Download or read book B zier and B Spline Techniques written by Hartmut Prautzsch and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a solid and uniform derivation of the various properties Bezier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer Aided Geometric Design and provides a clear and illustrative presentation of the basic principles, as well as a treatment of advanced material including multivariate splines, some subdivision techniques and constructions of free form surfaces with arbitrary smoothness. The text is beautifully illustrated with many excellent figures to emphasize the geometric constructive approach of this book.
Download or read book Bezier and B spline Techniques for Curve and Surface Generation written by Miles McQueen and published by . This book was released on 1983 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation and Modeling with B Splines written by Klaus Hollig and published by SIAM. This book was released on 2015-07-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bezier and B spline Techniques with Matlab written by Niyazi Ari and published by LAP Lambert Academic Publishing. This book was released on 2009-06-18 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to teach students the essential of Bezier and B-spline techniques with the aid of examples. Computer codes, which give an easy interface of Bezier and B-spline techniques to the users, are implemented as Matlab programs. The reason to choose Matlab is that it is easy to use and has a good graphical user interface. This book focuses on curves and surfaces using Bezier and B-spline techniques. It is based on the theory "Bezier and B-spline Techniques" which are known in mathematics. Interpolation and approximation methods have been illustrated intensively. Some of algorithms are represented using practical cases for example Casteljau algorithm. Students and researchers can use this book to succeed good understanding of Bezier and B-spline techniques for reliable and efficient studies in accordance within scientific applications.
Download or read book A Blossoming Development of Splines written by Stephen Mann and published by Morgan & Claypool Publishers. This book was released on 2006 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this lecture, author Stephen Mann presents Bezier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems. They are used to design aircraft and automobiles, as well as having uses in modeling packages used by the computer animation industry. Bezier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface.The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allow us to analyze their properties geometrically. Blossoming is used to explore both Bezier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.
Download or read book An Introduction to Splines for Use in Computer Graphics and Geometric Modeling written by Richard H. Bartels and published by Morgan Kaufmann. This book was released on 1987 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes on the Principles and Applications of B spline Curves and Surfaces written by Xinxiong Zhu and published by . This book was released on 1982 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods Of Shape preserving Spline Approximation written by Boris I Kvasov and published by World Scientific. This book was released on 2000-07-24 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces.Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.
Download or read book Knot Insertion and Deletion Algorithms for B Spline Curves and Surfaces written by Ronald N. Goldman and published by SIAM. This book was released on 1993-01-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: New approaches to knot insertion and deletion are presented in this unique, detailed approach to understanding, analyzing, and rendering B-spline curves and surfaces. Computer scientists, mechanical engineers, and programmers and analysts involved in CAD and CAGD will find innovative, practical applications using the blossoming approach to knot insertion, factored knot insertion, and knot deletion, as well as comparisons of many knot insertion algorithms. This book also serves as an excellent reference guide for graduate students involved in computer aided geometric design.
Download or read book Handbook on Splines for the User written by Eugene V. Shikin and published by CRC Press. This book was released on 1995-07-14 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Splines find ever increasing application in the numerical methods, computer-aided design, and computer graphics areas. The Handbook on Splines for the User not only provides an excellent introduction to basic concepts and methods but also includes the SplineGuide-a computer diskette that allows the reader to practice using important programs.These programs help the user to build interpolating and smoothing cubic and bicubic splines of all classes. Programs are described in Fortran for spline functions and C for geometric splines. The Handbook describes spline functions and geometric splines and provides simple, but effective algorithms. It covers virtually all of the important types of cubic and bicubic splines, functions, variables, curves, and surfaces. The book is written in a straightforward manner and requires little mathematical background. When necessary, the authors give theoretical treatments in an easy-to-use form. Through the Handbook on Splines for the User, introduce yourself to the exciting world of splines and learn to use them in practical applications and computer graphics.
Download or read book The NURBS Book written by Les Piegl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'U'R-BS 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.
Download or read book A Study of Splines written by Esmaail Mehvari Nikjeh and published by . This book was released on 1992 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Curves and Surfaces for Computer aided Geometric Design written by Gerald E. Farin and published by . This book was released on 1997 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer disk contains: "data sets, as well as all of the C routines found in the book."
Download or read book Application of Spline Interpolation Methods to Engineering Problems written by James B. Cheek and published by . This book was released on 1971 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper was prepared to familiarize practicing scientists and engineers with the cubic spline interpolation technique as a possible tool in curve fitting for computer programs for which more commonly used techniques may be unsuitable or of limited value. The spline technique is compared with more common methods, specifically piecewise linear and polynomial, and examples of applications of the technique to engineering problems are presented.
Download or read book Finite Element Methods with B splines written by Klaus Hollig and published by SIAM. This book was released on 2003-01-01 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Improved Model of Bezier B Spline Curves and Surfaces written by Haiyan Huan and published by . This book was released on 1998 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
