Computation of Curves and Surfaces

In the following, we will look at these questions focusing on offsetting and blending curves and surfaces, given parametrically or implicitly. While the algebraic approach delivers good techniques for defining offsets and blends with ...

Author: Wolfgang Dahmen

Publisher: Springer Science & Business Media

ISBN: 9789400920170

Category: Mathematics

Page: 536

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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.

Effective Computational Geometry for Curves and Surfaces

Point set surfaces. In IEEE, editor, Visualization, pages 21–28, 2001. [232] B. S. Alin Bostan, Philippe Flajolet and ́E. Schost. Fast computation of special resultants. Journal of Symbolic Computation, 41(1):1–29, January 2006.

Author: Jean-Daniel Boissonnat

Publisher: Springer Science & Business Media

ISBN: 9783540332596

Category: Mathematics

Page: 344

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This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. Coverage includes references to open source software and discussion of potential applications of the presented techniques.

Curves and Surfaces for Computer Graphics

Adding points provides some control over the shape of the curve, but slows down the computations. A practical, useful curve/surface design algorithm should be interactive. It should provide user-controlled parameters that modify the ...

Author: David Salomon

Publisher: Springer Science & Business Media

ISBN: 9780387284521

Category: Computers

Page: 460

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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.

Designing Fair Curves and Surfaces

The resulting surface spans the edges of the network forming a G" or Go continuous surface with G* continuity at the ... Previous Work The work described in this paper is naturally broken into curve, network, and surface computation.

Author: Nickolas S. Sapidis

Publisher: SIAM

ISBN: 9780898713329

Category: Computers

Page: 318

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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.

An Introduction to Computational Geometry for Curves and Surfaces

umu 9866589 ELTR Preface 20196 The computation of curves and surfaces is a very important topic in the area of design . The rapid development of high - speed computing facilities over the past 30 years has seen an ever - increasing ...

Author: Alan J. Davies

Publisher: Oxford University Press, USA

ISBN: UOM:39015037500231

Category: Geometry

Page: 205

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This is an introductory textbook for undergraduates studying mathematics, engineering, or computer science, and explains how differential and computational geometry are used to explain the mathematics of curves and surfaces. It assumes only a basic knowledge of vector and matrix algebra, andis filled with numerous exercises, solutions, and worked examples. Ideal for those interested in computer graphics or computer-aided design, this book will be invaluable for those needing to understand the complex mathematics which lies behind these important areas of application.

Computational Methods for Algebraic Spline Surfaces

Distance Separation Measures Between Parametric Curves and Surfaces Toward Intersection and Collision Detection Applications Gershon Elber Technion, Israel Institute of Technology, Haifa 32000, Israel, ...

Author: Tor Dokken

Publisher: Springer Science & Business Media

ISBN: 9783540271574

Category: Mathematics

Page: 238

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This volume contains revised papers that were presented at the international workshop entitled Computational Methods for Algebraic Spline Surfaces (“COMPASS”), which was held from September 29 to October 3, 2003, at Schloß Weinberg, Kefermarkt (A- tria). The workshop was mainly devoted to approximate algebraic geometry and its - plications. The organizers wanted to emphasize the novel idea of approximate implici- zation, that has strengthened the existing link between CAD / CAGD (Computer Aided Geometric Design) and classical algebraic geometry. The existing methods for exact implicitization (i. e. , for conversion from the parametric to an implicit representation of a curve or surface) require exact arithmetic and are too slow and too expensive for industrial use. Thus the duality of an implicit representation and a parametric repres- tation is only used for low degree algebraic surfaces such as planes, spheres, cylinders, cones and toroidal surfaces. On the other hand, this duality is a very useful tool for - veloping ef?cient algorithms. Approximate implicitization makes this duality available for general curves and surfaces. The traditional exact implicitization of parametric surfaces produce global rep- sentations, which are exact everywhere. The surface patches used in CAD, however, are always de?ned within a small box only; they are obtained for a bounded parameter domain (typically a rectangle, or – in the case of “trimmed” surface patches – a subset of a rectangle). Consequently, a globally exact representation is not really needed in practice.

Artificial Intelligence and Symbolic Computation

Becker, T., Weispfenning, V.: Gröbner Bases: A Computational Approach to Commutative Algebra. Springer, Berlin (1993). 3. ... Cox, D.: Equations of parametric curves and surfaces via syzygies. In: Symbolic Computation: Solving Equations ...

Author: Jaques Calmet

Publisher: Springer

ISBN: 9783540397304

Category: Computers

Page: 269

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Here are the refereed proceedings of the 8th International Conference on Artificial Intelligence and Symbolic Computation, AISC 2006. The book presents 18 revised full papers together with 4 invited papers, organized in topical sections on artificial intelligence and theorem proving, symbolic computation, constraint satisfaction/solving, and mathematical knowledge management. Coverage includes mathematical foundations, implementations, and applications in industry and academia.

Mathematical Methods for Curves and Surfaces

We also plan to apply these tools for the computation of convolutions of implicit algebraic hypersurfaces. Acknowledgments The authors were supported by the Research Plan MSM 4977751301. We thank to all referees for their comments which ...

Author: Morten Dæhlen

Publisher: Springer

ISBN: 9783642116209

Category: Computers

Page: 446

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This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008, held in Tønsberg, Norway, in June/July 2008. The 28 revised full papers presented were carefully reviewed and selected from 129 talks presented at the conference. The topics addressed by the papers range from mathematical analysis of various methods to practical implementation on modern graphics processing units.

Curves and Surfaces

Tu, C.H., Wang, W., Mourrain, B., Wang, J.Y.: Using signature sequences to classify intersection curves of two quadrics. ... In: SCG 2003: Proceedings of the Nineteenth Annual Symposium on Computational Geometry, pp. 246–255.

Author: Jean-Daniel Boissonnat

Publisher: Springer Science & Business Media

ISBN: 9783642274121

Category: Computers

Page: 748

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This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Curves and Surfaces, held in Avignon, in June 2010. The conference had the overall theme: "Representation and Approximation of Curves and Surfaces and Applications". The 39 revised full papers presented together with 9 invited talks were carefully reviewed and selected from 114 talks presented at the conference. The topics addressed by the papers range from mathematical foundations to practical implementation on modern graphics processing units and address a wide area of topics such as computer-aided geometric design, computer graphics and visualisation, computational geometry and topology, geometry processing, image and signal processing, interpolation and smoothing, scattered data processing and learning theory and subdivision, wavelets and multi-resolution methods.

Computational Geometry

[ 12 ] R.E. Barnhill , Surface in the computer aided geometric design : a survey with new results , CAGD , 2 ( 1985 ) ... ( 15 ) W. Böhm , Algebraic and differential geometric methods in C.A.G.D. , in Computation of Curves and Surfaces ...

Author: Renhong Wang

Publisher: American Mathematical Soc.

ISBN: 0821820443

Category: Mathematics

Page: 235

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Computational geometry is a borderline subject related to pure and applied mathematics, computer science, and engineering. The book contains articles on various topics in computational geometry based on invited lectures and contributed papers presented during the program on computational geometry at the Morningside Center of Mathematics at the Chinese Academy of Sciences (Beijing). The opening article by R.-H. Wang gives a nice survey of various aspects of computational geometry, many of which are discussed in detail in the volume. Topics of the other articles include problems of optimal triangulation, splines, data interpolation, problems of curve and surface design, problems of shape control, quantum teleportation, and more. The book is suitable for graduate students and researchers interested in computational geometry and specialists in theoretical computer science.