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Combinatorial Maps
This book gathers important ideas related to combinatorial maps and explains how the maps are applied in geometric modeling and image processing. It focuses on two subclasses of combinatorial maps: n-Gmaps and n-maps. The book presents the data structures, operations, and algorithms that are useful in handling subdivided geometric objects. It shows how to study data structures for the explicit representation of subdivided geometric objects and describes operations for handling the structures. The book also illustrates results of the design of data structures and operations.
eBook
Computer graphics : from pixels to programmable graphics hardware
\"Offering a complex view on the current state of the art in computer graphics, programmable graphics hardware, shaders, and shader-based effects, this unique text covers nearly all aspects of modern computer graphics. It presents the necessary mathematical background and algorithms and describes rasterization, hidden surface removal, and fixed and programmable pipeline. Suitable for a one-semester course, the book requires only basic knowledge of analytic geometry, linear algebra, and C++. It includes questions and practical examples (mostly using OpenGL3.0) and provides full source code and other materials on a supplementary website\"-- Provided by publisher.
Book
Markov random fields for vision and image processing
This volume demonstrates the power of the Markov random field (MRF) in vision, treating the MRF both as a tool for modeling image data and, utilizing recently developed algorithms, as a means of making inferences about images. These inferences concern underlying image and scene structure as well as solutions to such problems as image reconstruction, image segmentation, 3D vision, and object labeling. It offers key findings and state-of-the-art research on both algorithms and applications. After an introduction to the fundamental concepts used in MRFs, the book reviews some of the main algorithms for performing inference with MRFs; presents successful applications of MRFs, including segmentation, super-resolution, and image restoration, along with a comparison of various optimization methods; discusses advanced algorithmic topics; addresses limitations of the strong locality assumptions in the MRFs discussed in earlier chapters; and showcases applications that use MRFs in more complex ways, as components in bigger systems or with multiterm energy functions. The book will be an essential guide to current research on these powerful mathematical tools.
eBook
Mathematical structures for computer graphics
A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics.
eBook
3D math primer for graphics and game development
\"This book presents the essential math needed to describe, simulate, and render a 3D world. It provides an introduction to mathematics for game designers, including fundamentals of coordinate spaces, vectors, and matrices, orientation in three dimensions, introduction to calculus and dynamics, graphics, and parametric curves\"--Provided by publisher.
Book
When Life is Linear
Tim Chartier has written the perfect supplement to a linear algebra course. Every major topic is driven by applications, such as computer graphics, cryptography, webpage ranking, sports ranking and data mining. Anyone reading t his book will have a clear understanding of the power and scope of linear algebra. — Arthur Benjamin, Harvey Mudd College Not only is it true that \"Life Is Linear,\" as Tim Chartier asserts, but through his engaging style and modern, enticing applications he brings linear algebra to life. This small volume will be a popular read by math fans of all ages and of all backgrounds. Finally we have a little book that focuses on the utility and power of the theorems of linear algebra and makes that exploration joyful. — Edward B. Burger, President and Professor, Southwestern University I’m often asked which areas of mathematics should students study. I always say linear algebra. However, typical linear algebra texts I’ve seen either have very few applications, or the applications are contrived and not very relevant to students. Chartier’s text is a refreshing change as it is driven by real-world applications that are inspiring and familiar to his audience. From Google searches and image processing to sports rankings and (my favorite) computer graphics. — Tony DeRose, Pixar Animation Studios From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. When Life is Linear introduces concepts of matrix algebra with an emphasis on application, particularly in the fields of computer graphics and data mining. Readers will learn to make an image transparent, compress an image and rotate a 3D wireframe model. In data mining, readers will use linear algebra to read zip codes on envelopes and encrypt sensitive information. Chartier details methods behind web search, utilized by such companies as Google, and algorithms for sports ranking which have been applied to creating brackets for March Madness and predict outcomes in FIFA World Cup soccer. The book can serve as its own resource or to supplement a course on linear algebra.
eBook
Graph theoretic methods in multiagent networks
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA
eBook