Curve and Surface Fitting with Splines
Curve and Surface Fitting with Splines

Author: Paul Dierckx

Publisher: Oxford University Press

Published: 1995

Total Pages: 308

ISBN-13: 9780198534402

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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
Curve and Surface Fitting

Author: Peter Lancaster

Publisher:

Published: 1986

Total Pages: 296

ISBN-13:

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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.

Numerical Computing with MATLAB
Numerical Computing with MATLAB

Author: Cleve B. Moler

Publisher: SIAM

Published: 2010-08-12

Total Pages: 340

ISBN-13: 0898716608

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A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software.

Applied Numerical Methods Using MATLAB
Applied Numerical Methods Using MATLAB

Author: Won Y. Yang

Publisher: John Wiley & Sons

Published: 2005-05-20

Total Pages: 526

ISBN-13: 0471705187

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In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Over the years, many textbooks have been written on the subject of numerical methods. Based on their course experience, the authors use a more practical approach and link every method to real engineering and/or science problems. The main benefit is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems. An Instructor's Manual presenting detailed solutions to all the problems in the book is available online.

Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

Author: Rida T Farouki

Publisher: Springer Science & Business Media

Published: 2007-10-11

Total Pages: 725

ISBN-13: 3540733973

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By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.

An Introduction to Numerical Methods
An Introduction to Numerical Methods

Author: Abdelwahab Kharab

Publisher: CRC Press

Published: 2018-09-05

Total Pages: 447

ISBN-13: 1351605917

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Previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Fourth Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes a new chapter on Dynamical Systems and Chaos. Features Covers the most common numerical methods encountered in science and engineering Illustrates the methods using MATLAB Presents numerous examples and exercises, with selected answers at the back of the book

Fundamentals of Graphics Using MATLAB
Fundamentals of Graphics Using MATLAB

Author: Ranjan Parekh

Publisher: CRC Press

Published: 2019-11-26

Total Pages: 427

ISBN-13: 042959173X

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This book introduces fundamental concepts and principles of 2D and 3D graphics and is written for undergraduate and postgraduate students of computer science, graphics, multimedia, and data science. It demonstrates the use of MATLAB® programming for solving problems related to graphics and discusses a variety of visualization tools to generate graphs and plots. The book covers important concepts like transformation, projection, surface generation, parametric representation, curve fitting, interpolation, vector representation, and texture mapping, all of which can be used in a wide variety of educational and research fields. Theoretical concepts are illustrated using a large number of practical examples and programming codes, which can be used to visualize and verify the results. Key Features: Covers fundamental concepts and principles of 2D and 3D graphics Demonstrates the use of MATLAB® programming for solving problems on graphics Provides MATLAB® codes as answers to specific numerical problems Provides codes in a simple copy and execute format for the novice learner Focuses on learning through visual representation with extensive use of graphs and plots Helps the reader gain in-depth knowledge about the subject matter through practical examples Contains review questions and practice problems with answers for self-evaluation

A Practical Guide to Splines
A Practical Guide to Splines

Author: Carl de Boor

Publisher: Springer

Published: 2001-12-01

Total Pages: 348

ISBN-13: 0387953663

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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.

The NURBS Book
The NURBS Book

Author: Les Piegl

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 650

ISBN-13: 3642592236

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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.