Fitting Splines To A Parametric Function

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Fitting Splines to a Parametric Function

Author : Alvin Penner
Publisher : Springer
ISBN 13 : 3030125513
Total Pages : 79 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fitting Splines to a Parametric Function by : Alvin Penner

Download or read book Fitting Splines to a Parametric Function written by Alvin Penner and published by Springer. This book was released on 2019-02-23 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Brief investigates the intersections that occur between three different areas of study that normally would not touch each other: ODF, spline theory, and topology. The Least Squares Orthogonal Distance Fitting (ODF) method has become the standard technique used to develop mathematical models of the physical shapes of objects, due to the fact that it produces a fitted result that is invariant with respect to the size and orientation of the object. It is normally used to produce a single optimum fit to a specific object; this work focuses instead on the issue of whether the fit responds continuously as the shape of the object changes. The theory of splines develops user-friendly ways of manipulating six different splines to fit the shape of a simple family of epiTrochoid curves: two types of Bézier curve, two uniform B-splines, and two Beta-splines. This work will focus on issues that arise when mathematically optimizing the fit. There are typically multiple solutions to the ODF method, and the number of solutions can often change as the object changes shape, so two topological questions immediately arise: are there rules that can be applied concerning the relative number of local minima and saddle points, and are there different mechanisms available by which solutions can either merge and disappear, or cross over each other and interchange roles. The author proposes some simple rules which can be used to determine if a given set of solutions is internally consistent in the sense that it has the appropriate number of each type of solution.

CURVE and SURFACE FITTING with MATLAB. INTERPOLATION, SMOOTHING and SPLINE FITTING

Author : A Ramirez
Publisher :
ISBN 13 : 9781082263231
Total Pages : 242 pages
Book Rating : 4.2/5 (632 download)

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Book Synopsis CURVE and SURFACE FITTING with MATLAB. INTERPOLATION, SMOOTHING and SPLINE FITTING by : A Ramirez

Download or read book CURVE and SURFACE FITTING with MATLAB. INTERPOLATION, SMOOTHING and SPLINE FITTING written by A Ramirez and published by . This book was released on 2019-07-24 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Curve and Surface Fitting with Splines

Author : Paul Dierckx
Publisher : Oxford University Press
ISBN 13 : 9780198534402
Total Pages : 308 pages
Book Rating : 4.5/5 (344 download)

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Book Synopsis Curve and Surface Fitting with Splines by : Paul Dierckx

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.

Parametric Splines in Tension

Author : Surendra K. Gupta
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.:/5 (226 download)

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Book Synopsis Parametric Splines in Tension by : Surendra K. Gupta

Download or read book Parametric Splines in Tension written by Surendra K. Gupta and published by . This book was released on 1989 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A brief review of curve fitting terminology is presented, and the cubic spline interpolation scheme is outlined. Parametric and non-parametric curve fitting techniques are compared. The technique to fit parametric cubic splines is derived using the Euler- Lagrange formulation. Previous work on splines in tension is identified. Employing the notion of splines in tension, a method is proposed to fit a parametric curve to a set of (n + 1) points in ^-dimension space satisfying a specified set of boundary conditions. The curve fitted will not have any inflection points within any span and will be invariant with respect to coordinate translation and rotation. Using Euler-Lagrange formulation, a system of linear equations in terms of the unknown second derivatives at knots is developed. Three kinds of boundary conditions are investigated. Software is developed in VAX Fortran to fit both parametric splines in tension and parametric cubic splines. Applications where splines in tension may find use are identified. Some examples of such applications are presented and comparison to cubic spline made. Splines in tension offer a better alternative than Fourier transform in describing boundary of shape in digital image processing application. Possible extensions to the numerical scheme developed and related investigations by other workers in this field are also listed."--Abstract.

Curves and Surfaces for CAGD

Author : Gerald E. Farin
Publisher : Morgan Kaufmann
ISBN 13 : 1558607374
Total Pages : 522 pages
Book Rating : 4.5/5 (586 download)

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Book Synopsis Curves and Surfaces for CAGD by : Gerald E. Farin

Download or read book Curves and Surfaces for CAGD written by Gerald E. Farin and published by Morgan Kaufmann. This book was released on 2002 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface -- Chapter 1 P. B̌ezier: How a Simple System Was Born -- Chapter 2 Introductory Material -- Chapter 3 Linear Interpolation -- Chapter 4 The de Casteljau Algorithm -- Chapter 5 The Bernstein Form of a B̌ezier Curve -- Chapter 6 B̌ezier Curve Topics -- Chapter 7 Polynomial Curve Constructions -- Chapter 8 B-Spline Curves -- Chapter 9 Constructing Spline Curves -- Chapter 10 W. Boehm: Differential Geometry I -- Chapter 11 Geometric Continuity -- Chapter 12 ConicSections -- Chapter 13 Rational B̌ezier and B-Spline Curves -- Chapter 14 Tensor Product Patches -- Chapter 15 Constructing Polynomial Patches -- Chapter 16 Composite Surfaces -- Chapter 17 B̌ezier Triangles -- Chapter 18 Practical Aspects of B̌ezier Triangles -- Chapter 19 W. Boehm: Differential Geometry II -- Chapter 20 GeometricContinuityforSurfaces -- Chapter 21 Surfaces with Arbitrary Topology -- Chapter 22 Coons Patches -- Chapter 23 Shape -- Chapter 24 Evaluation of Some Methods -- Appendix A Quick Reference of Curve ...

Comparisons of Wilson-Fowler and Parametric Cubic Splines with the Curve-Fitting Algorithms of Several Computer-Aided Design Systems

Download Comparisons of Wilson-Fowler and Parametric Cubic Splines with the Curve-Fitting Algorithms of Several Computer-Aided Design Systems PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (684 download)

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Book Synopsis Comparisons of Wilson-Fowler and Parametric Cubic Splines with the Curve-Fitting Algorithms of Several Computer-Aided Design Systems by :

Download or read book Comparisons of Wilson-Fowler and Parametric Cubic Splines with the Curve-Fitting Algorithms of Several Computer-Aided Design Systems written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this report is to demonstrate that modern computer-aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) systems can be used in the Department of Energy (DOE) Nuclear Weapons Complex (NWC) to design new and remodel old products, fabricate old and new parts, and reproduce legacy data within the inspection uncertainty limits. In this study, two two-dimensional splines are compared with several modern CAD curve-fitting modeling algorithms. The first curve-fitting algorithm is called the Wilson-Fowler Spline (WFS), and the second is called a parametric cubic spline (PCS). Modern CAD systems usually utilize either parametric cubic and/or B-splines.

The Theory of Splines and Their Applications

Author : J. H. Ahlberg
Publisher : Elsevier
ISBN 13 : 1483222950
Total Pages : 297 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Theory of Splines and Their Applications by : J. H. Ahlberg

Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Curve and Surface Fitting

Author : Peter Lancaster
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Curve and Surface Fitting by : Peter Lancaster

Download or read book Curve and Surface Fitting written by Peter Lancaster and published by . This book was released on 1986 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to reveal the foundations and major features of several basic methods for curve and surface fitting that are currently in use.

Spline Fitting with MATLAB

Author : J. Braselton
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781534838840
Total Pages : 114 pages
Book Rating : 4.8/5 (388 download)

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Book Synopsis Spline Fitting with MATLAB by : J. Braselton

Download or read book Spline Fitting with MATLAB written by J. Braselton and published by Createspace Independent Publishing Platform. This book was released on 2016-06-22 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: You can work with splines in Curve Fitting Toolbox(tm) in several ways.Using the Curve Fitting app or the fit function you can:Fit cubic spline interpolants to curves or surfacesFit smoothing splines and shape-preserving cubic spline interpolants to curves (but not surfaces)Fit thin-plate splines to surfaces (but not curves)The toolbox also contains specific splines functions to allow greater control over what you can create. For example, you can use the csapi function for cubic spline interpolation. Why would you use csapi instead of the fit function 'cubicinterp' option? You might require greater flexibility to work with splines for the following reasons:You want to combine the results with other splines, You want vector-valued splines. You can use csapi with scalars, vectors, matrices, and ND-arrays. The fit function only allows scalar-valued splines.You want other types of splines such as ppform, B-form, tensor-product, rational, and stform thin-plate splines.You want to create splines without data.You want to specify breaks, optimize knot placement, and use specialized functions for spline manipulation such as differentiation and integration.If you require specialized spline functions, see the following sections for interactive and programmatic spline fitting.

Developing Econometrics

Author : Hengqing Tong
Publisher : John Wiley & Sons
ISBN 13 : 0470681772
Total Pages : 489 pages
Book Rating : 4.4/5 (76 download)

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Book Synopsis Developing Econometrics by : Hengqing Tong

Download or read book Developing Econometrics written by Hengqing Tong and published by John Wiley & Sons. This book was released on 2011-12-12 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Theories and Methods with Applications to Economics and Business highlights recent advances in statistical theory and methods that benefit econometric practice. It deals with exploratory data analysis, a prerequisite to statistical modelling and part of data mining. It provides recently developed computational tools useful for data mining, analysing the reasons to do data mining and the best techniques to use in a given situation. Provides a detailed description of computer algorithms. Provides recently developed computational tools useful for data mining Highlights recent advances in statistical theory and methods that benefit econometric practice. Features examples with real life data. Accompanying software featuring DASC (Data Analysis and Statistical Computing). Essential reading for practitioners in any area of econometrics; business analysts involved in economics and management; and Graduate students and researchers in economics and statistics.

Progress in Artificial Intelligence

Author : Nuno Moniz
Publisher : Springer Nature
ISBN 13 : 3031490088
Total Pages : 551 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Progress in Artificial Intelligence by : Nuno Moniz

Download or read book Progress in Artificial Intelligence written by Nuno Moniz and published by Springer Nature. This book was released on 2024-01-15 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNAI 14115 and 14116 constitutes the refereed proceedings of the 22nd EPIA Conference on Progress in Artificial Intelligence, EPIA 2023, held in Faial Island, Azores, in September 2023. The 85 full papers presented in these proceedings were carefully reviewed and selected from 163 submissions. The papers have been organized in the following topical sections: ambient intelligence and affective environments; ethics and responsibility in artificial intelligence; general artificial intelligence; intelligent robotics; knowledge discovery and business intelligence; multi-agent systems: theory and applications; natural language processing, text mining and applications; planning, scheduling and decision-making in AI; social simulation and modelling; artifical intelligence, generation and creativity; artificial intelligence and law; artificial intelligence in power and energy systems; artificial intelligence in medicine; artificial intelligence and IoT in agriculture; artificial intelligence in transportation systems; artificial intelligence in smart computing; artificial intelligence for industry and societies.

Richly Parameterized Linear Models

Author : James S. Hodges
Publisher : CRC Press
ISBN 13 : 1439866848
Total Pages : 464 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Richly Parameterized Linear Models by : James S. Hodges

Download or read book Richly Parameterized Linear Models written by James S. Hodges and published by CRC Press. This book was released on 2016-04-19 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Step toward a Unified Theory of Richly Parameterized Linear ModelsUsing mixed linear models to analyze data often leads to results that are mysterious, inconvenient, or wrong. Further compounding the problem, statisticians lack a cohesive resource to acquire a systematic, theory-based understanding of models with random effects.Richly Param

Longitudinal Data Analysis

Author : Garrett Fitzmaurice
Publisher : CRC Press
ISBN 13 : 142001157X
Total Pages : 633 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Longitudinal Data Analysis by : Garrett Fitzmaurice

Download or read book Longitudinal Data Analysis written by Garrett Fitzmaurice and published by CRC Press. This book was released on 2008-08-11 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory

Multi-State Survival Models for Interval-Censored Data

Author : Ardo van den Hout
Publisher : CRC Press
ISBN 13 : 1315356732
Total Pages : 323 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Multi-State Survival Models for Interval-Censored Data by : Ardo van den Hout

Download or read book Multi-State Survival Models for Interval-Censored Data written by Ardo van den Hout and published by CRC Press. This book was released on 2016-11-25 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-State Survival Models for Interval-Censored Data introduces methods to describe stochastic processes that consist of transitions between states over time. It is targeted at researchers in medical statistics, epidemiology, demography, and social statistics. One of the applications in the book is a three-state process for dementia and survival in the older population. This process is described by an illness-death model with a dementia-free state, a dementia state, and a dead state. Statistical modelling of a multi-state process can investigate potential associations between the risk of moving to the next state and variables such as age, gender, or education. A model can also be used to predict the multi-state process. The methods are for longitudinal data subject to interval censoring. Depending on the definition of a state, it is possible that the time of the transition into a state is not observed exactly. However, when longitudinal data are available the transition time may be known to lie in the time interval defined by two successive observations. Such an interval-censored observation scheme can be taken into account in the statistical inference. Multi-state modelling is an elegant combination of statistical inference and the theory of stochastic processes. Multi-State Survival Models for Interval-Censored Data shows that the statistical modelling is versatile and allows for a wide range of applications.

EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization

Author : H.C. Rodrigues
Publisher : Springer
ISBN 13 : 3319977733
Total Pages : 1486 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization by : H.C. Rodrigues

Download or read book EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization written by H.C. Rodrigues and published by Springer. This book was released on 2018-09-13 with total page 1486 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume focus on the following topics: design optimization and inverse problems, numerical optimization techniques,efficient analysis and reanalysis techniques, sensitivity analysis and industrial applications. The conference EngOpt brings together engineers, applied mathematicians and computer scientists working on research, development and practical application of optimization methods in all engineering disciplines and applied sciences.

Geometric Modeling with Splines

Author : Elaine Cohen
Publisher : CRC Press
ISBN 13 : 1439864209
Total Pages : 638 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Geometric Modeling with Splines by : Elaine Cohen

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

Design & Analysis of Clinical Trials for Economic Evaluation & Reimbursement

Author : Iftekhar Khan
Publisher : CRC Press
ISBN 13 : 1466505486
Total Pages : 332 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Design & Analysis of Clinical Trials for Economic Evaluation & Reimbursement by : Iftekhar Khan

Download or read book Design & Analysis of Clinical Trials for Economic Evaluation & Reimbursement written by Iftekhar Khan and published by CRC Press. This book was released on 2015-11-11 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic evaluation has become an essential component of clinical trial design to show that new treatments and technologies offer value to payers in various healthcare systems. Although many books exist that address the theoretical or practical aspects of cost-effectiveness analysis, this book differentiates itself from the competition by detailing