpolationViewing Planar Graphic ObjectsTwo-Dimensional Clipping Viewing Operations Comments and ReferencesExercises Spatial Graphics ObjectsDigital Geometry ProcessingSpatial Curves Surfaces Volumetric Objects Triangulations and Polyhedral SurfacesRepresentation of Parametric SurfacesRepresentation of Implicit Surfaces Representation of Volumetric ObjectsComments and ReferencesExercisesHierarchiesObjects with HierarchyHierarchy of Articulated ObjectsHierarchy of the Human BodyCurrent Transformation and Data StructureHierarchies of Composed ObjectsPartitioning Trees (BSP-Trees) Classification and Search using BSP-TreesComments and ReferencesExercises Geometric ModelingModeling and RepresentationCSG Representation Conversion between RepresentationsGenerative Modeling Modeling SystemsOperations with Models Comments and ReferencesExercises Virtual CameraA Basic ModelViewing Coordinate SystemsVirtual Camera ParametersViewing Operations Other Camera Models Camera Specification Comments and ReferencesExercisesClippingClassification, Partitioning, and Clipping Clipping Applications Clipping Acceleration Clipping MethodologyTwo-Dimensional ClippingClipping a Segment against the Virtual ScreenPolygon Clipping Three-Dimensional ClippingClipping and Viewing Comments and ReferencesExercisesVisibilityVisibility Foundations (YXZ) Algorithms: Visibility with Rasterization(XY)Z Algorithms: Visibility after RasterizationZ(XY) Algorithms: Visibility before RasterizationComments and ReferencesExercisesIlluminationFoundationsThe Nature of LightA Simple Illumination Model Illumination Calculation Ray Tracing Ray Tracing Acceleration Sampling and Ray TracingComments and ReferencesExercisesRasterizationSamplingPoint SamplingArea SamplingComments and ReferencesMappingsMapping Graphics ObjectsTwo-Dimensional Mapping Methods Calculating the "Computer Graphics: Theory and Practice provides complete and integrated coverage of the subject, including geometric modeling, graphics interface, and visualization. It focuses on conceptual aspects of computer graphics, covering fundamental mathematical models as well as the inherent problems encountered in the implementation of the models. The approach assumes only a fundamental knowledge of calculus and linear algebra and provides the basis for an introductory course. The text offers a global conceptual view of the field and an understanding of its main problems. For each problem, solution strategies are compared and presented in algorithmic form and complete working implementations are provided in the C language. The complete C source code for the implementation of all the algorithms can be accessed from the books website. Together, the book and electronic portion enable readers to understand and practice with the basic techniques involved in the implementation of a 3D graphics system"-- "This book focuses on conceptual aspects of computer graphics, covering the fundamental mathematical models as well as the inherent problems encountered in the implementation of those models. The approach assumes only a basic knowledge of calculus and linear algebra and provides the basis for an introductory course. It is accompanied by online materials that offer opportunities to practice concepts presented in the book"-- Annotation This book focuses on conceptual aspects of computer graphics, covering the fundamental mathematical models as well as the inherent problems encountered in the implementation of those models. The approach assumes only a fundamental knowledge of calculus and linear algebra and provides the basis for an introductory course. The accompanying CD contains a book in electronic form that delivers the practice necessary to understand the basic techniques of the implementation of a 3D graphics system. For each problem, solution strategies are compared and presented in algorithmic form and complete working implementations are provided in the C language. The complete C source code for the implementation of all the algorithms can be accessed at the book's website Link text . Together the printed book and its accompanying electronic portion present a comprehensive view of the theory and practice of computer graphics Computer 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. Front Cover 1 Dedication 6 Contents 8 Foreword 14 About the Cover 16 Preface 20 1. Introduction 22 2. Geometry 40 3. Coordinates 74 4. The Space of Rotations 96 5. Color 130 6. Image 158 7. Planar Graphics Objects 198 8. Spatial Graphics Objects 232 9. Hierarchies 268 10. Geometric Modeling 298 11. Virtual Camera 322 12. Clipping 348 13. Visibility 374 14. Illumination 388 15. Rasterization 420 16. Mappings 430 17. Composition 474 18. Radiometry and Photometry 490 19. The Illumination Equation 510 Bibliography 528 "This book focuses on conceptual aspects of computer graphics, covering the fundamental mathematical models as well as the inherent problems encountered in the implementation of those models. The approach assumes only a basic knowledge of calculus and linear algebra and provides the basis for an introductory course. It is accompanied by online materials that offer opportunities to practice concepts presented in the book"-- Provided by publisher Two-Dimensional MappingSome Two-Dimensional Mapping ApplicationsNoise FunctionScalar Noise Gradient Noise Comments and ReferencesExercisesCompositionThe Alpha Channel Composition and Pixel Geometry Composition Algebra Composition of Images and VisibilityComments and ReferencesExercises The Illumination EquationIllumination Model Ray Tracing Method Radiosity Method Comments and ReferencesAppendix: Radiometry and PhotometryBibliography