Download or read book Euclidean Shortest Paths on Polyhedra in Three Dimensions written by Yevgeny Schreiber and published by . This book was released on 2007 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Unobstructed Shortest Paths in Polyhedral Environments written by Varol Akman and published by Springer Science & Business Media. This book was released on 1987-03-11 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first examination of the cervical spine is always made using standard radiographs and, often enough, this suffices as a basis for diagnosis. Malformations, tumours, and more frequently traumas, rheumatism, and even ordinary neck pain require radiological examination of the spine. Interpretation, however, is difficult. Take a cervical vertebra in your hand and you will see that it is complex enough itself. In radiology the overlapping pieces of bone, summation phenomena and the diversity of viewing angles complicate interpretation of the images still further. The book by J.-F. Bonneville and F. Cattin suggests an original method of reading the radiographs, strict but very attractive, which considerably simplifies the interpretation of images of the cervical spine. This book shows that two- or threedimensional computed tomograms accompany standard radiographs as an excellent aid to comprehension. It is as though the reader had access to each part of the bony anatomy shown in the radiographs and from then on everything becomes easy, superimpositions disappear, traps become visible, anatomy triumphs, the image lives.
Download or read book Shortest paths in polyhedral obstacles in 3 dimensional euclidean space written by Varol Akman and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Shortest Paths Avoiding Polyhedral Obstacles in 3 dimensional Euclidean Space written by Varol Akman and published by . This book was released on 1985 with total page 104 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 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Tulane Symposium in Biomedical Engineering School of Engineering Tulane University 1 written by and published by . This book was released on 1973 with total page 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 Reshaping Convex Polyhedra written by Joseph O'Rourke and published by Springer. This book was released on 2024-02-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: ^ the="" study="" of="" convex="" polyhedra="" in="" ordinary="" space="" is="" a="" central="" piece="" classical="" and="" modern="" geometry="" that="" has="" had="" significant="" impact="" on="" many="" areas="" mathematics="" also="" computer="" science.="" present="" book="" project="" by="" joseph="" o’rourke="" costin="" vîlcu="" brings="" together="" two="" important="" strands="" subject="" —="" combinatorics="" polyhedra,="" intrinsic="" underlying="" surface.="" this="" leads="" to="" remarkable="" interplay="" concepts="" come="" life="" wide="" range="" very="" attractive="" topics="" concerning="" polyhedra.="" gets="" message="" across="" thetheory="" although="" with="" roots,="" still="" much="" alive="" today="" continues="" be="" inspiration="" basis="" lot="" current="" research="" activity.="" work="" presented="" manuscript="" interesting="" applications="" discrete="" computational="" geometry,="" as="" well="" other="" mathematics.="" treated="" detail="" include="" unfolding="" onto="" surfaces,="" continuous="" flattening="" convexity="" theory="" minimal="" length="" enclosing="" polygons.="" along="" way,="" open="" problems="" suitable="" for="" graduate="" students="" are="" raised,="" both="" a The focus of this monograph is converting—reshaping—one 3D convex polyhedron to another via an operation the authors call “tailoring.” A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a “vertex”) of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler’s “vertex truncation,” but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful “gluing” theorem of A.D. Alexandrov from 1950 guarantees that, after closing the hole, the result is a new convex polyhedron. Given two convex polyhedra P, and Q inside P, repeated tailoringallows P to be reshaped to Q. Rescaling any Q to fit inside P, the result is universal: any P can be reshaped to any Q. This is one of the main theorems in Part I, with unexpected theoretical consequences. Part II carries out a systematic study of “vertex-merging,” a technique that can be viewed as a type of inverse operation to tailoring. Here the start is P which is gradually enlarged as much as possible, by inserting new surface along slits. In a sense, repeated vertex-merging reshapes P to be closer to planarity. One endpoint of such a process leads to P being cut up and “pasted” inside a cylinder. Then rolling the cylinder on a plane achieves an unfolding of P. The underlying subtext is a question posed by Geoffrey Shephard in 1975 and already implied by drawings by Albrecht Dürer in the 15th century: whether every convex polyhedron can be unfolded to a planar “net.” Toward this end, the authors initiate an exploration of convexity on convex polyhedra, a topic rarely studiedin the literature but with considerable promise for future development. This monograph uncovers new research directions and reveals connections among several, apparently distant, topics in geometry: Alexandrov’s Gluing Theorem, shortest paths and cut loci, Cauchy’s Arm Lemma, domes, quasigeodesics, convexity, and algorithms throughout. The interplay between these topics and the way the main ideas develop throughout the book could make the “journey” worthwhile for students and researchers in geometry, even if not directly interested in specific topics. Parts of the material will be of interest and accessible even to undergraduates. Although the proof difficulty varies from simple to quite intricate, with some proofs spanning several chapters, many examples and 125 figures help ease the exposition and illustrate the concepts. ^>
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 Polyhedra written by Anthony Pugh and published by . This book was released on 1990 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polyhedra: A Visual Approach provides an introduction to polyhedra for readers who are not necessarily mathematicians. The study of polyhedra - fascinating figures constructed of interrelated shapes - is usually regarded as a branch of geometry. In fact, most books on the subject have been written for readers with a mathematical background. However, Polyhedra: A Visual Approach describes these figures in simple, visual terms. This book focuses on regular and semiregular convex polyhedra first. Then these are used as bases for the development of several families of irregular figures, including geodesic polyhedra - the domes made famous by R. Buckminster Fuller. Polyhedra: A Visual Approach will interest readers from many different backgrounds. Mathematicians and scientists may discover that a visual approach opens up new possibilities. Artists, architects, designers, and engineers should find it a valuable exercise in three dimensions that increases their abilities in manipulating space. And general readers will be drawn to the uncomplicated description of polyhedra - fascinating figures that have inspired many a brilliant thinker. -- from back cover.
Download or read book Euclidean Shortest Paths written by Fajie Li and published by Springer Science & Business Media. This book was released on 2011-11-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Topics and features: provides theoretical and programming exercises at the end of each chapter; presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms; discusses algorithms for calculating exact or approximate ESPs in the plane; examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves; describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems; includes lists of symbols and abbreviations, in addition to other appendices.
Download or read book Algorithms and Theory of Computation Handbook Volume 2 written by Mikhail J. Atallah and published by CRC Press. This book was released on 2009-11-20 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook, Second Edition: Special Topics and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems.Along with updating and revising many of
Download or read book On Finding Shortest Paths on Convex Polyhedra written by David M. Mount and published by . This book was released on 1985 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications in robotics and autonomous navigation have motivated the study of motion planning and obstacle avoidance algorithms. The special case considered here is that of moving a point (the object) along the surface of a convex polyhedron (the obstacle) with n vertices. Sharir and Schorr have developed an algorithm that, given a source point on the surface of a convex polyhedron, determines the shortest path from the source to any point on the polyhedron in linear time after O(n cubed log n) preprocessing time. The preprocessed output requires O(n squared) space. By using known algorithms for fast planar point location, the shortest path query time for Sharir and Schorr's algorithm is shown to be O(k + log n) where k is the number faces traversed by the path. We give an improved preprocessing algorithm that runs in O(n squared log n) time requiring the same query time and space. We also show how to store the output of the preprocessing algorithm in O(n log n) space while maintaining the same query time. (Author).
Download or read book Algorithms and Theory of Computation Handbook written by Mikhail J. Atallah and published by CRC Press. This book was released on 1998-11-23 with total page 1328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing
Download or read book An Optimal Algorithm for Intersecting Three dimensional Convex Polyhedra written by Princeton University. Dept. of Computer Science and published by . This book was released on 1989 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We describe a linear-time algorithm for computing the intersection of two convex polyhedra in 3-space. Applications of this result to computing intersections, convex hulls, and Voronoi diagrams are given."
Download or read book Discrete Geometry for Computer Imagery written by Isabelle Debled-Rennesson and published by Springer. This book was released on 2011-03-29 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 16th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2011, held in Nancy, France, in April 2011. The 20 revised full papers and 20 revised poster papers presented together with 3 invited lectures were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on models for discrete geometry, discrete and combinatorial topology, geometric transforms, discrete shape representation, recognition and analysis, discrete tomography, morphological analysis, as well as discrete and combinatorial tools for image segmentation and analysis.
