Geometric Continuity Of Curves And Surfaces

Author : Przemysław Kiciak
Publisher : Springer Nature
Page : 233 pages
File Size : 53,8 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031025907

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Geometric Continuity of Curves and Surfaces by Przemysław Kiciak Pdf

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 : Gerald E. Farin
Publisher : Morgan Kaufmann
Page : 522 pages
File Size : 53,8 Mb
Release : 2002
Category : Computers
ISBN : 9781558607378

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Curves and Surfaces for CAGD by Gerald E. Farin Pdf

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 : Jean H. Gallier
Publisher : Morgan Kaufmann
Page : 512 pages
File Size : 51,8 Mb
Release : 2000
Category : Computers
ISBN : 1558605991

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Curves and Surfaces in Geometric Modeling by Jean H. Gallier Pdf

"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 : Fujio Yamaguchi
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642489525

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Curves and Surfaces in Computer Aided Geometric Design by Fujio Yamaguchi Pdf

This book contains various types of mathematical descriptions of curves and surfaces, such as Ferguson, Coons, Spline, Bézier and B-spline curves and surfaces. The materials are classified and arranged in a unified way so that beginners can easily understand the whole spectrum of parametric curves and surfaces. This book will be useful to many researchers, designers, teachers, and students who are working on curves and surfaces. The book can be used as a textbook in computer aided design classes.

Author : Hans Hagen
Publisher : SIAM
Page : 205 pages
File Size : 42,9 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 9780898712810

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Curve and Surface Design by Hans Hagen Pdf

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 : Gerald E. Farin
Publisher : Unknown
Page : 460 pages
File Size : 51,5 Mb
Release : 1997
Category : Computers
ISBN : UOM:39015040985619

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Curves and Surfaces for Computer-aided Geometric Design by Gerald E. Farin Pdf

Computer disk contains: "data sets, as well as all of the C routines found in the book."

Author : Nickolas S. Sapidis
Publisher : SIAM
Page : 316 pages
File Size : 44,5 Mb
Release : 1994-01-01
Category : Computers
ISBN : 9780898713329

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Designing Fair Curves and Surfaces by Nickolas S. Sapidis Pdf

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,Alain Le Mehaute,Larry Schumaker
Publisher : CRC Press
Page : 490 pages
File Size : 41,6 Mb
Release : 1994-07-15
Category : Computers
ISBN : 9781439863596

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Curves and Surfaces by Pierre-Jean Laurent,Alain Le Mehaute,Larry Schumaker Pdf

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 : Gerald Farin
Publisher : Elsevier
Page : 473 pages
File Size : 54,5 Mb
Release : 2014-06-28
Category : Computers
ISBN : 9781483296999

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Curves and Surfaces for Computer-Aided Geometric Design by Gerald Farin Pdf

A leading expert in CAGD, Gerald Farin covers the representation, manipulation, and evaluation of geometric shapes in this the Third Edition of Curves and Surfaces for Computer Aided Geometric Design. The book offers an introduction to the field that emphasizes Bernstein-Bezier methods and presents subjects in an informal, readable style, making this an ideal text for an introductory course at the advanced undergraduate or graduate level. The Third Edition includes a new chapter on Topology, offers new exercises and sections within most chapters, combines the material on Geometric Continuity into one chapter, and updates existing materials and references. Implementation techniques are addressed for practitioners by the inclusion of new C programs for many of the fundamental algorithms. The C programs are available on a disk included with the text. System Requirements: IBM PC or compatibles, DOS version 2.0 or higher. Covers representation, manipulation, and evaluation of geometric shapes Emphasizes Bernstein-Bezier methods Written in an informal, easy-to-read style

Author : Victor Andreevich Toponogov
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 46,7 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9780817644024

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Differential Geometry of Curves and Surfaces by Victor Andreevich Toponogov Pdf

Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels

Author : Przemysław Kiciak
Publisher : Morgan & Claypool Publishers
Page : 251 pages
File Size : 40,9 Mb
Release : 2016-10-02
Category : Computers
ISBN : 9781627054676

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Geometric Continuity of Curves and Surfaces by Przemysław Kiciak Pdf

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 : Luther Pfahler Eisenhart
Publisher : Courier Corporation
Page : 496 pages
File Size : 55,9 Mb
Release : 2013-04-25
Category : Mathematics
ISBN : 9780486159461

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A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart Pdf

Created especially for graduate students by a leading writer on mathematics, this introduction to the geometry of curves and surfaces concentrates on problems that students will find most helpful.

Author : Brian A. Barsky
Publisher : Springer
Page : 154 pages
File Size : 41,7 Mb
Release : 2013-12-20
Category : Computers
ISBN : 9783642722929

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Computer Graphics and Geometric Modeling Using Beta-splines by Brian A. Barsky Pdf

Author : Thomas F. Banchoff,Stephen T. Lovett
Publisher : CRC Press
Page : 286 pages
File Size : 51,8 Mb
Release : 2016-04-05
Category : Mathematics
ISBN : 9781482247473

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Differential Geometry of Curves and Surfaces by Thomas F. Banchoff,Stephen T. Lovett Pdf

Differential Geometry of Curves and Surfaces, Second Edition takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra, it develops students' geometric intuition through interactive computer graphics applets suppor

Author : Hans Hagen
Publisher : SIAM
Page : 213 pages
File Size : 52,6 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 1611971659

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Curve and Surface Design by Hans Hagen Pdf

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.