This book covers Curve Modeling with solutions to real life problems relating to Computer Graphics, Vision, Image Processing, Geometric Modeling and CAD/CAM. Chapters deal with basic concepts, curve design techniques and their use to various applications and a wide range of problems with their automated solutions through computers. The book provides an invaluable resource which focuses on interdisciplinary methods and affiliates up-to-date methodologies. It aims to stimulate provide a source where the reader can find the latest developments in the field including a variety of techniques, applications, and systems necessary for solving real life problems.
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
The growing importance of animation and 3D design has caused computer-aided geometric design (CAGD) to be of interest to a wide audience of programmers and designers. This interactive software/book tutorial teaches fundamental CAGD concepts and discusses the growing number of applications in such areas as geological modeling, molecular modeling, commercial advertising, and animation. Using interactive examples and animations to illustrate the mathematical concepts, this hands-on multimedia tutorial enables users without a substantial mathematical background to quickly gain intuition about CAGD. Interactive Curves and Surfaces guides you in Learning the uses of CAGD as it is applied in computer graphics and engineering. Creating curved lines and surfaces using Bezier curves, B-Splines, and parametric surface patches. Understanding the mathematical tools behind the generation of these objects, and the development of computer-based CAGD algorithms. Experimenting with powerful interactive test benches to explore the behavior and characteristics of the most popular CAGD curves. Application oriented readers will find this animated tutorial presentation more accessible than the standard formal texts on the subject.
Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.
"Latent Growth Curve Modeling introduces students to a strategy for modeling change over time. This volume offers a unique chance to study this useful research method with easy-to-follow examples of common growth modeling approaches. It addresses ways to fit a variety of advanced statistical models to repeated-measures data, to model change over time, and to assess individual differences in change." "This graduate-level volume is a resource for individual researchers or courses covering longitudinal data analysis, structural equation modeling, developmental methodology, and multivariate techniques."--BOOK JACKET.
In the two decades since the development of the first eclipsing-binary modeling code, new analytic techniques and the availability of powerful, sometimes dedicated computing facilities have made possible vastly improved determinations of fundamental and even transient stellar parameters. The scale of these developments, of course, raises questions about modeling tools, techniques, and philosophies, such as: Who will maintain and upgrade the codes? Will the codes be open to improvement by outsiders, and if so, how? And, indeed, what should be the goals of a modeling program? Such questions had not been aired for a long time and, for this reason alone, deserved to be discussed in as general a forum as the community provides. This volume contains material presented by Commission 42 (Close Binary Stars) during the International Astronomical Union's XXI General Assembly in Argentina, July 1991, and during IAU Colloquium 151, Cordoba, Argentina, August 1991. The techniques discussed include simulations of stellar bright and dark spots, streams, partial and complete stellar disks, prominences, and other features characterizing active stars; modeling of polarization parameters; models that use radial velocities as well as line profile simulations to model velocity field variation across stellar disks; the weighted effects of brightness asymmetries; and models for translucent eclipsing agents such as stellar winds.
Sketching is a natural and intuitive communication tool used for expressing concepts and ideas that are difficult to communicate through text or speech alone. In design applications, drawings are used at various stages of the design process: from the early concept drawings scribbled on a piece of paper to immersive interactions in which users manipulate and adjust the 3D form of an object in virtual or augmented reality environments. This variety in drawing activities brings about the need for different interpretation strategies that support not only the sketching activity itself, but also allow sketch-based interactions, such as sketch-based queries, to take place. In this book, we explore the different drawing approaches used in design and the algorithms required for processing and interpreting the different sketches and drawings in design. The book is divided into two parts. The first part focuses on sketching in the 2D domain. This includes the digitization of offline and paperbased sketches, techniques for online sketch recognition, observations of user drawing habits, algorithms for inferring depth from 2D drawings, as well as non-photorealistic rendering techniques that are then applied to sketch-based queries. The second part of the book focuses on 3D sketching in virtual or augmented reality spaces. Here, we present the processing and rendering of the 3D strokes, the different interaction devices available for 3D sketching, and look at different applications where immersive 3D sketching has been applied with success.
This book provides a comprehensive introduction to latent variable growth curve modeling (LGM) for analyzing repeated measures. It presents the statistical basis for LGM and its various methodological extensions, including a number of practical examples of its use. It is designed to take advantage of the reader’s familiarity with analysis of variance and structural equation modeling (SEM) in introducing LGM techniques. Sample data, syntax, input and output, are provided for EQS, Amos, LISREL, and Mplus on the book’s CD. Throughout the book, the authors present a variety of LGM techniques that are useful for many different research designs, and numerous figures provide helpful diagrams of the examples. Updated throughout, the second edition features three new chapters—growth modeling with ordered categorical variables, growth mixture modeling, and pooled interrupted time series LGM approaches. Following a new organization, the book now covers the development of the LGM, followed by chapters on multiple-group issues (analyzing growth in multiple populations, accelerated designs, and multi-level longitudinal approaches), and then special topics such as missing data models, LGM power and Monte Carlo estimation, and latent growth interaction models. The model specifications previously included in the appendices are now available on the CD so the reader can more easily adapt the models to their own research. This practical guide is ideal for a wide range of social and behavioral researchers interested in the measurement of change over time, including social, developmental, organizational, educational, consumer, personality and clinical psychologists, sociologists, and quantitative methodologists, as well as for a text on latent variable growth curve modeling or as a supplement for a course on multivariate statistics. A prerequisite of graduate level statistics is recommended.
To find a mathematical model which describes (fits) data from a process which is fundamentally nonlinear, one usually uses nonlinear least-squares techniques on maxicomputers. These usually run in batch mode with the user supplying a model and initial ''guesstimates'' of its parameters. However, fitting the model to the data can be considered an art because computer algorithms either converge to true solutions, or converge to erroneous solutions, or fail to converge, depending on the quality of the guesstimates. It is slow and expensive to try enough runs to obtain a logical solution (unless one makes lucky initial guesses). An interactive BASIC procedure was developed which runs on either the PDP-11/34 under RT-11 or the PDP-11/70 under IAS. These programs help the investigator quickly fit the model to the data and statistically evaluate the differences between the two. The parameter estimates thus determined may then be used as guesstimates for the more precise maxicomputer codes. The key to the system is the re-enterant nature of the curve fitting routine (allowed only with a language such as INTERPRETED BASIC). The user supplies estimates of the parameters for the selected model (18 are currently available, and users can easily write their own). The computer tries a few iterative refinements (by using Taylor series expansion of partial derivatives to obtain linearization) of the estimates in an attempt to minimize the deviations between the values predicted by the model and the observed data. The user can observe as the program executes whether the result is a logical solution. If not, he may stop the process, enter new guesstimates, and examine those results, try again, or select a new model.
