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Curve and Surface Fitting with Splines by Paul Dierckx Pdf
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.
Curve and Surface Fitting by Peter Lancaster,Kȩstutis Šalkauskas Pdf
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.
Curve and Surface Fitting with MATLAB by J. Braselton Pdf
Curve Fitting Toolbox(tm) provides an app and functions for fitting curves and surfaces to data. The toolbox lets you perform exploratory data analysis, preprocess and post-process data, compare candidate models, and remove outliers. You can conduct regression analysis using the library of linear and nonlinear models provided or specify your own custom equations. The library provides optimized solver parameters and starting conditions to improve the quality of your fits. The toolbox also supports nonparametric modeling techniques, such as splines, interpolation, and smoothing.After creating a fit, you can apply a variety of post-processing methods for plotting, interpolation, and extrapolation; estimating confidence intervals; and calculating integrals and derivatives.Curve Fitting Toolbox(tm) software allows you to work in two different environments:An interactive environment, with the Curve Fitting app and the Spline ToolA programmatic environment that allows you to write object-oriented MATLAB(r) code using curve and surface fitting methods
This collection of ideas and results on topics of curve and surface design is intended for research in the academic environment as well as for practical use in industrial applications. Main emphasis is on minimal energy splines and geometric spline curves, and on techniques beyond tensor product surfaces.
Geometric Continuity of Curves and Surfaces by Przemysław Kiciak Pdf
This book is written for students, CAD system users and software developers who are interested in geometric continuity—a notion needed in everyday practice of Computer-Aided Design and also a hot subject of research. It contains a description of the classical geometric spline curves and a solid theoretical basis for various constructions of smooth surfaces. Textbooks on computer graphics usually cover the most basic and necessary information about spline curves and surfaces in order to explain simple algorithms. In textbooks on geometric design, one can find more details, more algorithms and more theory. This book teaches how various parts of the theory can be gathered together and turned into constructions of smooth curves and smooth surfaces of arbitrary topology. The mathematical background needed to understand this book is similar to what is necessary to read other textbooks on geometric design; most of it is basic linear algebra and analysis. More advanced mathematical material is introduced using elementary explanations. Reading Geometric Continuity of Curves and Surfaces provides an excellent opportunity to recall and exercise necessary mathematical notions and it may be your next step towards better practice and higher understanding of design principles.
Curves and Surfaces by Jean-Daniel Boissonnat,Patrick Chenin,Albert Cohen,Christian Gout,Tom Lyche,Marie-Laurence Mazure,Larry Schumaker Pdf
This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Curves and Surfaces, held in Avignon, in June 2010. The conference had the overall theme: "Representation and Approximation of Curves and Surfaces and Applications". The 39 revised full papers presented together with 9 invited talks were carefully reviewed and selected from 114 talks presented at the conference. The topics addressed by the papers range from mathematical foundations to practical implementation on modern graphics processing units and address a wide area of topics such as computer-aided geometric design, computer graphics and visualisation, computational geometry and topology, geometry processing, image and signal processing, interpolation and smoothing, scattered data processing and learning theory and subdivision, wavelets and multi-resolution methods.
Curve and Surface Fitting With Matlab by J. Braselton Pdf
MATLAB Curve Fitting Toolbox provides graphical tools and command-line functions for fitting curves and surfaces to data. The toolbox lets you perform exploratory data analysis, preprocess and post-process data, compare candidate models, and remove outliers. You can conduct regression analysis using the library of linear and nonlinear models provided or specify your own custom equations. The library provides optimized solver parameters and starting conditions to improve the quality of your fits. The toolbox also supports nonparametric modeling techniques, such as splines, interpolation, and smoothing. After creating a fit, you can apply a variety of post-processing methods for plotting, interpolation, and extrapolation; estimating confidence intervals; and calculating integrals and derivatives. The most important topics in this book are: Interactive Curve and Surface Fitting Introducing the Curve Fitting Tool Fitting a Curve Fitting a Surface Model Types for Curves and Surfaces Interactive Fit Comparison Refining Your Fit Creating Multiple Fits Duplicating a Fit Deleting a Fit Displaying Multiple Fits Simultaneously Using the Statistics in the Table of Fits Generating MATLAB Code and Exporting Fits Interactive Code Generation and Programmatic Fitting Curve Fitting to Census Data Interactive Curve Fitting Workflow Loading Data and Creating Fits Determining the Best Fit Analyzing Your Best Fit in the Workspace Saving Your Work Surface Fitting to Franke Data Programmatic Curve and Surface Fitting Curve and Surface Fitting Objects and Methods Curve Fitting Objects Curve Fitting Methods Surface Fitting Objects and Methods
Fitting Splines to a Parametric Function by Alvin Penner Pdf
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.
Fitting Curves and Sourfaces Using Matlab by Perez C. Pdf
MATLAB Curve Fitting Toolbox lets you perform exploratory data analysis, preprocess and post-process data, compare candidate models, and remove outliers. You can conduct regression analysis using the library of linear and nonlinear models provided or specify your own custom equations. The library provides optimized solver parameters and starting conditions to improve the quality of your fits. The toolbox also supports nonparametric modeling techniques, such as splines, interpolation, and smoothing. After creating a fit, you can apply a variety of post-processing methods for plotting,interpolation, and extrapolation; estimating confidence intervals; and calculating integrals and derivatives.Curve Fitting Toolbox software allows you to work in two different environments:* An interactive environment, with the Curve Fitting app and the Spline Tool* A programmatic environment that allows you to write object-oriented MATLAB code using curve and surface fitting methodsThe more important features of this toolbox ar de next:* Curve Fitting app for curve and surface fitting* Linear and nonlinear regression with custom equations* Library of regression models with optimized starting points and solver parameters* Interpolation methods, including B-splines, thin plate splines, and tensor-productsplines* Smoothing techniques, including smoothing splines, localized regression, Savitzky-Golay filters, and moving averages* Preprocessing routines, including outlier removal and sectioning, scaling, and weighting data* Post-processing routines, including interpolation, extrapolation, confidence intervals, integrals and derivatives This book develops the following topics:* "Interpolation and Smoothing" * "Nonparametric Fitting" * "Interpolation Methods" * "Smoothing Splines" * "Lowess Smoothing" * "Filtering and Smoothing Data"* "Fit Postprocessing" * "Explore and Customize Plots" * "Remove Outliers" * "Select Validation Data" * "Evaluate a Curve Fit" * "Evaluate a Surface Fit"* "Compare Fits Programmatically" * "Evaluating Goodness of Fit"* "Residual Analysis" * "Confidence and Prediction Bounds"* "Differentiating and Integrating a Fit" * "Spline Fitting" * "Curve Fitting Toolbox Splines and MATLAB Splines" * "Cubic Spline Interpolation" * "Fitting Values at N-D Grid with Tensor-Product Splines" * "Postprocessing Splines"* "Types of Splines: ppform and B-form" * "B-Splines and Smoothing Splines"* "Multivariate and Rational Splines" * "Multivariate Tensor Product Splines"* "NURBS and Other Rational Splines" * "Least-Squares Approximation by Natural Cubic Splines" * "Solving A Nonlinear ODE" * "Construction of the Chebyshev Spline" * "Approximation by Tensor Product Splines"
Curve and Surface Fitting Functions with MATLAB by J. Braselton Pdf
This book develops the syntax of functions of Curve Fitting Toolbox(tm). This package provides an app and functions for fitting curves and surfaces to data. The toolbox lets you perform exploratory data analysis, preprocess and post-process data, compare candidate models, and remove outliers. You can conduct regression analysis using the library of linear and nonlinear models provided or specify your own custom equations. The library provides optimized solver parameters and starting conditions to improve the quality of your fits. The toolbox also supports nonparametric modeling techniques, such as splines, interpolation, and smoothing.After creating a fit, you can apply a variety of post-processing methods for plotting, interpolation, and extrapolation; estimating confidence intervals; and calculating integrals and derivatives.
Curve and Surface Fitting Functions With Matlab by J. Braselton Pdf
Curve Fitting Toolbox provides graphical tools and command-line functions for fitting curves and surfaces to data. The toolbox lets you perform exploratory data analysis, preprocess and post-process data, compare candidate models, and remove outliers. You can conduct regression analysis using the library of linear and nonlinear models provided or specify your own custom equations. The library provides optimized solver parameters and starting conditions to improve the quality of your fits. The toolbox also supports nonparametric modeling techniques, such as splines, interpolation, and smoothing. After creating a fit, you can apply a variety of post-processing methods for plotting, interpolation, and extrapolation; estimating confidence intervals; and calculating integrals and derivatives. This book explains through examples all Curve Fitting Toolbox functions
Nature-Inspired Computation in Engineering by Xin-She Yang Pdf
This timely review book summarizes the state-of-the-art developments in nature-inspired optimization algorithms and their applications in engineering. Algorithms and topics include the overview and history of nature-inspired algorithms, discrete firefly algorithm, discrete cuckoo search, plant propagation algorithm, parameter-free bat algorithm, gravitational search, biogeography-based algorithm, differential evolution, particle swarm optimization and others. Applications include vehicle routing, swarming robots, discrete and combinatorial optimization, clustering of wireless sensor networks, cell formation, economic load dispatch, metamodeling, surrogated-assisted cooperative co-evolution, data fitting and reverse engineering as well as other case studies in engineering. This book will be an ideal reference for researchers, lecturers, graduates and engineers who are interested in nature-inspired computation, artificial intelligence and computational intelligence. It can also serve as a reference for relevant courses in computer science, artificial intelligence and machine learning, natural computation, engineering optimization and data mining.
Optimal Surface Fitting of Point Clouds Using Local Refinement by GAEL. SKYTT KERMARREC (VIBEKE. DOKKEN, TOR.),Vibeke Skytt,Tor Dokken Pdf
This open access book provides insights into the novel Locally Refined B-spline (LR B-spline) surface format, which is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behavior and allows the modeling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area, LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The iterative method can be modified to improve the accuracy in particular domains of a point cloud. The use of statistical information criterion can help determining the optimal threshold, the number of iterations to perform as well as some parameters of the underlying mathematical functions (degree of the splines, parameter representation). The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. Also deformation analysis are potential applications of fitting point clouds with LR B-splines.
Curves and Surfaces in Computer Aided Geometric Design by Fujio Yamaguchi Pdf
This book contains various types of mathematical descriptions of curves and surfaces, such as Ferguson, Coons, Spline, Bézier and B-spline curves and surfaces. The materials are classified and arranged in a unified way so that beginners can easily understand the whole spectrum of parametric curves and surfaces. This book will be useful to many researchers, designers, teachers, and students who are working on curves and surfaces. The book can be used as a textbook in computer aided design classes.
