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| a practical guide to splines: A Practical Guide to Splines Carl De Boor, 1978 This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines. The B-spline theory is developed directly from the recurrence relations without recourse to divided differences. This reprint includes redrawn figures, and most formal statements are accompanied by proofs. |
| a practical guide to splines: A Practical Guide to Splines Carl De Boor, 1978-01-01 |
| a practical guide to splines: A Practical Guide to Splines Carl de Boor, 2001-12-13 This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines. The B-spline theory is developed directly from the recurrence relations without recourse to divided differences. This reprint includes redrawn figures, and most formal statements are accompanied by proofs. |
| a practical guide to splines: A Practical Guide to Splines Carl de Boor, 2001-12-01 This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines. The B-spline theory is developed directly from the recurrence relations without recourse to divided differences. This reprint includes redrawn figures, and most formal statements are accompanied by proofs. |
| a practical guide to splines: Practical Smoothing Paul H.C. Eilers, Brian D. Marx, 2021-03-18 This user guide presents a popular smoothing tool with practical applications in machine learning, engineering, and statistics. |
| a practical guide to splines: The NURBS Book Les Piegl, Wayne Tiller, 2012-12-06 Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS are now also being used for modeling scenes for virtual reality applications. These applications are expected to increase. Consequently, it is quite appropriate for The.N'URBS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my pro fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graph ics textbook to contain material on B-splines. That material was obtained through the good graces of Bill Gordon and Louie Knapp while they were at Syracuse University. A paper of mine, presented during the Summer of 1977 at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design. For many, B-splines, rational B-splines, and NURBS have been a bit mysterious. |
| a practical guide to splines: Curves and Surfaces for CAGD Gerald E. Farin, 2002 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 ... |
| a practical guide to splines: Box Splines Carl de Boor, Klaus Höllig, Sherman Riemenschneider, 2013-03-09 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. |
| a practical guide to splines: An Introduction to Splines for Use in Computer Graphics and Geometric Modeling Richard H. Bartels, John C. Beatty, Brian A. Barsky, 1995-09 As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities. |
| a practical guide to splines: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev, 2015-08-27 This book presents various contributions of splines to signal and image processing from a unified perspective that is based on the Zak transform (ZT). It expands the methodology from periodic splines, which were presented in the first volume, to non-periodic splines. Together, these books provide a universal toolbox accompanied by MATLAB software for manipulating polynomial and discrete splines, spline-based wavelets, wavelet packets and wavelet frames for signal/ image processing applications. In this volume, we see that the ZT provides an integral representation of discrete and polynomial splines, which, to some extent, is similar to Fourier integral. The authors explore elements of spline theory and design, and consider different types of polynomial and discrete splines. They describe applications of spline-based wavelets to data compression. These splines are useful for real-time signal processing and, in particular, real-time wavelet and frame transforms. Further topics addressed in this volume include: global splines, such as interpolating, self-dual and smoothing, whose supports are infinite; the compactly supported quasi-interpolating and smoothing splines including quasi-interpolating splines on non-uniform grids; and cubic Hermite splines as a source for the design of multiwavelets and multiwavelet frames. Readers from various disciplines including engineering, computer science and mathematical information technology will find the descriptions of algorithms, applications and software in this book especially useful. |
| a practical guide to splines: Finite Element Methods with B-splines Klaus Hollig, 2003-01-01 Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples. |
| a practical guide to splines: Modern Regression Techniques Using R Daniel B Wright, Kamala London, 2009-02-19 Statistics is the language of modern empirical social and behavioural science and the varieties of regression form the basis of this language. Statistical and computing advances have led to new and exciting regressions that have become the necessary tools for any researcher in these fields. In a way that is refreshingly engaging and readable, Wright and London describe the most useful of these techniques and provide step-by-step instructions, using the freeware R, to analyze datasets that can be located on the books′ webpage: www.sagepub.co.uk/wrightandlondon. Techniques covered in this book include multilevel modeling, ANOVA and ANCOVA, path analysis, mediation and moderation, logistic regression (generalized linear models), generalized additive models, and robust methods. These are all tested out using a range of real research examples conducted by the authors in every chapter. Given the wide coverage of techniques, this book will be essential reading for any advanced undergraduate and graduate student (particularly in psychology) and for more experienced researchers wanting to learn how to apply some of the more recent statistical techniques to their datasets. The Authors are donating all royalties from the book to the American Partnership for Eosinophilic Disorders. |
| a practical guide to splines: Approximation and Modeling with B-Splines Klaus Hollig, Jorg Horner, 2015-07-01 B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos. |
| a practical guide to splines: The Theory of Splines and Their Applications J. H. Ahlberg, E. N. Nilson, J. L. Walsh, 2016-06-03 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. |
| a practical guide to splines: Differential Models of Hysteresis Augusto Visintin, 2013-06-29 Hysteresis effects occur in science and engineering: plasticity, ferromagnetism, ferroelectricity are well-known examples. This volume provides a self-contained and comprehensive introduction to the analysis of hysteresis models, and illustrates several new results in this field. |
| a practical guide to splines: Handbook of Splines Gheorghe Micula, Sanda Micula, 2012-12-06 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. |
| a practical guide to splines: An Introduction to the Advanced Theory and Practice of Nonparametric Econometrics Jeffrey S. Racine, 2019-06-27 Interest in nonparametric methodology has grown considerably over the past few decades, stemming in part from vast improvements in computer hardware and the availability of new software that allows practitioners to take full advantage of these numerically intensive methods. This book is written for advanced undergraduate students, intermediate graduate students, and faculty, and provides a complete teaching and learning course at a more accessible level of theoretical rigor than Racine's earlier book co-authored with Qi Li, Nonparametric Econometrics: Theory and Practice (2007). The open source R platform for statistical computing and graphics is used throughout in conjunction with the R package np. Recent developments in reproducible research is emphasized throughout with appendices devoted to helping the reader get up to speed with R, R Markdown, TeX and Git. |
| a practical guide to splines: Splines And Compartment Models: An Introduction Karl-ernst Erich Biebler, Michael Wodny, 2013-07-23 This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given.In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics. |
| a practical guide to splines: Generalized Additive Models Simon Wood, 2006-02-27 Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for this, there has been a long-standing need for an accessible introductory treatment of the subject that also emphasizes recent penalized regression spline approaches to GAMs and the mixed model extensions of these models. Generalized Additive Models: An Introduction with R imparts a thorough understanding of the theory and practical applications of GAMs and related advanced models, enabling informed use of these very flexible tools. The author bases his approach on a framework of penalized regression splines, and builds a well-grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of the freely available R software helps explain the theory and illustrates the practicalities of linear, generalized linear, and generalized additive models, as well as their mixed effect extensions. The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix. Concise, comprehensive, and essentially self-contained, Generalized Additive Models: An Introduction with R prepares readers with the practical skills and the theoretical background needed to use and understand GAMs and to move on to other GAM-related methods and models, such as SS-ANOVA, P-splines, backfitting and Bayesian approaches to smoothing and additive modelling. |
| a practical guide to splines: An Introduction to Wavelets Charles K. Chui, 2016-06-03 Wavelet Analysis and its Applications, Volume 1: An Introduction to Wavelets provides an introductory treatise on wavelet analysis with an emphasis on spline-wavelets and time-frequency analysis. This book is divided into seven chapters. Chapter 1 presents a brief overview of the subject, including classification of wavelets, integral wavelet transform for time-frequency analysis, multi-resolution analysis highlighting the important properties of splines, and wavelet algorithms for decomposition and reconstruction of functions. The preliminary material on Fourier analysis and signal theory is covered in Chapters 2 and 3. Chapter 4 covers the introductory study of cardinal splines, while Chapter 5 describes a general approach to the analysis and construction of scaling functions and wavelets. Spline-wavelets are deliberated in Chapter 6. The last chapter is devoted to an investigation of orthogonal wavelets and wavelet packets. This volume serves as a textbook for an introductory one-semester course on wavelet analysis for upper-division undergraduate or beginning graduate mathematics and engineering students. |
| a practical guide to splines: Curve and Surface Fitting with Splines Paul Dierckx, 1995 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. |
| a practical guide to splines: Theory and Practice of Geometric Modeling Wolfgang Straßer, Hans-Peter Seidel, 2012-12-06 This book is a result of the lectures and discussions during the conference Theory and Practice of Geometric Modeling. The event has been organized by the Wilhelm-Schickard-Institut fiir Informatik, Universitat Tiibingen and took place at the Heinrich-Fabri-Institut in Blaubeuren from October 3 to 7, 1988. The conference brought together leading experts from academic and industrial research institutions, CAD system developers and experien ced users to exchange their ideas and to discuss new concepts and future directions in geometric modeling. The main intention has been to bridge the gap between theoretical results, performance of existing CAD systems and the real problems of users. The contents is structured in five parts: A Algorithmic Aspects B Surface Intersection, Blending, Ray Tracing C Geometric Tools D Different Representation Schemes in Solid Modeling E Product Modeling in High Level Specifications The material presented in this book reflects the current state of the art in geometric modeling and should therefore be of interest not only to university and industry researchers, but also to system developers and practitioners who wish to keep up to date on recent advances and new concepts in this rapidly expanding field. The editors express their sincere appreciation to the contributing authors, and to the members of the program committee, W. Boehm, J. Hoschek, A. Massabo, H. Nowacki, M. Pratt, J. Rossignac, T. Sederberg and W. Tiller, for their close cooperation and their time and effort that made the conference and this book a success. |
| a practical guide to splines: Insight Through Computer Graphics - Proceedings Of The Computer Graphics International 1994 (Cg194) Michael Gigante, Tosiyasu L Kunii, 1997-01-03 Computer graphics has been advancing to the level of creating completely new worlds inside computers. Through such computer graphics worlds, we human beings now have far improved insight into wide varieties of real worlds starting from fairly simple but exact worlds of curves and surfaces and reaching to complex human worlds. This volume presents a quite concrete and advanced methods, techniques, modeling and mathematical backgrounds which are indispensable in order to carry out end researches to increase insight through computer graphics. |
| a practical guide to splines: Modern developments in multivariate approximation Werner Haussmann, 2003-10-24 This volume contains a selection of eighteen peer-reviewed articles that were presented at the 5th International Conference on Multivariate Approximation, held in Witten-Bommerholz in September 2002. The contributions cover recent developments of constructive approximation on manifolds, approximation by splines and kernels, subdivision techniques and wavelet methods. The main topics are: - applications of multivariate approximation in finance - approximation and stable reconstruction of images, data reduction - multivariate splines for Lagrange interpolation and quasi-interpolation - radial basis functions - spherical point sets - refinable function vectors and non-stationary subdivision - applications of adaptive wavelet methods - blending functions and cubature formulae - singularities of harmonic functions The book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computer science and geophysics. |
| a practical guide to splines: Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes Michel Bercovier, Tanya Matskewich, 2017-10-03 Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM). The recent explosion of IgA, strongly tying Computer Aided Geometry Design to Analysis, does not easily apply to the rich variety of complex shapes that engineers have to design and analyse. Therefore new developments have studied the extension of IgA to unstructured unions of meshes, similar to those one can find in FEM. The following problem arises: given an unstructured planar quadrilateral mesh, construct a C1-surface, by piecewise Bézier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bézier patches, the corresponding results for B-Splines then being simple consequences. The method can be extended to higher-order quadrilaterals and even to three dimensions, and the most recent developments in this direction are also mentioned here. |
| a practical guide to splines: Spline Models for Observational Data Grace Wahba, 1990-01-01 This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. The estimate is a polynomial smoothing spline. By placing this smoothing problem in the setting of reproducing kernel Hilbert spaces, a theory is developed which includes univariate smoothing splines, thin plate splines in d dimensions, splines on the sphere, additive splines, and interaction splines in a single framework. A straightforward generalization allows the theory to encompass the very important area of (Tikhonov) regularization methods for ill-posed inverse problems. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a wide variety of problems which fall within this framework. Methods for including side conditions and other prior information in solving ill-posed inverse problems are included. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals. |
| a practical guide to splines: Smoothing Spline ANOVA Models Chong Gu, 2013-03-09 Smoothing methods are an active area of research. In this book, the author presents a comprehensive treatment of penalty smoothing under a unified framework. Methods are developed for (i) regression with Gaussian and non-Gaussian responses as well as with censored life time data; (ii) density and conditional density estimation under a variety of sampling schemes; and (iii) hazard rate estimation with censored life time data and covariates. Extensive discussions are devoted to model construction, smoothing parameter selection, computation, and asymptotic convergence. Most of the computational and data analytical tools discussed in the book are implemented in R, an open-source clone of the popular S/S- PLUS language. |
| a practical guide to splines: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev, 2018-06-19 This book provides a practical guide, complete with accompanying Matlab software, to many different types of polynomial and discrete splines and spline-based wavelets, multiwavelets and wavelet frames in signal and image processing applications. In self-contained form, it briefly outlines a broad range of polynomial and discrete splines with equidistant nodes and their signal-processing-relevant properties. In particular, interpolating, smoothing, and shift-orthogonal splines are presented. |
| a practical guide to splines: Advances in Geometric Modeling and Processing Bernard Mourrain, Scott Schaefer, Guoliang Xu, 2010-06-09 This volume contains the papers presented at 6th Conference on Geometric Modeling and Processing (GMP 2010) held in Castro Urdiales, Spain during June16–18,2010. GeometricModelingandProcessingisabiannualinternational conference series on geometric modeling, simulation and computing. Previously, GMPhasbeenheldinHongKong(2000),Saitama,Japan(2002),Beijing,China (2004), Pittsburgh, USA (2006) and Hangzhou, China (2008). GMP 2010 received a total of 30 submissions that were reviewed by three to four Program Committee members on average. While the number of subm- sions dropped signi?cantly from previous years, the quality did not and was still quite high overall. Based on the reviews received, the committee decided to - cept 20 papers for inclusion in the proceedings. Additionally, extended versions of selected papers were considered for a special issue of Computer-Aided - sign (CAD) and Computer-Aided Geometric Design (CAGD). The paper topics spanned a wide variety and include: – Solutions of transcendental equations – Volume parameterization – Smooth curves and surfaces – Isogeometric analysis – Implicit surfaces – Computational geometry Many people helped make this conference happen and we are grateful for their help. We would especially like to thank the Conference Chair, all of the authors who submitted papers, the ProgramCommittee members who reviewed the papers and all of the participants at the conference. |
| a practical guide to splines: Handbook of Item Response Theory Modeling Steven P. Reise, Dennis A. Revicki, 2014-11-20 Item response theory (IRT) has moved beyond the confines of educational measurement into assessment domains such as personality, psychopathology, and patient-reported outcomes. Classic and emerging IRT methods and applications that are revolutionizing psychological measurement, particularly for health assessments used to demonstrate treatment effectiveness, are reviewed in this new volume. World renowned contributors present the latest research and methodologies about these models along with their applications and related challenges. Examples using real data, some from NIH-PROMIS, show how to apply these models in actual research situations. Chapters review fundamental issues of IRT, modern estimation methods, testing assumptions, evaluating fit, item banking, scoring in multidimensional models, and advanced IRT methods. New multidimensional models are provided along with suggestions for deciding among the family of IRT models available. Each chapter provides an introduction, describes state-of-the art research methods, demonstrates an application, and provides a summary. The book addresses the most critical IRT conceptual and statistical issues confronting researchers and advanced students in psychology, education, and medicine today. Although the chapters highlight health outcomes data the issues addressed are relevant to any content domain. The book addresses: IRT models applied to non-educational data especially patient reported outcomes Differences between cognitive and non-cognitive constructs and the challenges these bring to modeling. The application of multidimensional IRT models designed to capture typical performance data. Cutting-edge methods for deriving a single latent dimension from multidimensional data A new model designed for the measurement of constructs that are defined on one end of a continuum such as substance abuse Scoring individuals under different multidimensional IRT models and item banking for patient-reported health outcomes How to evaluate measurement invariance, diagnose problems with response categories, and assess growth and change. Part 1 reviews fundamental topics such as assumption testing, parameter estimation, and the assessment of model and person fit. New, emerging, and classic IRT models including modeling multidimensional data and the use of new IRT models in typical performance measurement contexts are examined in Part 2. Part 3 reviews the major applications of IRT models such as scoring, item banking for patient-reported health outcomes, evaluating measurement invariance, linking scales to a common metric, and measuring growth and change. The book concludes with a look at future IRT applications in health outcomes measurement. The book summarizes the latest advances and critiques foundational topics such a multidimensionality, assessment of fit, handling non-normality, as well as applied topics such as differential item functioning and multidimensional linking. Intended for researchers, advanced students, and practitioners in psychology, education, and medicine interested in applying IRT methods, this book also serves as a text in advanced graduate courses on IRT or measurement. Familiarity with factor analysis, latent variables, IRT, and basic measurement theory is assumed. |
| a practical guide to splines: Articulated Motion and Deformable Objects Francisco J. Perales, Robert B. Fisher, 2008-07-06 This book constitutes the refereed proceedings of the 5th International Conference on Articulated Motion and Deformable Objects, AMDO 2008, held in Port d'Andratx, Mallorca, Spain, in July 2008. The 36 revised full papers and 7 poster papers presented were carefully reviewed and selected from 64 submissions. The papers are organized in topical section on computer graphics: human modelling and animation, human motion: analysis, tracking, 3D reconstruction and recognition, multimodal user interaction: VR and ar, speech, biometrics, and advanced multimedia systems: standards, indexed video contents. |
| a practical guide to splines: Image Technology Jorge L.C. Sanz, 1996-02-22 §vImage processing and machine vision are fields of renewed interest in the commercial market. People in industry, managers, and technical engineers are looking for new technologies to move into the market. Many of the most promising developments are taking place in the field of image processing and its applications. The book offers a broad coverage of advances in a range of topics in image processing and machine vision. |
| a practical guide to splines: Proceedings of the 7th International Conference on Construction, Architecture and Technosphere Safety Andrey A. Radionov, |
| a practical guide to splines: Control Theoretic Splines Magnus Egerstedt, Clyde Martin, 2009-12-07 Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data. |
| a practical guide to splines: An Introduction to Numerical Methods and Analysis James F. Epperson, 2013-06-06 Praise for the First Edition . . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises. —Zentrablatt Math . . . carefully structured with many detailed worked examples . . . —The Mathematical Gazette . . . an up-to-date and user-friendly account . . . —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis. |
| a practical guide to splines: Geometric Modeling with Splines Elaine Cohen, Richard F. Riesenfeld, Gershon Elber, 2001-07-18 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. |
| a practical guide to splines: Fundamentals of Computer Graphics Steve Marschner, Peter Shirley, 2018-10-24 Drawing on an impressive roster of experts in the field, Fundamentals of Computer Graphics, Fourth Edition offers an ideal resource for computer course curricula as well as a user-friendly personal or professional reference. Focusing on geometric intuition, the book gives the necessary information for understanding how images get onto the screen by using the complementary approaches of ray tracing and rasterization. It covers topics common to an introductory course, such as sampling theory, texture mapping, spatial data structure, and splines. It also includes a number of contributed chapters from authors known for their expertise and clear way of explaining concepts. Highlights of the Fourth Edition Include: Updated coverage of existing topics Major updates and improvements to several chapters, including texture mapping, graphics hardware, signal processing, and data structures A text now printed entirely in four-color to enhance illustrative figures of concepts The fourth edition of Fundamentals of Computer Graphics continues to provide an outstanding and comprehensive introduction to basic computer graphic technology and theory. It retains an informal and intuitive style while improving precision, consistency, and completeness of material, allowing aspiring and experienced graphics programmers to better understand and apply foundational principles to the development of efficient code in creating film, game, or web designs. Key Features Provides a thorough treatment of basic and advanced topics in current graphics algorithms Explains core principles intuitively, with numerous examples and pseudo-code Gives updated coverage of the graphics pipeline, signal processing, texture mapping, graphics hardware, reflection models, and curves and surfaces Uses color images to give more illustrative power to concepts |
| a practical guide to splines: An Introduction to Numerical Analysis Endre Süli, David F. Mayers, 2003-08-28 An introduction to numerical analysis combining rigour with practical applications, and providing numerous exercises plus solutions. |
| a practical guide to splines: Computational Modelling of Objects Represented in Images. Fundamentals, Methods and Applications João Manuel R.S. Tavares, Jorge R.M. Natal, 2018-05-08 This book contains keynote lectures and full papers presented at the International Symposium on Computational Modelling of Objects Represented in Images (CompIMAGE), held in Coimbra, Portugal, on 20-21 October 2006. International contributions from nineteen countries provide a comprehensive coverage of the current state-of-the-art in the fields of: - Image Processing and Analysis; - Image Segmentation; - Data Interpolation; - Registration, Acquisition and Compression; - 3D Reconstruction; - Objects Tracking; - Motion and Deformation Analysis; - Objects Simulation; - Medical Imaging; - Computational Bioimaging and Visualization. Related techniques also covered in this book include the finite element method, modal analyses, stochastic methods, principal and independent components analyses and distribution models. Computational Modelling of Objects Represented in Images will be useful to academics, researchers and professionals in Computational Vision (image processing and analysis), Computer Sciences, and Computational Mechanics. |
| a practical guide to splines: Computational Geometry Su Bu-qing, Liu Ding-yuan, 2014-05-10 Computational Geometry: Curve and Surface Modeling provides information pertinent to the fundamental aspects of computational geometry. This book discusses the geometric properties of parametric polynomial curves by using the theory of affine invariants for algebraic curves. Organized into eight chapters, this book begins with an overview of the objects studies in computational geometry, namely surfaces and curves. This text then explores the developments in the theory and application of spline functions, which began with cubic spline functions. Other chapters consider the mechanical background of the cubic spline functions, which is the wooden spline with small deflection. This book discusses as well that in mathematical lofting the information of a geometric shape is given by a set of data points, while in geometric design other ways of representations are available. The final chapter deals with the concepts in the theory of algebraic curves. This book is a valuable resource for mathematicians. |
A Practical Guide to Splines - ResearchGate
Carl de Boor. A Practical Guide to Splines. Revised Edition. With 32 figures. Springer. Contents. Preface. Notation. I • Polynomial Interpolation.
A Practical Guide To Splines (PDF) - armchairempire.com
Bézier curves, B-splines, and NURBS, highlighting their individual strengths and limitations. The guide will provide a step-by-step breakdown of spline construction and manipulation techniques. Moving beyond the theoretical framework, we will explore the practical applications of splines in various domains. We will showcase how splines are ...
A Practical Guide To Splines
A Practical Guide to Splines Carl de Boor,2001-12-13 This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as …
A Practical Guide To Splines
Enter the realm of "A Practical Guide To Splines," a mesmerizing literary masterpiece penned with a distinguished author, guiding readers on a profound journey to unravel the secrets and potential hidden within every word.
A Practical Guide To Splines - archive.norml.org
Practical Smoothing Paul H.C. Eilers,Brian D. Marx,2021-03-18 This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties.
A Practical Guide To Splines - shackleton.pansandcompany.com
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.
A Practical Guide to Splines - dandelon.com
Practical Guide to Splines. Springer-Verlag New York Heidelberg Berlin. Table of Contents. Chapter I. Polynomial Interpolation Lagrange form Divided differences and Newton form Definition 1: The k-th divided difference Oscillatory interpolation Definition 2: Agreement of f and g at T Divided difference table Page. 4. 7.
A Practical Guide To Splines - survey.moorlandassociation.org
Practical Smoothing Paul H.C. Eilers,Brian D. Marx,2021-03-18 This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties.
A Practical Guide To Splines (2024)
This guide aims to provide a comprehensive understanding of splines, their applications, and their practical implementation. We will delve into the theoretical foundation of splines, exploring different types, their properties, and their advantages.
A Practical Guide To Splines - data.visitlincscoast.co.uk
A Practical Guide to Splines Carl De Boor,1978 This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines.
A Practical Guide To Splines - unap.edu.pe
A "Practical Guide to Splines" begins with a clear understanding of what splines are. In essence, splines are piecewise polynomial functions used to approximate complex curves or surfaces. Unlike simple polynomial interpolation which can suffer from oscillations (especially with high-degree polynomials and widely spaced data points), splines ...
AN INTRODUCTION TO SPLINE THEORY - Universitetet i Oslo
For the theory of B-splines, we refer the reader to the book by de Boor [2] and the lecture notes by Lyche and K. M˝rken used in earlier versions of the Spline Methods course.
Chapter One - Princeton University
The goal of this book is to show that smoothing splines arise as a natural part of control theory, and that, by using control theoretic concepts, we can construct and interpret smoothing splines in an efficient, algorithmic manner.
A Practical Guide To Splines - li.ijcaonline.org
A practical guide to splines - SciSpace by Typeset WEBThis book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. A Practical Guide To Splines Copy ...
A practical guide to splines - SciSpace by Typeset
This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines.
Math 321 Lecture 3 Cubic Splines. - University of Wollongong
Approximation of functions by spline functions was popularised by Carl De Boor: A Practical Guide to Splines, Springer 1978. They are used in one and more dimensions to generate functions with desirable smoothness properties. On each interval (xi, xi+1), S(x) is a cubic.
A Practical Guide To Splines - cdn2.mhpbooks.com
A Practical Guide to Splines Carl de Boor,2001-12-13 This book is based on the author s experience with calculations involving polynomial splines presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B splines The B spline theory is developed
A Practical Guide To Splines - cpv2.pressidium.com
practical guide to splines (download only) WEBChapter One - Princeton University WEBThe goal of this book is to show that smoothing splines arise as a natural part of control theory, and that, by using control theoretic concepts, we can construct and interpret smoothing splines in ...
A Practical Guide to Splines - ResearchGate
Carl de Boor. A Practical Guide to Splines. Revised Edition. With 32 figures. Springer. Contents. Preface. Notation. I • Polynomial Interpolation.
A Practical Guide To Splines (PDF) - armchairempire.com
Bézier curves, B-splines, and NURBS, highlighting their individual strengths and limitations. The guide will provide a step-by-step breakdown of spline construction and …
A Practical Guide To Splines
A Practical Guide to Splines Carl de Boor,2001-12-13 This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts …
A Practical Guide To Splines
Enter the realm of "A Practical Guide To Splines," a mesmerizing literary masterpiece penned with a distinguished author, guiding readers on a profound journey to unravel the …
A Practical Guide To Splines - archive.norml.org
Practical Smoothing Paul H.C. Eilers,Brian D. Marx,2021-03-18 This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine …
