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Polygons, Polyominoes and Polycubes
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many oth...
Find the Polygon
Discover Shapes Level B Reader: Find the Polygon Beginning readers identify things that are polygons in this very simple 20-page reader. Sample Text: I see a polygon. The gem is a polygon. This book is a step-up from the paired book in the Discover Shapes series, POLYGON.
Polygon
Discover Shapes Level A Reader: Polygon Beginning readers identify things that are polygons in this very simple 12-page reader. Sample Text: The sign is an oval. This book is the first step for beginning readers in the Discover Shapes series, and can be paired with the Level B text, FIND THE POLYGON.
Near Polygons
Dedicated to the Russian mathematician Albert Shiryaev on his 70th birthday, this is a collection of papers written by his former students, co-authors and colleagues. The book represents the state-of-the-art of a quickly maturing theory and will be an essential source for researchers in this area. The diversity of topics and comprehensive style of the papers make the book attractive for Ph.D. students and young researchers.
Polygon Mesh Processing
Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.
Introduction to Geometric Computing
Computing is quickly making much of geometry intriguing not only for philosophers and mathematicians, but also for scientists and engineers. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer. Every programmer tackling a geometric computing problem encounters design decisions that need to be solved. This book reviews the geometric theory then applies it in an attempt to find that elusive "right" design.
Algorithms for Parallel Polygon Rendering
This richly illustrated volume draws from a variety of sources to present a reference work for this remarkable volcanic province. Detailed descriptions of 44 major potentially active (Holocene) volcanoes form the core of the book. A compendium of geographical and morphological data on location, type, synonyms, summit elevation, edifice height, and status for each center, is followed by a summary of the structural and volcanological evolution of the edi- fice, historic and present activity, petrological and geochemical data, and an assessment of volcanic hazard. Each entry is superbly illustrated with a false color Landsat Thematic Mapper image, maps and ground photographs. Chapters on Holoce...
Generalized Polygons
Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-bu...
Discover Polygons
Learn how polygons have specific attributes and learn the names of a variety of polygons.
Mapping Polygons
This thesis focuses on the exploration of polygonal environments with simple agents. The goal is to understand what minimal capabilities such agents need in order to draw a map of their environment. Starting from a very basic agent model, we investigate what extra capabilities agents need in order to reconstruct the visibility graph of their environment. Some combinations of capabilities are shown to be insufficient, while others are shown to be sufficient. For the latter, we present reconstruction algorithms and algorithms for meeting with other agents.
