Bézier and B-Spline Techniques

Bézier and B-Spline Techniques PDF

Author: Hartmut Prautzsch

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 299

ISBN-13: 3662049198

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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.

Approximation and Modeling with B-Splines

Approximation and Modeling with B-Splines PDF

Author: Klaus Hollig

Publisher: SIAM

Published: 2015-07-01

Total Pages: 228

ISBN-13: 1611972949

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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.

Computer Aided Geometric Design

Computer Aided Geometric Design PDF

Author: Robert E. Barnhill

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 337

ISBN-13: 1483268489

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Computer Aided Geometric Design covers the proceedings of the First International Conference on Computer Aided Geometric Design, held at the University of Utah on March 18-21, 1974. This book is composed of 15 chapters and starts with reviews of the properties of surface patch equation and the use of computers in geometrical design. The next chapters deal with the principles of smooth interpolation over triangles and without twist constraints, as well as the graphical representation of surfaces over triangles and rectangles. These topics are followed by discussions of the B-spline curves and surfaces; mathematical and practical possibilities of UNISURF; nonlinear splines; and some piecewise polynomial alternatives to splines under tension. Other chapters explore the smooth parametric surfaces, the space curve as a folded edge, and the interactive computer graphics application of the parametric bi-cubic surface to engineering design problems. The final chapters look into the three-dimensional human-machine communication and a class of local interpolating splines. This book will prove useful to design engineers.

An Introduction to Splines for Use in Computer Graphics and Geometric Modeling

An Introduction to Splines for Use in Computer Graphics and Geometric Modeling PDF

Author: Richard H. Bartels

Publisher: Morgan Kaufmann

Published: 1995-09

Total Pages: 504

ISBN-13: 9781558604001

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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.

An Introduction to NURBS

An Introduction to NURBS PDF

Author: David F. Rogers

Publisher: Morgan Kaufmann

Published: 2001

Total Pages: 344

ISBN-13: 1558606696

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NURBS (Non-uniform Rational B-Splines) are the computer graphics industry standard for curve and surface description. They are now incorporated into all standard computer-aided design and drafting programs (for instance, Autocad). They are also extensively used in all aspects of computer graphics including much of the modeling used for special effects in film and animation, consumer products, robot control, and automobile and aircraft design. So, the topic is particularly important at this time because NURBS are really at the peak of interest as applied to computer graphics and CAD of all kind.

Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces

Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces PDF

Author: Ronald N. Goldman

Publisher: SIAM

Published: 1993-01-01

Total Pages: 204

ISBN-13: 1611971586

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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.

The NURBS Book

The NURBS Book PDF

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.

Curves and Surfaces for Computer Graphics

Curves and Surfaces for Computer Graphics PDF

Author: David Salomon

Publisher: Springer Science & Business Media

Published: 2007-03-20

Total Pages: 466

ISBN-13: 0387284524

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Requires only a basic knowledge of mathematics and is geared toward the general educated specialists. Includes a gallery of color images and Mathematica code listings.

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