Mathematical optimization is used in nearly all computer graphics applications, from computer vision to animation. This book teaches readers the core set of techniques that every computer graphics professional should understand in order to envision and expand the boundaries of what is possible in their work.
Study of this authoritative reference will help readers develop a very powerful tool- the ability to create and decipher mathematical models that can better realize solutions to even the toughest problems confronting computer graphics community today.
The authors are renowned researchers from IMPA, the Brazilian National Institute for Pure and Applied Mathematics.
*Distils down a vast and complex world of info on optimization into one short, self-contained volume especially for computer graphics
*Helps CG professionals identify the best technique for solving particular problems quickly, by categorizing the most effective algorithms by application
*Keeps readers current by supplementing the focus on key, classic methods with special end-of-chapter sections on cutting-edge developments

This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.

Implicit definition and description of geometric objects and surfaces plays a critical role in the appearance and manipulation of computer graphics. In addition, the mathematical definition of shapes, using an implicit form, has pivotal applications for geometric modeling, visualization and animation. Until recently, the parametric form has been by far the most popular geometric representation used in computer graphics and computer-aided design. Whereas parametric objects and the techniques associated with them have been exhaustively developed, the implicit form has been used as a complementary geometric representation, mainly in the restricted context of specific applications. However, recent developments in graphics are changing this situation, and the community is beginning to draw its attention to implicit objects. This is reflected in the current research of aspects related to this subject. Employing a coherent conceptual framework, Implicit Objects in Computer Graphics addresses the role of implicitly defined objects in the following parts: mathematical foundations of geometric models, implicit formulations for the specification of shapes, implicit primitives, techniques for constructing and manipulating implicit objects, modeling, rendering and animation implicit objects. Topics and features: *Broad, conceptual approach covers the fundamental algorithms and ideas *Integrated and up-to-date overview of the main developments surrounding implicit objects *Organized and cohesive presentation combines theory and practice *Provides thorough explanation of key problems and challenges in the field

Design and Implementation of 3D Graphics Systems covers the computational aspects of geometric modeling and rendering 3D scenes. Special emphasis is given to the architectural aspects of interactive graphics, geometric modeling, rendering techniques, the graphics pipeline, and the architecture of 3D graphics systems. The text describes basic 3D computer graphics algorithms and their implementation in the C language. The material is complemented by library routines for constructing graphics systems, which are available for download from the book's website. This book, along with its companion Computer Graphics: Theory and Practice, gives readers a full understanding of the principles and practices of implementing 3D graphics systems.

Key features include: Introduction to Projective Geometry, Image Based Lighting (IBL), Global Illumination solved by the Monte Carlo Method (Pathtracing), an explanation of a set of Optimization Methods, and the techniques used for Calibrating One, Two, and Many cameras, including how to use the RANSAC algorithm in order to make the process robust, and providing code to be implemented using the Gnu Scientific Library. C/C++ code using the OpenCV library, to be used in the process of tracking points on a movie (an important step for the matchmove process), and in the construction of Modeling Tools for Visual Effects. A simple model of the Bidirectional Reflectance Distribution Function (BRDF) of surfaces and the Differential Rendering Method, allowing the reader to generate consistent shadows, supported by a code that can be used in combination with a software like Luminance HDR.

Image processing is concerned with the analysis and manipulation of images by computer. Providing a thorough treatment of image processing with an emphasis on those aspects most used in computer graphics, the authors concentrate on describing and analyzing the underlying concepts rather than on presenting algorithms or pseudocode. As befits a modern introduction to this topic, a good balance is struck between discussing the underlying mathematics and the main topics: signal processing, data discretization, the theory of colour and different colour systems, operations in images, dithering and half-toning, warping and morphing and image processing. This second edition reflects recent trends in science andtechnology that exploit image processing in computer graphics and vision applications. Stochastic image models and statistical methods for image processing are covered as are: A modern approach and new developments in the area, Probability theory for image processing, Applications in image analysis and computer vision.

Implicit definition and description of geometric objects and surfaces plays a critical role in the appearance and manipulation of computer graphics. In addition, the mathematical definition of shapes, using an implicit form, has pivotal applications for geometric modeling, visualization and animation. Until recently, the parametric form has been by far the most popular geometric representation used in computer graphics and computer-aided design. Whereas parametric objects and the techniques associated with them have been exhaustively developed, the implicit form has been used as a complementary geometric representation, mainly in the restricted context of specific applications. However, recent developments in graphics are changing this situation, and the community is beginning to draw its attention to implicit objects. This is reflected in the current research of aspects related to this subject. Employing a coherent conceptual framework, Implicit Objects in Computer Graphics addresses the role of implicitly defined objects in the following parts: mathematical foundations of geometric models, implicit formulations for the specification of shapes, implicit primitives, techniques for constructing and manipulating implicit objects, modeling, rendering and animating implicit objects.

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 book 's 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 text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.

Design and Implementation of 3D Graphics Systems covers the computational aspects of geometric modeling and rendering 3D scenes. Special emphasis is given to the architectural aspects of interactive graphics, geometric modeling, rendering techniques, the graphics pipeline, and the architecture of 3D graphics systems. The text describes basic 3D computer graphics algorithms and their implementation in the C language. The material is complemented by library routines for constructing graphics systems, which are available for download from the book's website. This book, along with its companion Computer Graphics: Theory and Practice, gives readers a full understanding of the principles and practices of implementing 3D graphics systems.