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Monday, May 18, 2020 | History

4 edition of Discrete surfaces and manifolds found in the catalog.

Discrete surfaces and manifolds

a theory of digital-discrete geometry and topology

by Li Chen

  • 75 Want to read
  • 1 Currently reading

Published by Scientific & Practical Computing in Rockville, Md .
Written in English

    Subjects:
  • Geometry -- Data processing.,
  • Geometrical constructions.,
  • Surfaces.,
  • Manifolds (Mathematics),
  • Algorithms.

  • Edition Notes

    StatementLi Chen.
    Classifications
    LC ClassificationsQA448.D38 C44 2004
    The Physical Object
    Paginationxii, 162 p. :
    Number of Pages162
    ID Numbers
    Open LibraryOL3312803M
    ISBN 100975512218
    LC Control Number2004094541
    OCLC/WorldCa56796457

    Balazs Csik os DIFFERENTIAL GEOMETRY E otv os Lor and University Faculty of Science Typotex Unlike discrete surface theory based on discretization or approximations of continuous surfaces, the notion of subdivisions of discrete surfaces (embedded graphs) is unclear. We would like to establish the notion of subdivision of 3-valent discrete surfaces, and study the convergence of subdivisions to a continuous by: 4.

      This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. My goal was set to write a complete introductory and comprehensive book to digital and discrete geometry. As I was reviewing my writing today, I found that 7 Discrete Manifolds: The Graph-Based Theory Discrete Curves on Graphs.. Discrete Surfaces.. A Special Set of 2-cells .. Discrete Semi.

    Buy Differential Geometry (Student Mathematical Library): Curves - Surfaces - Manifolds 2nd Revised edition by Wolfgang Kuhnel (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders/5(4).   The book provides an excellent introduction to the differential geometry of curves, surfaces and Riemannian manifolds that should be accessible to a variety of readers. The author includes a number of examples, illustrations, and exercises making this book well-suited for .


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Discrete surfaces and manifolds by Li Chen Download PDF EPUB FB2

Geometrical objects: curves, surfaces, and manifolds are no exception. This self-contained monograph focuses on the constructive method for digital and discrete objects especially for surfaces and manifolds.

This book primarily consists of research done by the author and his collaborators with relation to other researchers' : Li Chen. Open Library is an open, editable library catalog, building towards a web page for every book ever published. Discrete surfaces and manifolds by Li Chen,Pages:   Abstract.

This chapter presents a general-purpose definition of discrete curves, surfaces, and manifolds. This definition only refers to a simple graph, \(G=(V,E)\) and its topological structure.

Similar to digital manifolds defined in Chap. 5, the ideas presented in this chapter still use recursive definitions for discrete curves, surfaces, solid objects, and so : Li M.

Chen. Discrete surfaces and manifolds book PDF | Surfaces and Manifolds in Digital Space | The digital surface is one of the main topics of this book. We know that digital curves are digital paths and discrete surfaces can be.

crete Y amabe flow on surfaces and a discrete curv ature flo w on 3-manifolds. Through these work the power of curv ature flows has been extended from the pure theoretical study to solving. Discrete Differential Geometry.

This note covers the following topics: Discrete Curves, Curves and curvature, Flows on curves, Elastica, Darboux transforms, Discrete Surfaces, Abstract discrete surfaces, Polyhedral surfaces and piecewise flat surfaces, Discrete cotan Laplace operator, Delaunay tessellations, Line congruences over simplicial surfaces, Polyhedral surfaces with parallel Gauss map.

The second part, chapters 10 is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of by: The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms.

The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and advanced : Springer International Publishing. Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean space.

Simply put, digitizing is replacing an object by a discrete set of its points. The images we see on the TV screen, the raster display of a computer, or in newspapers are in fact digital images.

Its main application areas are computer. Discrete Curvature Flows for Surfaces and 3-Manifolds Xiaotian Yin 1, Miao Jin2,FengLuo3, and Xianfeng David Gu 1 Computer Science Department, State University of New York at Stony Brook {xyin,gu}@ 2 Center for Advanced Computer Studies, University of Louisiana at Lafayette.

Chen, A Digital-Discrete Method For Smooth-Continuous Data Reconstruction Journal of the Washington Academy of Sciences, No 2,pp (ISSN ). Chen, and Y. Rong, Digital topological method for computing genus and the Betti numbers, Topology and its Applications, VolumeIsPages n-Manifolds.

The real coordinate space R n is an n-manifold. Any discrete space is a 0-dimensional manifold. A circle is a compact 1-manifold. A torus and a Klein bottle are compact 2-manifolds (or surfaces). The n-dimensional sphere S n is a compact n-manifold. The n-dimensional torus T n (the product of n circles) is a compact n-manifold.

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds Mark Meyer 1,MathieuDesbrun,2, Peter Schr¨oder, and Alan H.

Barr1 1 Caltech 2 USC Summary. This paper proposes a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and cur-vatures on arbitrary triangle meshes. Search within book. Front Matter.

Pages i-xvii. PDF. Basic Geometry Li M. Chen. Pages Euclidean Space and Continuous Space. Li M. Chen. Pages Digital Curves, Surfaces, and Manifolds. Front Matter.

Pages PDF. Digital Planar Geometry: Curves and Connected Regions Cloud Data Processing Digital Spaces Digital Surfaces. Discrete Surfaces and Manifolds 作者: Li Chen 出版社: Scientific & Practical Computing 副标题: A Theory of Digital-Discrete Geometry and Topology 出版年: 页数: 定价: USD 装帧: Paperback ISBN: In these cases, discrete surfaces are used to represent the geometry of the surface of an existing solid object.

Surface of solid objects are always orientable and are always locally homeomorphic to a disk. We can thus reduce the notion of discrete surfaces to the notion of discrete orientable 2-manifolds. Orientation is of acute. The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms.

The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and advanced topics.

Publisher Summary. This chapter discusses the existence of spline manifolds. The chapter presents a condition under which a positive function defined in ℝ n is called a temperate weight function and describes an example in which a polynomial is defined on ℝ n with real or complex coefficients.

If Ω is an open subset of ℝ n, then the local space consisting of the set of restrictions to. This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences.

It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData. The author investigates digital geometry and its related constructive methods in discrete geometry.

• “Discrete Differential‐Geometry Operators for Triangulated 2‐ Manifolds”, Meyer et al., ’02 • “Restricted Delaunay triangulations and normal cycle”, Cohen‐Steiner et al., SoCG ‘03 • “On the convergence of metric and geometric properties of polyhedral surfaces”, Hildebrandt et al., ’.

Differential Geometry: Curves — Surfaces — Manifolds, Third Edition Share this page Wolfgang Kühnel. This carefully written book is an introduction to the beautiful ideas and results of differential geometry.

The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory.If you prefer a transition from differential curves and surfaces focusing on riemannian geometry you have Kühnel - "Differential Geometry: Curves, Surfaces, Manifolds".

However, I would argue that one of the best introductions to manifolds is the old soviet book published by MIR, Mishchenko/Fomenko - "A Course of Differential Geometry and.Get this from a library! Hyperbolic manifolds and discrete groups. [Michael Kapovich] -- This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis.

The main focus.