Topological Data Structures For Surfaces
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| Author | : Sanjay Rana |
| Publisher | : John Wiley & Sons |
| Total Pages | : 214 |
| Release | : 2005-12-13 |
| Genre | : Science |
| ISBN | : 047002027X |
In Geography and GIS, surfaces can be analysed and visualised through various data structures, and topological data structures describe surfaces in the form of a relationship between certain surface-specific features. Drawn from many disciplines with a strong applied aspect, this is a research-led, interdisciplinary approach to the creation, analysis and visualisation of surfaces, focussing on topological data structures. Topological Data Structures for Surfaces: an introduction for Geographical Information Science describes the concepts and applications of these data structures. The book focuses on how these data structures can be used to analyse and visualise surface datasets from a range of disciplines such as human geography, computer graphics, metrology, and physical geography. Divided into two Parts, Part I defines the topological surface data structures and explains the various automated methods used for their generation. Part II demonstrates a number of applications of surface networks in diverse fields, ranging from sub-atomic particle collision visualisation to the study of population density patterns. To ensure that the material is accessible, each Part is prefaced by an overview of the techniques and application. Provides GI scientists and geographers with an accessible overview of current surface topology research. Algorithms are presented and explained with practical examples of their usage. Features an accompanying website developed by the Editor - http://geog.le.ac.uk/sanjayrana/surface-networks/ This book is invaluable for researchers and postgraduate students working in departments of GI Science, Geography and Computer Science. It also constitutes key reference material for Masters students working on surface analysis projects as part of a GI Science or Computer Science programme.
| Author | : Sanjay Rana |
| Publisher | : John Wiley & Sons |
| Total Pages | : 222 |
| Release | : 2004-05-21 |
| Genre | : Science |
| ISBN | : 9780470851517 |
In Geography and GIS, surfaces can be analysed and visualised through various data structures, and topological data structures describe surfaces in the form of a relationship between certain surface-specific features. Drawn from many disciplines with a strong applied aspect, this is a research-led, interdisciplinary approach to the creation, analysis and visualisation of surfaces, focussing on topological data structures. Topological Data Structures for Surfaces: an introduction for Geographical Information Science describes the concepts and applications of these data structures. The book focuses on how these data structures can be used to analyse and visualise surface datasets from a range of disciplines such as human geography, computer graphics, metrology, and physical geography. Divided into two Parts, Part I defines the topological surface data structures and explains the various automated methods used for their generation. Part II demonstrates a number of applications of surface networks in diverse fields, ranging from sub-atomic particle collision visualisation to the study of population density patterns. To ensure that the material is accessible, each Part is prefaced by an overview of the techniques and application. Provides GI scientists and geographers with an accessible overview of current surface topology research. Algorithms are presented and explained with practical examples of their usage. Features an accompanying website developed by the Editor - http://geog.le.ac.uk/sanjayrana/surface-networks/ This book is invaluable for researchers and postgraduate students working in departments of GI Science, Geography and Computer Science. It also constitutes key reference material for Masters students working on surface analysis projects as part of a GI Science or Computer Science programme.
| Author | : Norbert A'Campo |
| Publisher | : Springer Nature |
| Total Pages | : 282 |
| Release | : 2021-10-27 |
| Genre | : Mathematics |
| ISBN | : 3030890325 |
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
| Author | : You-Sheng Wu |
| Publisher | : Elsevier |
| Total Pages | : 721 |
| Release | : 2001-08-22 |
| Genre | : Technology & Engineering |
| ISBN | : 0080539351 |
This proceedings contains the papers presented at The 8th International Symposium on Practical Design of Ships and Other Floating Structures held in China in September 2001 - the first PRADS of the 21st Century. The overall aim of PRADS symposia is to advance the design of ships and other floating structures as a professional discipline and science by exchanging knowledge and promoting discussion of relevant topics in the fields of naval architecture and marine and offshore engineering. In line with the aim, in welcoming the new era, this Symposium is intended to increase international co-operation and give a momentum for the new development of design and production technology of ships and other floating structures for efficiency, economy, safety, and environmental production. The main themes of this Symposium are Design Synthesis, Production, Hydrodynamics, Structures and Materials of Ships and Floating Systems. Proposals for over 270 papers from 26 countries and regions within the themes were received for PRADS 2001, and about 170 papers were accepted for presentation at the symposium. With the high quality of the proposed papers the Local Organising Committee had a difficult task to make a balanced selection and to control the total number of papers for fitting into the allocated time schedule approved by the Standing Committee of PRADS. Volume I covers design synthesis, production and part of hydrodynamics. Volume II contains the rest of hydrodynamics, and structures and materials.
| Author | : Martin Raubal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 430 |
| Release | : 2006-09-19 |
| Genre | : Computers |
| ISBN | : 3540445269 |
This book constitutes the refereed proceedings of the 4th International Conference on Geographic Information Science, GIScience 2006. The book presents 26 revised full papers. Among traditional topics addressed are spatial representations and data structures, spatial and temporal reasoning, computational geometry, spatial analysis, and databases. Many papers deal with navigation, interoperability, dynamic modeling, ontology, and semantics. Geosensors, location privacy, social issues and GI research networks rank among the new directions covered.
| Author | : Andreas Riedl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 947 |
| Release | : 2006-09-01 |
| Genre | : Science |
| ISBN | : 3540355898 |
Since the first symposium in 1984 the International Symposia on Spatial Data Handling (SDH) has become a major resource for recent advances in GIS research. The International Symposium on Spatial Data Handling is regarded as a premier international research forum for GIS. All papers are fully reviewed by an international program committee composed of experts in the field.
| Author | : Anthony G. Cohn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 505 |
| Release | : 2005-09 |
| Genre | : Computers |
| ISBN | : 354028964X |
This book constitutes the refereed proceedings of the International Conference on Spatial Information Theory, COSIT 2005, held in Elliottville, NY, USA in September 2005. The 30 revised full papers presented were carefully reviewed and selected from 82 submissions. The papers are organized in topical sections on vagueness, uncertainty, and gradation; paths and routes; ontologies and semantics; ontologies and spatial relations; spatial reasoning: cognitive maps and spatial reasoning; time, change, and dynamics; landmarks and navigation; geographic information, and spatial behaviour.
| Author | : Lidija Čomić |
| Publisher | : Springer |
| Total Pages | : 127 |
| Release | : 2014-10-27 |
| Genre | : Computers |
| ISBN | : 1493921495 |
This book describes the mathematical background behind discrete approaches to morphological analysis of scalar fields, with a focus on Morse theory and on the discrete theories due to Banchoff and Forman. The algorithms and data structures presented are used for terrain modeling and analysis, molecular shape analysis, and for analysis or visualization of sensor and simulation 3D data sets. It covers a variety of application domains including geography, geology, environmental sciences, medicine and biology. The authors classify the different approaches to morphological analysis which are all based on the construction of Morse or Morse-Smale decompositions. They describe algorithms for computing such decompositions for both 2D and 3D scalar fields, including those based on the discrete watershed transform. Also addressed are recent developments in the research on morphological shape analysis, such as simplification operators for Morse and Morse-Smale complexes and their multi-resolution representation. Designed for professionals and researchers involved with modeling and algorithm analysis, Morphological Modeling of Terrains and Volume Data is a valuable resource. Advanced-level students of computer science, mathematics and geography will also find the content very helpful.
| Author | : Tamal Krishna Dey |
| Publisher | : Cambridge University Press |
| Total Pages | : 456 |
| Release | : 2022-03-10 |
| Genre | : Mathematics |
| ISBN | : 1009103199 |
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
| Author | : |
| Publisher | : |
| Total Pages | : 876 |
| Release | : 1995 |
| Genre | : Airframes |
| ISBN | : |
