Nurbs For Curve Surface Design
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| Author | : Gerald Farin |
| Publisher | : A K Peters, Ltd. |
| Total Pages | : 294 |
| Release | : 1999-03-02 |
| Genre | : Computers |
| ISBN | : 9781568810843 |
Non-Uniform Rational B-Splines have become the de facto standard in CAD/CAM and computer graphics. This well-known book covers NURBS from their geometric beginnings to their industrial applications. The second edition incorporates new results and a chapter on Pythagorean curves, a development that shows promise in applications such as NC machining or robot motion control. Includes more than fifty new figures.
| Author | : Les Piegl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 650 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3642592236 |
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.
| Author | : Gerald Farin |
| Publisher | : CRC Press |
| Total Pages | : 284 |
| Release | : 1999-03-02 |
| Genre | : Computers |
| ISBN | : 1439863903 |
Non-Uniform Rational B-Splines have become the de facto standard in CAD/CAM and computer graphics. This well-known book covers NURBS from their geometric beginnings to their industrial applications. The second edition incorporates new results and a chapter on Pythagorean curves, a development that shows promise in applications such as NC machining
| Author | : David F. Rogers |
| Publisher | : Morgan Kaufmann |
| Total Pages | : 344 |
| Release | : 2001 |
| Genre | : Computers |
| ISBN | : 1558606696 |
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.
| Author | : Gerald E. Farin |
| Publisher | : A K Peters/CRC Press |
| Total Pages | : 256 |
| Release | : 1995 |
| Genre | : Computers |
| ISBN | : |
NURBS (Non-uniform rational B-splines) have become a de facto standard for geometric definition in CAD/CAM and computer graphics. This book covers NURBS from their geometric beginnings to their industrial applications. The text begins with an introduction to projective geometry for which only an elementary background in linear algebra is necessary. Conics are then treated in terms of projective geometry as well as rational quadratic NURBS. A similar treatment is given to the general case of NURBS curves and surfaces. Each chapter concludes with a set of problems.
| Author | : Gerald E. Farin |
| Publisher | : Morgan Kaufmann |
| Total Pages | : 522 |
| Release | : 2002 |
| Genre | : Computers |
| ISBN | : 1558607374 |
Preface -- Chapter 1 P. B̌ezier: How a Simple System Was Born -- Chapter 2 Introductory Material -- Chapter 3 Linear Interpolation -- Chapter 4 The de Casteljau Algorithm -- Chapter 5 The Bernstein Form of a B̌ezier Curve -- Chapter 6 B̌ezier Curve Topics -- Chapter 7 Polynomial Curve Constructions -- Chapter 8 B-Spline Curves -- Chapter 9 Constructing Spline Curves -- Chapter 10 W. Boehm: Differential Geometry I -- Chapter 11 Geometric Continuity -- Chapter 12 ConicSections -- Chapter 13 Rational B̌ezier and B-Spline Curves -- Chapter 14 Tensor Product Patches -- Chapter 15 Constructing Polynomial Patches -- Chapter 16 Composite Surfaces -- Chapter 17 B̌ezier Triangles -- Chapter 18 Practical Aspects of B̌ezier Triangles -- Chapter 19 W. Boehm: Differential Geometry II -- Chapter 20 GeometricContinuityforSurfaces -- Chapter 21 Surfaces with Arbitrary Topology -- Chapter 22 Coons Patches -- Chapter 23 Shape -- Chapter 24 Evaluation of Some Methods -- Appendix A Quick Reference of Curve ...
| Author | : David Salomon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 466 |
| Release | : 2007-03-20 |
| Genre | : Computers |
| ISBN | : 0387284524 |
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.
| Author | : Alyn Rockwood |
| Publisher | : Morgan Kaufmann |
| Total Pages | : 232 |
| Release | : 1996-08 |
| Genre | : Computers |
| ISBN | : 9781558604056 |
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.
| Author | : Nickolas S. Sapidis |
| Publisher | : SIAM |
| Total Pages | : 330 |
| Release | : 1994-01-01 |
| Genre | : Computers |
| ISBN | : 9781611971521 |
This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design. The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. Aesthetic aspects of geometric modeling are of vital importance in industrial design and modeling, particularly in the automobile and aerospace industries. Any engineer working in computer-aided design, computer-aided manufacturing, or computer-aided engineering will want to add this volume to his or her library. Researchers who have a familiarity with basic techniques in computer-aided graphic design and some knowledge of differential geometry will find this book a helpful reference. It is essential reading for statisticians working on approximation or smoothing of data with mathematical curves or surfaces.
| Author | : Nicholas M. Patrikalakis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 428 |
| Release | : 2002-02-14 |
| Genre | : Computers |
| ISBN | : 9783540424543 |
Shape interrogation is the process of extraction of information from a geometric model. It is a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. The authors focus on shape interrogation of geometric models bounded by free-form surfaces. Free-form surfaces, also called sculptured surfaces, are widely used in the bodies of ships, automobiles and aircraft, which have both functionality and attractive shape requirements. Many electronic devices as well as consumer products are designed with aesthetic shapes, which involve free-form surfaces. This book provides the mathematical fundamentals as well as algorithms for various shape interrogation methods including nonlinear polynomial solvers, intersection problems, differential geometry of intersection curves, distance functions, curve and surface interrogation, umbilics and lines of curvature, geodesics, and offset curves and surfaces. This book will be of interest both to graduate students and professionals.
