Download or read book Box Splines written by Carl de Boor and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and other smooth functions of one and several arguments. Since they are locally polynomial, they are easy to evaluate. Since they are smooth, they can be used when smoothness is required, as in the numerical solution of partial differential equations (in the Finite Element method) or the modeling of smooth sur faces (in Computer Aided Geometric Design). Since they are compactly supported, their linear span has the needed flexibility to approximate at all, and the systems to be solved in the construction of approximations are 'banded'. The construction of compactly supported smooth piecewise polynomials becomes ever more difficult as the dimension, s, of their domain G ~ IRs, i. e. , the number of arguments, increases. In the univariate case, there is only one kind of cell in any useful partition, namely, an interval, and its boundary consists of two separated points, across which polynomial pieces would have to be matched as one constructs a smooth piecewise polynomial function. This can be done easily, with the only limitation that the num ber of smoothness conditions across such a breakpoint should not exceed the polynomial degree (since that would force the two joining polynomial pieces to coincide). In particular, on any partition, there are (nontrivial) compactly supported piecewise polynomials of degree ~ k and in C(k-l), of which the univariate B-spline is the most useful example.
Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.
Download or read book Topics in Hyperplane Arrangements Polytopes and Box Splines written by Corrado De Concini and published by Springer Science & Business Media. This book was released on 2010-08-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory. This book, written by two distinguished authors, engages a broad audience by proving the a strong foudation. This book may be used in the classroom setting as well as a reference for researchers.
Download or read book Box Splines written by University of Wisconsin--Madison. Computer Sciences Dept and published by . This book was released on 1986 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Modeling with Splines written by Elaine Cohen and published by CRC Press. This book was released on 2001-07-18 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by researchers who have helped found and shape the field, this book is a definitive introduction to geometric modeling. The authors present all of the necessary techniques for curve and surface representations in computer-aided modeling with a focus on how the techniques are used in design. They achieve a balance between mathematical rigor
Download or read book An Integrated Introduction to Computer Graphics and Geometric Modeling written by Ronald Goldman and published by CRC Press. This book was released on 2009-07-14 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with f
Download or read book B zier and B Spline Techniques written by Hartmut Prautzsch and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a solid and uniform derivation of the various properties Bezier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer Aided Geometric Design and provides a clear and illustrative presentation of the basic principles, as well as a treatment of advanced material including multivariate splines, some subdivision techniques and constructions of free form surfaces with arbitrary smoothness. The text is beautifully illustrated with many excellent figures to emphasize the geometric constructive approach of this book.
Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.
Download or read book Geometric Modeling and Processing GMP 2006 written by Myung-Soo Kim and published by Springer Science & Business Media. This book was released on 2006-07-11 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Geometric Modeling and Processing, GMP 2006, held in Pittsburgh, PA, USA in July 2006. The 36 revised full papers and 21 revised short papers presented were carefully reviewed and selected from a total of 84 submissions. All current issues in the area of geometric modeling and processing are addressed and the impact in such areas as computer graphics, computer vision, machining, robotics, and scientific visualization is shown. The papers are organized in topical sections on shape reconstruction, curves and surfaces, geometric processing, shape deformation, shape description, shape recognition, geometric modeling, subdivision surfaces, and engineering applications.
Download or read book Handbook of Computer Aided Geometric Design written by G. Farin and published by Elsevier. This book was released on 2002-08-13 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 exposureto this subject.
Download or read book Quasi Interpolation written by Martin Buhmann and published by Cambridge University Press. This book was released on 2022-03-03 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relatively easy to formulate for scattered and meshed nodes and for any number of data. This book provides an introduction into the field for graduate students and researchers, outlining all the mathematical background and methods of implementation. The mathematical analysis of quasi-interpolation is given in three directions, namely on the basis (spline spaces, radial basis functions) from which the approximation is taken, on the form and computation of the quasi-interpolants (point evaluations, averages, least squares), and on the mathematical properties (existence, locality, convergence questions, precision). Learn which type of quasi-interpolation to use in different contexts and how to optimise its features to suit applications in physics and engineering.
Download or read book Geometric Modeling written by Hans Hagen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.
Download or read book Geometric Challenges in Isogeometric Analysis written by Carla Manni and published by Springer Nature. This book was released on 2022-08-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects selected contributions presented at the INdAM Workshop "Geometric Challenges in Isogeometric Analysis", held in Rome, Italy on January 27-31, 2020. It gives an overview of the forefront research on splines and their efficient use in isogeometric methods for the discretization of differential problems over complex and trimmed geometries. A variety of research topics in this context are covered, including (i) high-quality spline surfaces on complex and trimmed geometries, (ii) construction and analysis of smooth spline spaces on unstructured meshes, (iii) numerical aspects and benchmarking of isogeometric discretizations on unstructured meshes, meshing strategies and software. Given its scope, the book will be of interest to both researchers and graduate students working in the areas of approximation theory, geometric design and numerical simulation. Chapter 10 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Download or read book Multivariate Approximation and Splines written by Günther Nürnberger and published by Birkhäuser. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the refereed papers which were presented at the interna tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996. Fifty experts from Bulgaria, England, France, Israel, Netherlands, Norway, Poland, Switzerland, Ukraine, USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation, data fit ting, interpolation, splines, radial basis functions, neural networks, computer aided design methods, subdivision algorithms and wavelets. The research has applications in areas like industrial production, visualization, pattern recognition, image and signal processing, cognitive systems and modeling in geology, physics, biology and medicine. In the following, we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul the paper of BABENKO, KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV, DISHLIEV and HRISTOVA investigate initial value problems for non linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques, sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.
Download or read book Mathematical Methods in Computer Aided Geometric Design II written by Tom Lyche and published by Academic Press. This book was released on 2014-05-10 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Methods in Computer Aided Geometric Design II covers the proceedings of the 1991 International Conference on Curves, Surfaces, CAGD, and Image Processing, held at Biri, Norway. This book contains 48 chapters that include the topics of blossoming, cyclides, data fitting and interpolation, and finding intersections of curves and surfaces. Considerable chapters explore the geometric continuity, geometrical optics, image and signal processing, and modeling of geological structures. The remaining chapters discuss the principles of multiresolution analysis, NURBS, offsets, radial basis functions, rational splines, robotics, spline and Bézier methods for curve and surface modeling, subdivision, terrain modeling, and wavelets. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.
Download or read book Advances in Visual Computing written by George Bebis and published by Springer. This book was released on 2014-12-02 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volume set LNCS 8887 and 8888 constitutes the refereed proceedings of the 10th International Symposium on Visual Computing, ISVC 2014, held in Las Vegas, NV, USA. The 74 revised full papers and 55 poster papers presented together with 39 special track papers were carefully reviewed and selected from more than 280 submissions. The papers are organized in topical sections: Part I (LNCS 8887) comprises computational bioimaging, computer graphics; motion, tracking, feature extraction and matching, segmentation, visualization, mapping, modeling and surface reconstruction, unmanned autonomous systems, medical imaging, tracking for human activity monitoring, intelligent transportation systems, visual perception and robotic systems. Part II (LNCS 8888) comprises topics such as computational bioimaging , recognition, computer vision, applications, face processing and recognition, virtual reality, and the poster sessions.
Download or read book Number Theory written by Matti Jutila and published by Walter de Gruyter. This book was released on 2014-01-02 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings contain 22 refereed research and survey articles based on lectures given at the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, held in Turku, Finland, from May 31 to June 4, 1999. The subject of the symposium was number theory in a broad sense with an emphasis on recent advances and modern methods. The topics covered in this volume include various questions in elementary number theory, new developments in classical Diophantine problems - in particular of the Fermat and Catalan type, the ABC-conjecture, arithmetic algebraic geometry, elliptic curves, Diophantine approximations, Abelian fields, exponential sums, sieve methods, box splines, the Riemann zeta-function and other Dirichlet series, and the spectral theory of automorphic functions with its arithmetical applications.
