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The Spaces Of Shapes And Geodesic Triangulations On Surfaces
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Book Synopsis The Spaces of Shapes and Geodesic Triangulations on Surfaces by : Yanwen Luo
Download or read book The Spaces of Shapes and Geodesic Triangulations on Surfaces written by Yanwen Luo and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the geometry and topology of surfaces has been well-established during the last century from various perspectives. In recent developments of discrete differential geometry, mathematicians started to think rigorously about the discrete counterparts of concepts in the smooth setting, including triangulations, metrics, curvatures. We study the geometry of discrete surfaces via discrete metrics, discrete curvatures, and discrete conformal maps, not only as approximations to the smooth counterparts, but as geometric objects in their own right. They provide fast algorithms in computer graphics, and also a parallel theory, such as discrete uniformization theorems.This thesis is concerned with these types of problems. We study the geometry and topology of "shape" spaces of different geometric objects, including high genus surfaces in R3 and geodesic triangulations on surfaces with constant curvature. In Chapter 2, we study the global comparison problem for two surfaces with the same high genus, constructing a metric on the shape space and producing a correspondence between two given shapes. This leads to an algorithm to compute the distance between a pair of shapes via energy minimization. In Chapter 3, we consider the topology of the space of geodesic triangulations on a surface with a fixed combinatorial type in a fixed isotopy class, which can be regarded as a discrete version of the group of surface diffeomorphisms. We show that these spaces, after appropriate normalization, are contractible when the surface is a convex polygon. Furthermore, we provide an algorithm to generate geodesic triangulations when the surface is a star-shaped polygon.
Book Synopsis Mostly Surfaces by : Richard Evan Schwartz
Download or read book Mostly Surfaces written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2011 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Book Synopsis Computational Geometry, Topology and Physics of Digital Images with Applications by : James F. Peters
Download or read book Computational Geometry, Topology and Physics of Digital Images with Applications written by James F. Peters and published by Springer Nature. This book was released on 2019-10-03 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.
Book Synopsis The Geometry of Geodesics by : Herbert Busemann
Download or read book The Geometry of Geodesics written by Herbert Busemann and published by . This book was released on 1955 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is concerned with a geometric approach to qualitative problems in intrinsic differential geometry, with an emphasis on spaces in which the geodesics have only local uniqueness properties. Finsler spaces are the principal subject, both in terms of a type of space and of an approach. Some familiarity with non-Euclidean geometry and classical differential geometry is necessary to grasp the significance of the problems.
Book Synopsis Energy Minimization Methods in Computer Vision and Pattern Recognition by : Daniel Cremers
Download or read book Energy Minimization Methods in Computer Vision and Pattern Recognition written by Daniel Cremers and published by Springer. This book was released on 2009-08-17 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2009, held in Bonn, Germany in August 2009. The 18 revised full papers, 18 poster papers and 3 keynote lectures presented were carefully reviewed and selected from 75 submissions. The papers are organized in topical sections on discrete optimization and Markov random fields, partial differential equations, segmentation and tracking, shape optimization and registration, inpainting and image denoising, color and texture and statistics and learning.
Book Synopsis Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths by : Sergey Fomin
Download or read book Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths written by Sergey Fomin and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmüller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface.
Book Synopsis Graph Drawing and Network Visualization by : Helen C. Purchase
Download or read book Graph Drawing and Network Visualization written by Helen C. Purchase and published by Springer Nature. This book was released on 2021-12-22 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 28th International Symposium on Graph Drawing and Network Visualization, GD 2021, which was held in Tübingen, Germany, during September 14-17, 2021. The 23 full papers and 5 short papers presented in these proceedings were carefully reviewed and selected from 74 submissions. The abstracts of 13 posters presented at the conference can be found in the back matter of the volume. The contributions were organized in topical sections as follows: Best Paper (Track 1: Combinatorial and Algorithmic Aspects); Best Paper (Track 2: Experimental, Applied, and Network Visualization Aspects); Crossing Minimization and Beyond-Planarity; Morphing and Graph Abstraction; Geometric Constraints; Topological and Upward Drawings; Linear Layouts; Contact and Visibility Representations; Geometric Aspects in Graph Drawing; AI applications; and Graph Drawing Contest Report.
Book Synopsis The Geodesic Geometry of Surfaces in Non-Euclidean Space by : Alfred North Whitehead
Download or read book The Geodesic Geometry of Surfaces in Non-Euclidean Space written by Alfred North Whitehead and published by . This book was released on 1897 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Geometry and Topology of Three-Manifolds by : William P. Thurston
Download or read book The Geometry and Topology of Three-Manifolds written by William P. Thurston and published by American Mathematical Society. This book was released on 2023-06-16 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.
Book Synopsis Realization Spaces of Polytopes by : Jürgen Richter-Gebert
Download or read book Realization Spaces of Polytopes written by Jürgen Richter-Gebert and published by Springer. This book was released on 2006-11-13 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes". It is a comprehensive survey of the important results that have been obtained in that direction. The approaches chosen are direct and very geometric in nature. The book is addressed to researchers and to graduate students. The former will find a comprehensive source for the above mentioned results. The latter will find a readable introduction to the field. The reader is assumed to be familiar with basic concepts of linear algebra.
Book Synopsis Collected Works of William P. Thurston with Commentary by : Benson Farb
Download or read book Collected Works of William P. Thurston with Commentary written by Benson Farb and published by American Mathematical Society. This book was released on 2023-06-05 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume I contains William Thurston's papers on foliations, mapping classes groups, and differential geometry.
Book Synopsis Remote Sensing of Earth Resources by : NASA Scientific and Technical Information Facility
Download or read book Remote Sensing of Earth Resources written by NASA Scientific and Technical Information Facility and published by . This book was released on 1970 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Transactions on Computational Science XXVI by : Marina L. Gavrilova
Download or read book Transactions on Computational Science XXVI written by Marina L. Gavrilova and published by Springer. This book was released on 2016-01-22 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This, the 26th issue of the Transactions on Computational Science journal, is comprised of ten extended versions of selected papers from the International Conference on Cyberworlds 2014, held in Santander, Spain, in June 2014. The topics covered include areas of virtual reality, games, social networks, haptic modeling, cybersecurity, and applications in education and arts.
Book Synopsis Harmonic Mappings in the Plane by : Peter Duren
Download or read book Harmonic Mappings in the Plane written by Peter Duren and published by Cambridge University Press. This book was released on 2004-03-29 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.
Book Synopsis The Shape of Space by : Jeffrey R. Weeks
Download or read book The Shape of Space written by Jeffrey R. Weeks and published by Marcel Dekker. This book was released on 1985 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Shape of Space brings topology to the general reader by showing how to visualize manifolds directly ... complements existing textbooks, which often deal only in abstractions, by offering a wealth of concrete examples ... includes the first elementary exposition of William P. Thurston's revolutionary discoveries ... applies topology to cosmology ... gives the first simple pictorial exposition of the Gauss-Bonnet formula ... builds intuition with more than 140 hands-on exercises, all with complete solutions ... and offers over 170 illustrations. An annotated bibliography lists useful references for further study on specific topics.
Book Synopsis An Invitation to Alexandrov Geometry by : Stephanie Alexander
Download or read book An Invitation to Alexandrov Geometry written by Stephanie Alexander and published by Springer. This book was released on 2019-05-08 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
Book Synopsis Mathematical Tools for Shape Analysis and Description by : Silvia Biasotti
Download or read book Mathematical Tools for Shape Analysis and Description written by Silvia Biasotti and published by Springer Nature. This book was released on 2022-06-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a guide for researchers and practitioners to the new frontiers of 3D shape analysis and the complex mathematical tools most methods rely on. The target reader includes students, researchers and professionals with an undergraduate mathematics background, who wish to understand the mathematics behind shape analysis. The authors begin with a quick review of basic concepts in geometry, topology, differential geometry, and proceed to advanced notions of algebraic topology, always keeping an eye on the application of the theory, through examples of shape analysis methods such as 3D segmentation, correspondence, and retrieval. A number of research solutions in the field come from advances in pure and applied mathematics, as well as from the re-reading of classical theories and their adaptation to the discrete setting. In a world where disciplines (fortunately) have blurred boundaries, the authors believe that this guide will help to bridge the distance between theory and practice. Table of Contents: Acknowledgments / Figure Credits / About this Book / 3D Shape Analysis in a Nutshell / Geometry, Topology, and Shape Representation / Differential Geometry and Shape Analysis / Spectral Methods for Shape Analysis / Maps and Distances between Spaces / Algebraic Topology and Topology Invariants / Differential Topology and Shape Analysis / Reeb Graphs / Morse and Morse-Smale Complexes / Topological Persistence / Beyond Geometry and Topology / Resources / Bibliography / Authors' Biographies
