An Intuitive Approach To Geometric Continuity For Parametric Curves And Surfaces
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An Intuitive Approach To Geometric Continuity For Parametric Curves And Surfaces
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Author : Tony D. DeRose
language : en
Publisher:
Release Date : 1986
An Intuitive Approach To Geometric Continuity For Parametric Curves And Surfaces written by Tony D. DeRose and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
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).
Computation Of Curves And Surfaces
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Author : Wolfgang Dahmen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computation Of Curves And Surfaces written by Wolfgang Dahmen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Assembled here is a collection of articles presented at a NATO ADVANCED STU DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing committee. The contents of the contribu tions fall within the heading of COMPUTATION OF CURVES AND SURFACES and therefore address mathematical and computational issues pertaining to the dis play, modeling, interrogation and representation of complex geometrical objects in various scientific and technical environments. As is the intent of the NATO ASI program the meeting was two weeks in length and the body of the scientific activities was organized around prominent experts. Each of them presented lectures on his current research activity. We were fortunate to have sixteen distinguished invited speakers representing nine NATO countries: W. Bohm (Federal Republic of Germany), C. de Boor (USA), C.K. Chui (USA), W. Dahmen (Federal Republic of Germany), F. Fontanella (Italy), M. Gasca (Spain), R. Goldman (Canada), T.N.T. Goodman (UK), J.A. Gregory (UK), C. Hoffman (USA), J. Hoschek (Federal Republic of Germany), A. Le Mehaute (France), T. Lyche (Norway), C.A. Micchelli (USA), 1.1. Schumaker (USA), C. Traas (The Netherlands). The audience consisted of both young researchers as well as established scientists from twelve NATO countries and several non-NATO countries.
An Introduction To Splines For Use In Computer Graphics And Geometric Modeling
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Author : Richard H. Bartels
language : en
Publisher: Morgan Kaufmann
Release Date : 1995-09
An Introduction To Splines For Use In Computer Graphics And Geometric Modeling written by Richard H. Bartels and has been published by Morgan Kaufmann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09 with Computers categories.
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.
Computer Graphics And Geometric Modeling Using Beta Splines
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Author : Brian A. Barsky
language : en
Publisher: Springer
Release Date : 2013-12-20
Computer Graphics And Geometric Modeling Using Beta Splines written by Brian A. Barsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Computers categories.
Mathematical Methods In Computer Aided Geometric Design
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Author : Tom Lyche
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Mathematical Methods In Computer Aided Geometric Design written by Tom Lyche and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Mathematical Methods in Computer Aided Geometric Design covers the proceedings of the 1988 International Conference by the same title, held at the University of Oslo, Norway. This text contains papers based on the survey lectures, along with 33 full-length research papers. This book is composed of 39 chapters and begins with surveys of scattered data interpolation, spline elastic manifolds, geometry processing, the properties of Bézier curves, and Gröbner basis methods for multivariate splines. The next chapters deal with the principles of box splines, smooth piecewise quadric surfaces, some applications of hierarchical segmentations of algebraic curves, nonlinear parameters of splines, and algebraic aspects of geometric continuity. These topics are followed by discussions of shape preserving representations, box-spline surfaces, subdivision algorithm parallelization, interpolation systems, and the finite element method. Other chapters explore the concept and applications of uniform bivariate hermite interpolation, an algorithm for smooth interpolation, and the three B-spline constructions. The concluding chapters consider the three B-spline constructions, design tools for shaping spline models, approximation of surfaces constrained by a differential equation, and a general subdivision theorem for Bézier triangles. This book will prove useful to mathematicians and advance mathematics students.
Approximation And Modeling With B Splines
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Author : Klaus Hollig
language : en
Publisher: SIAM
Release Date : 2015-07-01
Approximation And Modeling With B Splines written by Klaus Hollig and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-01 with Mathematics categories.
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.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1987
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Aeronautics categories.
Geometric Modeling
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Author : Gerald E. Farin (Mathematician)
language : en
Publisher:
Release Date : 1987
Geometric Modeling written by Gerald E. Farin (Mathematician) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Computer Generated Images
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Author : Nadia Magnenat-Thalmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computer Generated Images written by Nadia Magnenat-Thalmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Research, development, and applications in computer graphics have dramatically expanded in recent years. Because of decreasing prices, superior hardware is now being used and image quality is better than ever. Many people now require image-synthesis techniques and software for their applicaions. Moreover, the techniques of computer ani mation have become very popular. In this book, we present a wide range of applications of computer graphics. This book is a collection of 44 papers in various areas of computer graphics selected from papers presented at Graphics Interface '85. Graphics Interface '85, held from May 27 to 31 in Montreal, was the first truly international computer graphics conference in Canada. This year, for the first time, the conference was presented jointly by the Com puter Graphics Society and the Canadian Man-Computer Communications Society. This new arrangement gave the conference international scope. The conference was spon sored by the Department of Communications in Ottawa, the Department of Science and Technology in Quebec, Supply and Services Canada, the Natural Sciences and Engineer ing Research Council of Canada, Hydro-Quebec, the "Association Canadienne Fran«aise pour I' Avancement des Sciences", and the Canadian Broadcasting Corpora tion. Graphics Interface '85 was organized by "1'Ecole des Hautes Etudes Commerciales" of the University of Montreal. Over 100 papers were submitted to the conference , but 64 were selected by the inter national program committee for presentation. This book contains new expanded versions of the papers.
Handbook Of Computer Aided Geometric Design
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Author : G. Farin
language : en
Publisher: Elsevier
Release Date : 2002-08-13
Handbook Of Computer Aided Geometric Design written by G. Farin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-13 with Computers categories.
This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include: Historical outline Curve and surface methods Scientific Visualization Implicit methods Reverse engineering. This book is meant to be a reference text for researchers in the field as well as an introduction to graduate students wishing to get some exposure to this subject.