Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

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Author: Rida T Farouki

Publisher: Springer Science & Business Media

ISBN: 3540733981

Category: Mathematics

Page: 728

View: 311

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.

Mathematical Methods for Curves and Surfaces

7th International Conference, MMCS 2008, Tønsberg, Norway, June 26-July 1, 2008, Revised Selected Papers

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Author: Morten Dæhlen,Michael S. Floater,Tom Lyche,Jean-Louis Merrien,Knut Moerken,Larry L. Schumaker

Publisher: Springer

ISBN: 3642116205

Category: Computers

Page: 446

View: 3485

Advances in Geometric Modeling and Processing

6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010, Proceedings

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Author: Bernard Mourrain

Publisher: Springer Science & Business Media

ISBN: 3642134106

Category: Computers

Page: 315

View: 8577

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

Results from the Marie Curie Initial Training Network

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Author: Tor Dokken,Georg Muntingh

Publisher: Springer

ISBN: 3319086359

Category: Mathematics

Page: 323

View: 3148

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

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Author: Abraham Berman

Publisher: Springer Science & Business Media

ISBN: 3642807305

Category: Mathematics

Page: 98

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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

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Author: Weizhang Huang,Robert D. Russell

Publisher: Springer Science & Business Media

ISBN: 1441979166

Category: Mathematics

Page: 434

View: 7253

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.

Matrix-Based Multigrid

Theory and Applications

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Author: Yair Shapira

Publisher: Springer Science & Business Media

ISBN: 0387497641

Category: Mathematics

Page: 318

View: 6802

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.

Subdivision Surfaces

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Author: Jörg Peters,Ulrich Reif

Publisher: Springer Science & Business Media

ISBN: 3540764062

Category: Mathematics

Page: 204

View: 7892

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.

An Atlas of Functions

with Equator, the Atlas Function Calculator

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Author: Keith B. Oldham,Jan Myland,Jerome Spanier

Publisher: Springer Science & Business Media

ISBN: 9780387488073

Category: Mathematics

Page: 748

View: 3779

This book comprehensively covers several hundred functions or function families. In chapters that progress by degree of complexity, it starts with simple, integer-valued functions then moves on to polynomials, Bessel, hypergeometric and hundreds more.

Continuous-Time Markov Decision Processes

Theory and Applications

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Author: Xianping Guo,Onesimo Hernandez-Lerma

Publisher: Springer Science & Business Media

ISBN: 3642025471

Category: Mathematics

Page: 234

View: 549

Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.

Geometry, Algebra and Applications: From Mechanics to Cryptography

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Author: Marco Castrillón López,Luis Hernández Encinas,Pedro Martínez Gadea,Ma Eugenia Rosado María

Publisher: Springer

ISBN: 3319320858

Category: Science

Page: 198

View: 3833

This volume collects contributions written by different experts in honor of Prof. Jaime Muñoz Masqué. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.

Introduction to Process Algebra

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Author: Wan Fokkink

Publisher: Springer Science & Business Media

ISBN: 3662042932

Category: Mathematics

Page: 168

View: 8372

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.

Image and Geometry Processing for 3-D Cinematography

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Author: Rémi Ronfard,Gabriel Taubin

Publisher: Springer Science & Business Media

ISBN: 3642123929

Category: Mathematics

Page: 305

View: 5505

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.

Optimization and Control of Bilinear Systems

Theory, Algorithms, and Applications

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Author: Panos M. Pardalos,Vitaliy A. Yatsenko

Publisher: Springer Science & Business Media

ISBN: 9780387736693

Category: Science

Page: 370

View: 4137

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

A History of Algorithms

From the Pebble to the Microchip

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Author: Jean-Luc Chabert

Publisher: Springer Science & Business Media

ISBN: 3642181929

Category: Mathematics

Page: 524

View: 2848

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.

Handbook of Computer Aided Geometric Design

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Author: Gerald E. Farin,Josef Hoschek,Myung-Soo Kim

Publisher: Elsevier

ISBN: 0444511040

Category: Computers

Page: 820

View: 7326

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.

Convex Analysis and Minimization Algorithms II

Advanced Theory and Bundle Methods

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Author: Jean-Baptiste Hiriart-Urruty,Claude Lemarechal

Publisher: Springer Science & Business Media

ISBN: 366206409X

Category: Business & Economics

Page: 348

View: 9810

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

Continuous-Time Markov Chains and Applications

A Two-Time-Scale Approach

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Author: G. George Yin,Qing Zhang

Publisher: Springer Science & Business Media

ISBN: 1461443466

Category: Mathematics

Page: 430

View: 2041

This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.

Ludwig Boltzmann

The Man Who Trusted Atoms

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Author: Carlo Cercignani

Publisher: OUP Oxford

ISBN: 0191606987

Category: Science

Page: 348

View: 5288

This book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th- to 20th-Century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific upheaval, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved: others are still at the level of likely but unproven conjectures. The main text of this biography is written almost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject.

Rethinking Quaternions

Theory and Computation

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Author: Ron Goldman

Publisher: Morgan & Claypool Publishers

ISBN: 1608454207

Category: Computers

Page: 157

View: 2188

In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover, we show how to avoid distortions due to floating point computations with rotations by using unit quaternions to represent rotations. We also derive the formula for spherical linear interpolation, and we explain how to apply this formula to interpolate between two rotations for key frame animation. Finally, we explain the role of quaternions in low-dimensional Clifford algebras, and we show how to apply the Clifford algebra for R3 to model rotations, reflections, and perspective projections. To help the reader understand the concepts and formulas presented here, we have incorporated many exercises in order to clarify and elaborate some of the key points in the text."--Page 4 of cover.