Methods of Shape-preserving Spline Approximation PDF Download

Author: Boris I. Kvasov
Publisher: World Scientific
ISBN: 9789810240103
Category : Mathematics
Languages : en
Pages : 360

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Book Description
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.

Author: Sorin G. Gal
Publisher: Springer Science & Business Media
ISBN: 0817647031
Category : Mathematics
Languages : en
Pages : 359

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Book Description
First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables Of interest to grad students and researchers in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineering Contains many open problems to spur future research Rich and updated bibliography

Author: National Physical Laboratory (Great Britain). Division of Information Technology & Computing
Publisher:
ISBN:
Category :
Languages : en
Pages : 14

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Book Description

Author: A Ramirez
Publisher:
ISBN: 9781082263231
Category :
Languages : en
Pages : 242

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Book Description
The Curve Fitting Toolbox software supports these nonparametric fitting methods: -"Interpolation Methods" - Estimate values that lie between known data points.-"Smoothing Splines" - Create a smooth curve through the data. You adjust the level of smoothness by varying a parameter that changes the curve from a least-squares straight-line approximation to a cubic spline interpolant.-"Lowess Smoothing" - Create a smooth surface through the data using locally weighted linear regression to smooth data.Interpolation is a process for estimating values that lie between known data points. There are several interpolation methods: - Linear: Linear interpolation. This method fit a different linear polynomial between each pair of data points for curves, or between sets of three points for surfaces.- Nearest neighbor: Nearest neighbor interpolation. This method sets the value of an interpolated point to the value of the nearest data point. Therefore, this method does not generate any new data points.- Cubic spline: Cubic spline interpolation. This method fit a different cubic polynomial between each pair of data points for curves, or between sets of three points for surfaces.After fitting data with one or more models, you should evaluate the goodness of fit A visual examination of the fitte curve displayed in Curve Fitting app should be your firs step. Beyond that, the toolbox provides these methods to assess goodness of fi for both linear and nonlinear parametric fits-"Goodness-of-Fit Statistics" -"Residual Analysis" -"Confidence and Prediction Bounds" The Curve Fitting Toolbox spline functions are a collection of tools for creating, viewing, and analyzing spline approximations of data. Splines are smooth piecewise polynomials that can be used to represent functions over large intervals, where it would be impractical to use a single approximating polynomial. The spline functionality includes a graphical user interface (GUI) that provides easy access to functions for creating, visualizing, and manipulating splines. The toolbox also contains functions that enable you to evaluate, plot, combine, differentiate and integrate splines. Because all toolbox functions are implemented in the open MATLAB language, you can inspect the algorithms, modify the source code, and create your own custom functions. Key spline features: -GUIs that let you create, view, and manipulate splines and manage and compare spline approximations-Functions for advanced spline operations, including differentiation integration, break/knot manipulation, and optimal knot placement-Support for piecewise polynomial form (ppform) and basis form (B-form) splines-Support for tensor-product splines and rational splines (including NURBS)- Shape-preserving: Piecewise cubic Hermite interpolation (PCHIP). This method preserves monotonicity and the shape of the data. For curves only.- Biharmonic (v4): MATLAB 4 grid data method. For surfaces only.- Thin-plate spline: Thin-plate spline interpolation. This method fit smooth surfaces that also extrapolate well. For surfaces only.If your data is noisy, you might want to fit it using a smoothing spline. Alternatively, you can use one of the smoothing methods. The smoothing spline s is constructed for the specified smoothing parameter p and the specified weights wi.

Author: Paul Dierckx
Publisher: Oxford University Press
ISBN: 9780198534402
Category : Computers
Languages : en
Pages : 308

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Book Description
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.

Author: Charles K. Chui
Publisher: SIAM
ISBN: 0898712262
Category : Mathematics
Languages : en
Pages : 192

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Book Description
Subject of multivariate splines presented from an elementary point of view; includes many open problems.

Author: National Physical Laboratory (Great Britain). Division of Information Technology and Computing
Publisher:
ISBN:
Category :
Languages : en
Pages : 14

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Book Description

Author: Eugene V. Shikin
Publisher: CRC Press
ISBN: 9780849394041
Category : Mathematics
Languages : en
Pages : 238

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Book Description
Splines find ever increasing application in the numerical methods, computer-aided design, and computer graphics areas. The Handbook on Splines for the User not only provides an excellent introduction to basic concepts and methods but also includes the SplineGuide-a computer diskette that allows the reader to practice using important programs.These programs help the user to build interpolating and smoothing cubic and bicubic splines of all classes. Programs are described in Fortran for spline functions and C for geometric splines. The Handbook describes spline functions and geometric splines and provides simple, but effective algorithms. It covers virtually all of the important types of cubic and bicubic splines, functions, variables, curves, and surfaces. The book is written in a straightforward manner and requires little mathematical background. When necessary, the authors give theoretical treatments in an easy-to-use form. Through the Handbook on Splines for the User, introduce yourself to the exciting world of splines and learn to use them in practical applications and computer graphics.

Author: Frans Kuijt
Publisher:
ISBN:
Category :
Languages : en
Pages : 21

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Author: J. H. Ahlberg
Publisher: Elsevier
ISBN: 1483222950
Category : Mathematics
Languages : en
Pages : 297

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Book Description
The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.