Download or read book On Shortest Paths Amidst Convex Polyhedra Classic Reprint written by Micha Sharir and published by Forgotten Books. This book was released on 2017-12-04 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On Shortest Paths Amidst Convex Polyhedra The paper is organized as follows. In Section 2 we prove our main result about a polynomial upper bound on the number of sequences of edges crossed by shortest paths along a convex polyhedron. In Section 3 we extend the observations made above to obtain polynomial time shortest-path algorithms for any fixed number of convex polyhedral obstacles. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book On Shortest Paths Between Two Convex Polyhedra Classic Reprint written by A. Baltsan and published by Forgotten Books. This book was released on 2017-11-09 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On Shortest Paths Between Two Convex Polyhedra As a matter of fact, the problem we face here can be formulated as that of calculating all possible sequences of edges of B which can be crossed by shortest paths from any point on e to any point on e'. If we had all these sequences available, then we could unfold each such sequence C in turn so as to make the middle portion of the corresponding candidate path into a straight segment, and then find the shortest path from so to Z constrained to contain such a segment, a task which can be accomplished in much the same way as was done in Sections 3 and 4. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book On Shortest Paths Amidst Convex Polyhedra written by Micha Sharir and published by . This book was released on 1985 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Shortest Paths Amidst Convex Polyhedra written by Micha Sharir and published by . This book was released on 1985 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Shortest Paths Between Two Convex Polyhedra written by Avikam Baltsan and published by Palala Press. This book was released on 2015-09-09 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Proceedings of the ACM Symposium on Theory of Computing written by and published by . This book was released on 2000 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Methods in Image Processing and Inverse Problems written by Xue-Cheng Tai and published by Springer Nature. This book was released on 2021-09-25 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.
Download or read book Computing the Continuous Discretely written by Matthias Beck and published by Springer. This book was released on 2015-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE
Download or read book A Fuller Explanation written by Amy C. Edmondson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a broad sense Design Science is the grammar of a language of images rather than of words. Modern communication techniques enable us to transmit and reconstitute images without the need of knowing a specific verbal sequential language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multidimensional. Architectural renderings commonly show projections onto three mutually perpendicular planes, or consist of cross sections at differ ent altitudes representing a stack of floor plans. Such renderings make it difficult to imagine buildings containing ramps and other features which disguise the separation between floors; consequently, they limit the creativity of the architect. Analogously, we tend to analyze natural structures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures.
Download or read book Spherical Models written by Magnus J. Wenninger and published by Courier Corporation. This book was released on 2014-05-05 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just a ruler and compass. 1979 edition.
Download or read book Dual Models written by Magnus J. Wenninger and published by Cambridge University Press. This book was released on 2003-10-16 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: An enthusiastic presentation of the complex set of uniform duals of uniform polyhedral shapes.
Download or read book Computational Geometry written by Mark de Berg and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.
Download or read book Simulating Humans written by Norman I. Badler and published by Oxford University Press, USA. This book was released on 1993-09-02 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of simulated human figures is an active research area in computer graphics, and Norman Badler's group at the University of Pennsylvania is one of the leaders in the field. This book summarizes the state of the art in simulating human figures, discusses many of the interesting application areas, and makes some assumptions and predictions about where the field is going.
Download or read book Computational Geometry in C written by Joseph O'Rourke and published by Cambridge University Press. This book was released on 1998-10-13 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.
Download or read book Embeddings in Manifolds written by Robert J. Daverman and published by American Mathematical Soc.. This book was released on 2009-10-14 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.
Download or read book 5000 Years of Geometry written by Christoph J. Scriba and published by Birkhäuser. This book was released on 2015-04-22 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)
Download or read book Computer Science Today written by Jan Leeuwen and published by Lecture Notes in Computer Science. This book was released on 1995-10-18 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This specially commissioned volume presents a unique collection of expository papers on major topics that are representative for computer science today. The 38 contributions, written by internationally leading experts in the computer science area on personal invitation, demonstrate the scope and stature of the field today and give an impression of the chief motivations and challenges for tomorrow's computer science and information technology. This anthology marks a truly extraordinary and festive moment: it is the 1000th volume published in the Lecture Notes in Computer Science series. It addresses all computer scientists and anybody interested in a representative overview of the field.
