The Sensitivity of Spline Functions on Triangulations to Vertex Perturbation PDF Download
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Author: David Assaf
Publisher:
ISBN:
Category : Perturbation (Mathematics)
Languages : en
Pages : 144
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Book Description
Author: David Assaf
Publisher:
ISBN:
Category : Perturbation (Mathematics)
Languages : en
Pages : 144
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Book Description
Author: Ming-Jun Lai
Publisher: Cambridge University Press
ISBN: 0521875927
Category : Mathematics
Languages : en
Pages : 28
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Book Description
Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Author: Larry L. Schumaker
Publisher: SIAM
ISBN: 1611973902
Category : Science
Languages : en
Pages : 420
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Book Description
This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.
Author: American Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 584
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Book Description
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 700
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Book Description
Author: Hideyuki Azegami
Publisher: Springer Nature
ISBN: 9811576181
Category : Mathematics
Languages : en
Pages : 646
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Book Description
This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.
Author: Franco P. Preparata
Publisher: Springer Science & Business Media
ISBN: 1461210984
Category : Mathematics
Languages : en
Pages : 413
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Book Description
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
Author: Steven M. LaValle
Publisher: Cambridge University Press
ISBN: 9780521862059
Category : Computers
Languages : en
Pages : 844
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Book Description
Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. Written for computer scientists and engineers with interests in artificial intelligence, robotics, or control theory, this is the only book on this topic that tightly integrates a vast body of literature from several fields into a coherent source for teaching and reference in a wide variety of applications. Difficult mathematical material is explained through hundreds of examples and illustrations.
Author: Nicholas M. Patrikalakis
Publisher: Springer Science & Business Media
ISBN: 9783540424543
Category : Computers
Languages : en
Pages : 428
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Book Description
Shape interrogation is the process of extraction of information from a geometric model. It is a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. The authors focus on shape interrogation of geometric models bounded by free-form surfaces. Free-form surfaces, also called sculptured surfaces, are widely used in the bodies of ships, automobiles and aircraft, which have both functionality and attractive shape requirements. Many electronic devices as well as consumer products are designed with aesthetic shapes, which involve free-form surfaces. This book provides the mathematical fundamentals as well as algorithms for various shape interrogation methods including nonlinear polynomial solvers, intersection problems, differential geometry of intersection curves, distance functions, curve and surface interrogation, umbilics and lines of curvature, geodesics, and offset curves and surfaces. This book will be of interest both to graduate students and professionals.
Author: David Salomon
Publisher: Springer Science & Business Media
ISBN: 0387284524
Category : Computers
Languages : en
Pages : 466
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Book Description
Requires only a basic knowledge of mathematics and is geared toward the general educated specialists. Includes a gallery of color images and Mathematica code listings.
