Triangle Of Transformation
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The Getme Mesh Smoothing Framework
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Author : Dimitris Vartziotis
language : en
Publisher: CRC Press
Release Date : 2018-12-07
The Getme Mesh Smoothing Framework written by Dimitris Vartziotis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Computers categories.
High quality meshes play a key role in many applications based on digital modeling and simulation. The finite element method is a paragon for such an approach and it is well known that quality meshes can significantly improve computational efficiency and solution accuracy of this method. Therefore, a lot of effort has been put in methods for improving mesh quality. These range from simple geometric approaches, like Laplacian smoothing, with a high computational efficiency but possible low resulting mesh quality, to global optimization-based methods, resulting in an excellent mesh quality at the cost of an increased computational and implementational complexity. The geometric element transformation method (GETMe) aims to fill the gap between these two approaches. It is based on geometric mesh element transformations, which iteratively transform polygonal and polyhedral elements into their regular counterparts or into elements with a prescribed shape. GETMe combines a Laplacian smoothing-like computational efficiency with a global optimization-like effectiveness. The method is straightforward to implement and its variants can also be used to improve tangled and anisotropic meshes. This book describes the mathematical theory of geometric element transformations as foundation for mesh smoothing. It gives a thorough introduction to GETMe-based mesh smoothing and its algorithms providing a framework to focus on effectively improving key mesh quality aspects. It addresses the improvement of planar, surface, volumetric, mixed, isotropic, and anisotropic meshes and addresses aspects of combining mesh smoothing with topological mesh modification. The advantages of GETMe-based mesh smoothing are demonstrated by the example of various numerical tests. These include smoothing of real world meshes from engineering applications as well as smoothing of synthetic meshes for demonstrating key aspects of GETMe-based mesh improvement. Results are compared with those of other smoothing methods in terms of runtime behavior, mesh quality, and resulting finite element solution efficiency and accuracy. Features: • Helps to improve finite element mesh quality by applying geometry-driven mesh smoothing approaches. • Supports the reader in understanding and implementing GETMe-based mesh smoothing. • Discusses aspects and properties of GETMe smoothing variants and thus provides guidance for choosing the appropriate mesh improvement algorithm. • Addresses smoothing of various mesh types: planar, surface, volumetric, isotropic, anisotropic, non-mixed, and mixed. • Provides and analyzes geometric element transformations for polygonal and polyhedral elements with regular and non-regular limits. • Includes a broad range of numerical examples and compares results with those of other smoothing methods.
Lobachevski Illuminated
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Author : Seth Braver
language : en
Publisher: MAA
Release Date : 2011
Lobachevski Illuminated written by Seth Braver and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
A historical introduction to non-Euclidean geometry.
Key Maths Gcse
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Author :
language : en
Publisher: Nelson Thornes
Release Date : 2003
Key Maths Gcse written by and has been published by Nelson Thornes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Juvenile Nonfiction categories.
Developed for the CCEA Specification, this Teacher File contains detailed support and guidance on advanced planning, points of emphasis, key words, notes for the non-specialist, useful supplementary ideas and homework sheets.
Maths Connect
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Author : Dave Kirkby
language : en
Publisher: Heinemann
Release Date : 2004
Maths Connect written by Dave Kirkby and has been published by Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Education categories.
Maths connect provides consolidation, stretch and challenge for pupils of all abilities. This pupil's text in the blue tier provides an ideal route through Key Stage 3 for the middle-ability pupils.
Manual Of Plane Geometry On The Heuristic Plan
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Author : George Irving Hopkins
language : en
Publisher:
Release Date : 1891
Manual Of Plane Geometry On The Heuristic Plan written by George Irving Hopkins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1891 with Geometry, Plane categories.
Computer Vision Imaging And Computer Graphics Theory And Applications
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Author : José Braz
language : en
Publisher: Springer
Release Date : 2017-08-08
Computer Vision Imaging And Computer Graphics Theory And Applications written by José Braz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-08 with Computers categories.
This book constitutes thoroughly revised and selected papers from the 11th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, VISIGRAPP 2016, held in Rome, Italy, in February 2016. VISIGRAPP comprises GRAPP, International Conference on Computer Graphics Theory and Applications; IVAPP, International Conference on Information Visualization Theory and Applications; and VISAPP, International Conference on Computer Vision Theory and Applications. The 28 thoroughly revised and extended papers presented in this volume were carefully reviewed and selected from 338 submissions. The book also contains one invited talk in full-paper length. The regular papers were organized in topical sections named: computer graphics theory and applications; information visualization theory and applications; and computer vision theory and applications.
The Mathematical Gazette
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Author :
language : en
Publisher:
Release Date : 1896
The Mathematical Gazette written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1896 with Mathematics categories.
Automorphic Functions
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Author : Lester R. Ford
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Automorphic Functions written by Lester R. Ford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Lester Ford's book was the first treatise in English on automorphic functions. At the time of its publication (1929), it was welcomed for its elegant treatment of groups of linear transformations and for the remarkably clear and explicit exposition throughout the book. Ford's extraordinary talent for writing has been memorialized in the prestigious award that bears his name. The book, in the meantime, has become a recognized classic. Ford's approach is primarily through analytic function theory. The first part of the book covers groups of linear transformations, especially Fuchsian groups, fundamental domains, and functions that are invariant under the groups, including the classical elliptic modular functions and Poincare theta series. The second part of the book covers conformal mappings, uniformization, and connections between automorphic functions and differential equations with regular singular points, such as the hypergeometric equation.
Developing Thinking In Geometry
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Author : Sue Johnston-Wilder
language : en
Publisher: SAGE
Release Date : 2005-08-18
Developing Thinking In Geometry written by Sue Johnston-Wilder and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-18 with Education categories.
'Geometry is often given less time in the teaching timetable than other aspects of mathematics. This book encourages practitioners to think about and raise its profile, indeed achieving what its title suggest' - Primary Practice `This creative, innovative and fascinating book/CD package is one you "MUST BUY". All prospective, new and experienced teachers of mathematics can use it to transform their teaching. All readers can use it to reignite their fascination with mathematics' - Professor Sylvia Johnson, Sheffield Hallam University 'This book exudes activity and interactivity. Moreover, it provides challenge in the context of a significant pedagogy, one that is not just present but actually made explicit. It is undoubtedly a book to learn geometry with, but also one to learn to think more deeply about geometry, about its nature and essence, and also about its teaching and learning' - David Pimm Developing Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. As well as discussing key teaching principles, the book and accompanying interactive CD include many activities that encourage readers to extend their own learning, and consequently their teaching practices. The book is constructed around the following key themes: - invariance; - language and points of view; - reasoning using invariance; - visualising and representing. These themes draw on teaching principles developed by the team at the Open University's Centre for Mathematics Education which has a 20-year track record of innovative approaches to teaching and learning geometry. This is a 'must have' text for all primary mathematics specialists, secondary and Further Education mathematics teachers and their support staff. Anyone who wishes to create an understanding and enthusiasm for geometry based upon firm research and effective practice, will enjoy this book. This is the course reader for the Open University Course ME627 Developing Geometric Thinking
Topology Of Numbers
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Author : Allen Hatcher
language : en
Publisher: American Mathematical Society
Release Date : 2022-10-19
Topology Of Numbers written by Allen Hatcher and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-19 with Mathematics categories.
This book serves as an introduction to number theory at the undergraduate level, emphasizing geometric aspects of the subject. The geometric approach is exploited to explore in some depth the classical topic of quadratic forms with integer coefficients, a central topic of the book. Quadratic forms of this type in two variables have a very rich theory, developed mostly by Euler, Lagrange, Legendre, and Gauss during the period 1750–1800. In this book their approach is modernized by using the splendid visualization tool introduced by John Conway in the 1990s called the topograph of a quadratic form. Besides the intrinsic interest of quadratic forms, this theory has also served as a stepping stone for many later developments in algebra and number theory. The book is accessible to students with a basic knowledge of linear algebra and arithmetic modulo $n$. Some exposure to mathematical proofs will also be helpful. The early chapters focus on examples rather than general theorems, but theorems and their proofs play a larger role as the book progresses.