Download or read book Shape preserving Spline Approximation in the L1 norm written by Maurice G. Cox and published by . This book was released on 1985 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods of Shape preserving Spline Approximation written by Boris I. Kvasov and published by World Scientific. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces. Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.
Download or read book Shape preserving Spline Approximation in the I subscript norm written by National Physical Laboratory (Great Britain). Division of Information Technology & Computing and published by . This book was released on 1985 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Shape Preserving Spline Approximation in the 1 Norm written by National Physical Laboratory (Great Britain). Division of Information Technology and Computing and published by . This book was released on 1985 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Shape preserving Spline Approximation in the Lambdasub 1 norm written by M. G. Cox and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Curve and Surface Fitting with Splines written by Paul Dierckx and published by Oxford University Press. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.
Download or read book Theory and Algorithms for Shape preserving Bivariate Cubic L1 Splines written by Yong Wang and published by . This book was released on 2005 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: spline function, tensor-product, cubic L1 spline, interpolation, geometric programming, primal-dual method.
Download or read book A Linear Approach to Shape Preserving Spline Approximation written by Frans Kuijt and published by . This book was released on 1998 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2013-08-19 with total page 863 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds and Lie Groups, Deformations in Shape Spaces, Differential Geometry in Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I and II, Computational Aspects of Information Geometry in Statistics, Optimization on Matrix Manifolds, Optimal Transport Theory, Probability on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, Tensor-Valued Mathematical Morphology, Machine/Manifold/Topology Learning, Geometry of Audio Processing, Geometry of Inverse Problems, Algebraic/Infinite dimensional/Banach Information Manifolds, Information Geometry Manifolds, and Algorithms on Manifolds.
Download or read book Curves and Surfaces written by Jean-Daniel Boissonnat and published by Springer Science & Business Media. This book was released on 2012-01-07 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Curves and Surfaces, held in Avignon, in June 2010. The conference had the overall theme: "Representation and Approximation of Curves and Surfaces and Applications". The 39 revised full papers presented together with 9 invited talks were carefully reviewed and selected from 114 talks presented at the conference. The topics addressed by the papers range from mathematical foundations to practical implementation on modern graphics processing units and address a wide area of topics such as computer-aided geometric design, computer graphics and visualisation, computational geometry and topology, geometry processing, image and signal processing, interpolation and smoothing, scattered data processing and learning theory and subdivision, wavelets and multi-resolution methods.
Download or read book Algorithms for Approximation written by J.C. Mason and published by Chapman and Hall/CRC. This book was released on 1990-05-15 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the proceedings of the second Shrivenham conference on Algorithms for Approximation. The term 'approximation' here refers to 'the approximation of functions and data by similar functions', and leads to such topics as curve and surface fitting, spline and piecewise polynomial methods, finite element modelling, and computer-aided design. Applications are given to a wide variety of areas such as surveying, meteorology, radar antenna and acoustic array design, topography, engineering metrology, and CAD/CAM. Emphasis at the meeting was placed on the development of useful algorithms, and on practical applications in defence and industry. In addition, some 40 submitted papers were selected and presented on a multitude of topics such as multivariate interpolation, optimization methods, constrained problems, spline fitting, data modelling, and applications in microwave measurement, isotropic antennas, sound measurement, and digitized contours.
Download or read book Theory and Algorithms for Cubic L1 Splines written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In modern geometric modeling, one of the requirements for interpolants is that they 'preserve shape well.' Shape preservation has often been associated with preservation of monotonicity and convexity/concavity. While shape preservation cannot yet be defined quantitatively, it is generally agreed that shape preservation involves eliminating extraneous non-physical oscillation. Classical splines, which exhibit extraneous oscillation, do not 'preserve shape well.' Recently, Lavery introduced a new class of cubic L1 splines. Empirical experiment has shown that cubic L1 splines are cable of providing C1-smooth, shape-preserving, multi-scale interpolation of arbitrary data, including data with abrupt changes in spacing and magnitude, with no need for monotonicity or convexity constraints, node adjustment or other user input. However, the shape-preserving capability of cubic L1 splines has not been proved theoretically. The currently available algorithm only provides an approximation to the coefficients of cubic L1 splines. To lay the groundwork for theoretical analysis and the development of an exact algorithm, this dissertation proposes to treat cubic L1 spline problems in a geometric programming framework. Such a framework leads to a geometric dual problem with a linear objective function and convex quadratic constraints. It also provides a linear system for dual-to-primal conversion. We prove that cubic L1 splines preserve shape well, in particular, in eliminating non-physical oscillations, without review of raw data or any human intervention. We also show that cubic L1 splines perform well for multi-scale data, as well as preserve linearity and convexity/concavity under mild conditions. An exact algorithm based on the geometric programming model is proposed for solving cubic L1 splines. It decomposes the geometric programming problem into several independent small-sized sub-problems and applies a specialized active set algorithm to solve the sub-problems. The alg.
Download or read book Constructive Approximation written by Ronald A. DeVore and published by Springer Science & Business Media. This book was released on 1993-11-04 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators. Other topics include Weierstrauss and best approximation theorems, properties of polynomials and splines. It contains history and proofs with an emphasis on principal results.
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 Bicubic L1 Spline Fits for 3D Data Approximation written by Muhammad Adib Uz Zaman and published by . This book was released on 2018 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Univariate cubic L1 spline fits have been successful to preserve the shapes of 2D data with abrupt changes. The reason is that the minimization of L1 norm of the data is considered, as opposite to L2 norm. While univariate L1 spline fits for 2D data are discussed by many, bivariate L1 spline fits for 3D data are yet to be fully explored. This thesis aims to develop bicubic L1 spline fits for 3D data approximation. This can be achieved by solving a bi-level optimization problem. One level is bivariate cubic spline interpolation and the other level is L1 error minimization. In the first level, a bicubic interpolated spline surface will be constructed on a rectangular grid with necessary first and second order derivative values estimated by using a 5-point window algorithm for univariate L1 interpolation. In the second level, the absolute error (i.e. L1 norm) will be minimized using an iterative gradient search. This study may be extended to higher dimensional cubic L1 spline fits research.
Download or read book Trends in Approximation Theory written by Kirill Kopotun and published by . This book was released on 2001 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a carefully edited selection of papers that were presented at the Symposium on Trends in Approximation Theory, held in May 2000, and at the Oslo Conference on Mathematical Methods for Curves and Surfaces, held in July 2000. Mathematical Methods for Curves and Surfaces covers topics from abstract approximation to wavelets.
Download or read book A One pass Algorithm for Shape preserving Quadratic Spline Interpolation written by R. Iqbal and published by . This book was released on 1990 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
