Geometric Continuity Of Curves And Surfaces
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Author |
: Przemysław Kiciak |
Publisher |
: Springer Nature |
Total Pages |
: 233 |
Release |
: 2022-05-31 |
ISBN-10 |
: 9783031025907 |
ISBN-13 |
: 3031025903 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Geometric Continuity of Curves and Surfaces by : Przemysław Kiciak
This book is written for students, CAD system users and software developers who are interested in geometric continuity—a notion needed in everyday practice of Computer-Aided Design and also a hot subject of research. It contains a description of the classical geometric spline curves and a solid theoretical basis for various constructions of smooth surfaces. Textbooks on computer graphics usually cover the most basic and necessary information about spline curves and surfaces in order to explain simple algorithms. In textbooks on geometric design, one can find more details, more algorithms and more theory. This book teaches how various parts of the theory can be gathered together and turned into constructions of smooth curves and smooth surfaces of arbitrary topology. The mathematical background needed to understand this book is similar to what is necessary to read other textbooks on geometric design; most of it is basic linear algebra and analysis. More advanced mathematical material is introduced using elementary explanations. Reading Geometric Continuity of Curves and Surfaces provides an excellent opportunity to recall and exercise necessary mathematical notions and it may be your next step towards better practice and higher understanding of design principles.
Author |
: Jean H. Gallier |
Publisher |
: Morgan Kaufmann |
Total Pages |
: 512 |
Release |
: 2000 |
ISBN-10 |
: 1558605991 |
ISBN-13 |
: 9781558605992 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Curves and Surfaces in Geometric Modeling by : Jean H. Gallier
"Curves and Surfaces in Geometric Modeling: Theory and Algorithms offers a theoretically unifying understanding of polynomial curves and surfaces as well as an effective approach to implementation that you can apply to your own work as a graduate student, scientist, or practitioner." "The focus here is on blossoming - the process of converting a polynomial to its polar form - as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for more than just its theoretical elegance - the author demonstrates the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and other related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more." "It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
Author |
: University of Wisconsin--Madison. Computer Sciences Dept |
Publisher |
: |
Total Pages |
: 24 |
Release |
: 1986 |
ISBN-10 |
: OCLC:17932225 |
ISBN-13 |
: |
Rating |
: 4/5 (25 Downloads) |
Synopsis Geometric Continuity of Spline Curves and Surfaces by : University of Wisconsin--Madison. Computer Sciences Dept
Author |
: Gerald E. Farin |
Publisher |
: Morgan Kaufmann |
Total Pages |
: 522 |
Release |
: 2002 |
ISBN-10 |
: 9781558607378 |
ISBN-13 |
: 1558607374 |
Rating |
: 4/5 (78 Downloads) |
Synopsis Curves and Surfaces for CAGD by : Gerald E. Farin
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 |
: Gerald E. Farin |
Publisher |
: |
Total Pages |
: 460 |
Release |
: 1997 |
ISBN-10 |
: UOM:39015040985619 |
ISBN-13 |
: |
Rating |
: 4/5 (19 Downloads) |
Synopsis Curves and Surfaces for Computer-aided Geometric Design by : Gerald E. Farin
Computer disk contains: "data sets, as well as all of the C routines found in the book."
Author |
: Tony D. DeRose |
Publisher |
: |
Total Pages |
: 11 |
Release |
: 1986 |
ISBN-10 |
: OCLC:227680975 |
ISBN-13 |
: |
Rating |
: 4/5 (75 Downloads) |
Synopsis An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces by : Tony D. DeRose
This report defines the nth order geometric continuity for parametric curves and surfaces, and derived the Beta constraints that are necessary and sufficient for it. Derivation of the Beta constraints is based on a simple principle of reparametrisation in conjunction with the univariate chain rule for curves, and the bivariate chain rule for surfaces. This approach uncovers the connection between geometric continuity for curves and geometric continuity for surfaces, provides new insight into the nature of geometric continuity in general, and allows the determination of the Beta constraints with less effort than previously required. Use of the Beta constraints for G to the nth power continuity allows the introduction of n shape parameters for curves, and n (n +3) shape functions for surfaces. The shape parameters and shape functions may be used to modify the shape of a geometrically continuous curve or surface, respectively. However, geometric continuity is only appropriate for applications where rate aspects of the parametrisations are unimportant since discontinuities in rate are allowed. (Reprints).
Author |
: Nickolas S. Sapidis |
Publisher |
: SIAM |
Total Pages |
: 316 |
Release |
: 1994-01-01 |
ISBN-10 |
: 9780898713329 |
ISBN-13 |
: 0898713323 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Designing Fair Curves and Surfaces by : Nickolas S. Sapidis
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. A valuable resource for engineers working in CAD, CAM, or computer-aided engineering.
Author |
: Pierre-Jean Laurent |
Publisher |
: CRC Press |
Total Pages |
: 490 |
Release |
: 1994-07-15 |
ISBN-10 |
: 9781439863596 |
ISBN-13 |
: 1439863598 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Curves and Surfaces by : Pierre-Jean Laurent
This volume documents the results and presentations, related to aspects of geometric design, of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993. The papers represent directions for future research and development in many areas of application. From the table of contents: - Object Oriented Spline Software - An Int
Author |
: Hans Hagen |
Publisher |
: SIAM |
Total Pages |
: 205 |
Release |
: 1992-01-01 |
ISBN-10 |
: 9780898712810 |
ISBN-13 |
: 0898712815 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Curve and Surface Design by : Hans Hagen
This collection of ideas and results on topics of curve and surface design is intended for research in the academic environment as well as for practical use in industrial applications. Main emphasis is on minimal energy splines and geometric spline curves, and on techniques beyond tensor product surfaces.
Author |
: Robert E. Barnhill |
Publisher |
: Academic Press |
Total Pages |
: 337 |
Release |
: 2014-05-10 |
ISBN-10 |
: 9781483268484 |
ISBN-13 |
: 1483268489 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Computer Aided Geometric Design by : Robert E. Barnhill
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.