Methods of Shape-preserving Spline Approximation
Title | Methods of Shape-preserving Spline Approximation PDF eBook |
Author | Boris I. Kvasov |
Publisher | World Scientific |
Pages | 360 |
Release | 2000 |
Genre | Mathematics |
ISBN | 9789810240103 |
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.
Shape-Preserving Approximation by Real and Complex Polynomials
Title | Shape-Preserving Approximation by Real and Complex Polynomials PDF eBook |
Author | Sorin G. Gal |
Publisher | Springer Science & Business Media |
Pages | 359 |
Release | 2010-06-09 |
Genre | Mathematics |
ISBN | 0817647031 |
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
Shape-preserving Spline Approximation in the I[subscript]-norm
Title | Shape-preserving Spline Approximation in the I[subscript]-norm PDF eBook |
Author | National Physical Laboratory (Great Britain). Division of Information Technology & Computing |
Publisher | |
Pages | 14 |
Release | 1985 |
Genre | |
ISBN |
CURVE and SURFACE FITTING with MATLAB. INTERPOLATION, SMOOTHING and SPLINE FITTING
Title | CURVE and SURFACE FITTING with MATLAB. INTERPOLATION, SMOOTHING and SPLINE FITTING PDF eBook |
Author | A Ramirez |
Publisher | |
Pages | 242 |
Release | 2019-07-24 |
Genre | |
ISBN | 9781082263231 |
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.
A Linear Approach to Shape Preserving Spline Approximation
Title | A Linear Approach to Shape Preserving Spline Approximation PDF eBook |
Author | Frans Kuijt |
Publisher | |
Pages | 21 |
Release | 1998 |
Genre | |
ISBN |
Curve and Surface Fitting with Splines
Title | Curve and Surface Fitting with Splines PDF eBook |
Author | Paul Dierckx |
Publisher | Oxford University Press |
Pages | 308 |
Release | 1995 |
Genre | Computers |
ISBN | 9780198534402 |
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.
Shape - Preserving Spline Approximation in the Γ1 - Norm
Title | Shape - Preserving Spline Approximation in the Γ1 - Norm PDF eBook |
Author | National Physical Laboratory (Great Britain). Division of Information Technology and Computing |
Publisher | |
Pages | 14 |
Release | 1985 |
Genre | |
ISBN |