Pythagorean Hodograph Curves Algebra and Geometry Inseparable

Author: Rida T Farouki
Publisher: Springer Science & Business Media
ISBN: 9783540733980
Release Date: 2008-02-01
Genre: Mathematics

By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.

Advances in Geometric Modeling and Processing

Author: Bernard Mourrain
Publisher: Springer Science & Business Media
ISBN: 9783642134104
Release Date: 2010-06-09
Genre: Computers

This book constitutes the refereed proceedings of the 6th International Conference on Geometric Modeling and Processing, GMP 2010, held in Castro Urdiales, Spain, in June 2010. The 20 revised full papers presented were carefully reviewed and selected from a total of 30 submissions. The papers cover a wide spectrum in the area of geometric modeling and processing and address topics such as solutions of transcendental equations; volume parameterization; smooth curves and surfaces; isogeometric analysis; implicit surfaces; and computational geometry.

SAGA Advances in ShApes Geometry and Algebra

Author: Tor Dokken
Publisher: Springer
ISBN: 9783319086354
Release Date: 2014-10-24
Genre: Mathematics

This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design.

Cones Matrices and Mathematical Programming

Author: Abraham Berman
Publisher: Springer Science & Business Media
ISBN: 9783642807305
Release Date: 2012-12-06
Genre: Mathematics

This monograph is a revised set of notes on recent applications of the theory of cones, arising from lectures I gave during my stay at the Centre de recherches mathematiques in Montreal. It consists of three chapters. The first describes the basic theory. The second is devoted to applications to mathematical programming and the third to matrix theory. The second and third chapters are independent. Natural links between them, such as mathematical programming over matrix cones, are only mentioned in passing. The choice of applications described in this paper is a reflection of my p«r9onal interests, for examples, the complementarity problem and iterative methods for singular systems. The paper definitely does not contain all the applications which fit its title. The same remark holds for the list of references. Proofs are omitted or sketched briefly unless they are very simple. However, I have tried to include proofs of results which are not widely available, e.g. results in preprints or reports, and proofs, based on the theory of cones, of classical theorems. This monograph benefited from helpful discussions with professors Abrams, Barker, Cottle, Fan, Plemmons, Schneider, Taussky and Varga.

Adaptive Moving Mesh Methods

Author: Weizhang Huang
Publisher: Springer Science & Business Media
ISBN: 9781441979162
Release Date: 2010-10-26
Genre: Mathematics

This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.

Subdivision Surfaces

Author: Jörg Peters
Publisher: Springer Science & Business Media
ISBN: 9783540764069
Release Date: 2008-08-24
Genre: Mathematics

Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.

Matrix Based Multigrid

Author: Yair Shapira
Publisher: Springer Science & Business Media
ISBN: 9780387497648
Release Date: 2008-07-02
Genre: Mathematics

Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge only in basic linear algebra and calculus.

A History of Vector Analysis

Author: Michael J. Crowe
Publisher: Courier Corporation
ISBN: 9780486679105
Release Date: 1967
Genre: Mathematics

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

Nonlinear Problems of Elasticity

Author: S.S Antman
Publisher: Springer Science & Business Media
ISBN: 9781475741476
Release Date: 2013-03-14
Genre: Mathematics

The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.

A History of Algorithms

Author: Jean-Luc Chabert
Publisher: Springer Science & Business Media
ISBN: 9783642181924
Release Date: 2012-12-06
Genre: Mathematics

The development of computing has reawakened interest in algorithms. Often neglected by historians and modern scientists, algorithmic procedures have been instrumental in the development of fundamental ideas: practice led to theory just as much as the other way round. The purpose of this book is to offer a historical background to contemporary algorithmic practice.

Image and Geometry Processing for 3 D Cinematography

Author: Rémi Ronfard
Publisher: Springer Science & Business Media
ISBN: 9783642123924
Release Date: 2010-06-29
Genre: Mathematics

papers, illustrated with examples. They include wavelet bases, implicit functions de ned on a space grid, etc. It appears that a common pattern is the recovery of a controllable model of the scene, such that the resulting images can be edited (interaction). Changing the viewpoint is only one (important) aspect, but changing the lighting and action is equally important [2]. Recording and representing three-dimensional scenes is an emerging technology made possible by the convergence of optics, geometry and computer science, with many applications in the movie industry, and more generally in entertainment. Note that the invention of cinema (camera and projector) was also primarily a scienti c invention that evolved into an art form. We suspect the same thing will probably happen with 3-D movies. 3 Book Contents The book is composed of 12 chapters, which elaborate on the content of talks given at the BANFF workshop. The chapters are organized into three sections. The rst section presents an overview of the inter-relations between the art of cinemat- raphy and the science of image and geometry processing; the second section is devoted to recent developments in geometry; and the third section is devoted to recent developmentsin image processing. 3.1 3-D Cinematography and Applications The rst section of the book presents an overview of the inter-relations between the art of cinematography and the science of image and geometry processing.

Introduction to Process Algebra

Author: Wan Fokkink
Publisher: Springer Science & Business Media
ISBN: 9783662042939
Release Date: 2013-03-09
Genre: Mathematics

Automated and semi-automated manipulation of so-called labelled transition systems has become an important means in discovering flaws in software and hardware systems. Process algebra has been developed to express such labelled transition systems algebraically, which enhances the ways of manipulation by means of equational logic and term rewriting. The theory of process algebra has developed rapidly over the last twenty years, and verification tools have been developed on the basis of process algebra, often in cooperation with techniques related to model checking. This textbook gives a thorough introduction into the basics of process algebra and its applications.

Handbook of Computer Aided Geometric Design

Author: Gerald E. Farin
Publisher: Elsevier
ISBN: 9780444511041
Release Date: 2002
Genre: Computers

This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include: Historical outline Curve and surface methods Scientific Visualization Implicit methods Reverse engineering. This book is meant to be a reference text for researchers in the field as well as an introduction to graduate students wishing to get some exposure to this subject.

Optimization and Control of Bilinear Systems

Author: Panos M. Pardalos
Publisher: Springer Science & Business Media
ISBN: 0387736697
Release Date: 2010-03-14
Genre: Science

Covers developments in bilinear systems theory Focuses on the control of open physical processes functioning in a non-equilibrium mode Emphasis is on three primary disciplines: modern differential geometry, control of dynamical systems, and optimization theory Includes applications to the fields of quantum and molecular computing, control of physical processes, biophysics, superconducting magnetism, and physical information science