Curves And Surfaces In Geometric Modeling

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Curves and Surfaces in Geometric Modeling

Jean H. Gallier
Curves and Surfaces in Geometric Modeling Book PDF

Author : Jean H. Gallier
Publisher : Morgan Kaufmann
Page : 512 pages
File Size : 47,5 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

Modeling of Curves and Surfaces with MATLAB®

Vladimir Rovenski
Modeling of Curves and Surfaces with MATLAB Book PDF

Author : Vladimir Rovenski
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 46,5 Mb
Release : 2010-06-10
Category : Mathematics
ISBN : 9780387712772

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Modeling of Curves and Surfaces with MATLAB® by Vladimir Rovenski Pdf

This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.

Computer Graphics and Geometric Modelling

Max K. Agoston
Computer Graphics and Geometric Modelling Book PDF

Author : Max K. Agoston
Publisher : Springer Science & Business Media
Page : 908 pages
File Size : 42,8 Mb
Release : 2005-12-06
Category : Computers
ISBN : 9781846281082

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Computer Graphics and Geometric Modelling by Max K. Agoston Pdf

Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Implementation and Algorithms, covers the computer graphics part of the field of geometric modelling and includes all the standard computer graphics topics. The first part deals with basic concepts and algorithms and the main steps involved in displaying photorealistic images on a computer. The second part covers curves and surfaces and a number of more advanced geometric modelling topics including intersection algorithms, distance algorithms, polygonizing curves and surfaces, trimmed surfaces, implicit curves and surfaces, offset curves and surfaces, curvature, geodesics, blending etc. The third part touches on some aspects of computational geometry and a few special topics such as interval analysis and finite element methods. The volume includes two companion programs.

Designing Fair Curves and Surfaces

Nickolas S. Sapidis
Designing Fair Curves and Surfaces Book PDF

Author : Nickolas S. Sapidis
Publisher : SIAM
Page : 316 pages
File Size : 48,6 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.

Designing Fair Curves and Surfaces

Nickolas S. Sapidis
Designing Fair Curves and Surfaces Book PDF

Author : Nickolas S. Sapidis
Publisher : SIAM
Page : 330 pages
File Size : 51,5 Mb
Release : 1994-01-01
Category : Computers
ISBN : 1611971527

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Designing Fair Curves and Surfaces by Nickolas S. Sapidis Pdf

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.

Geometric Modeling

Michael E. Mortenson
Geometric Modeling Book PDF

Author : Michael E. Mortenson
Publisher : Unknown
Page : 788 pages
File Size : 40,7 Mb
Release : 1985
Category : Computers
ISBN : UOM:39015018238785

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Geometric Modeling by Michael E. Mortenson Pdf

The first comprehensive and complete coverage of geometric modeling. This text accurately treats the parametric geometry of curves, surfaces and solids, the construction of geometric models and the analytical techniques that can be used and applications. Extensive use is made of end-of-chapter problems.

Modeling of Curves and Surfaces in CAD/CAM

Mamoru Hosaka
Modeling of Curves and Surfaces in CAD CAM Book PDF

Author : Mamoru Hosaka
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642765988

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Modeling of Curves and Surfaces in CAD/CAM by Mamoru Hosaka Pdf

1 Aims and Features of This Book The contents of t. his book were originally planned t. o be included in a book en titled Geometric lIIodeling and CAD/CAM to be written by M. Hosaka and F. Kimura, but since the draft. of my part of the book was finished much earlier than Kimura's, we decided to publish this part separately at first. In it, geometrically oriented basic methods and tools used for analysis and synthesis of curves and surfaces used in CAD/CAM, various expressions and manipulations of free-form surface patches and their connection, interference as well as their qualit. y eval uation are treated. They are important elements and procedures of geometric models. And construction and utilization of geometric models which include free-form surfaces are explained in the application examples, in which the meth ods and the techniques described in this book were used. In the succeeding book which Kimura is to write, advanced topics such as data structures of geometric models, non-manifold models, geometric inference as well as tolerance problems and product models, process planning and so on are to be included. Conse quently, the title of this book is changed to Modeling of Curves and Surfaces in CAD/CAM. Features of this book are the following. Though there are excellent text books in the same field such as G. Farin's Curves and Surfaces for CAD /CAM[l] and C. M.

Curves and Surfaces for CAGD

Gerald E. Farin
Curves and Surfaces for CAGD Book PDF

Author : Gerald E. Farin
Publisher : Morgan Kaufmann
Page : 522 pages
File Size : 54,9 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 ...

Modeling of Curves and Surfaces with MATLAB®

Vladimir Rovenski
Modeling of Curves and Surfaces with MATLAB Book PDF

Author : Vladimir Rovenski
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 54,8 Mb
Release : 2010-07-03
Category : Mathematics
ISBN : 9780387712789

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Modeling of Curves and Surfaces with MATLAB® by Vladimir Rovenski Pdf

This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.

Handbook of Computer Aided Geometric Design

G. Farin,J. Hoschek,M.-S. Kim
Handbook of Computer Aided Geometric Design Book PDF

Author : G. Farin,J. Hoschek,M.-S. Kim
Publisher : Elsevier
Page : 849 pages
File Size : 48,9 Mb
Release : 2002-08-13
Category : Computers
ISBN : 9780444511041

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Handbook of Computer Aided Geometric Design by G. Farin,J. Hoschek,M.-S. Kim Pdf

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.

Curves and Surfaces for Computer Graphics

David Salomon
Curves and Surfaces for Computer Graphics Book PDF

Author : David Salomon
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 43,6 Mb
Release : 2007-03-20
Category : Computers
ISBN : 9780387284521

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Curves and Surfaces for Computer Graphics by David Salomon Pdf

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.

Interactive Curves and Surfaces

Alyn Rockwood,Peter Chambers
Interactive Curves and Surfaces Book PDF

Author : Alyn Rockwood,Peter Chambers
Publisher : Morgan Kaufmann
Page : 232 pages
File Size : 50,5 Mb
Release : 1996-08
Category : Computers
ISBN : 1558604057

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Interactive Curves and Surfaces by Alyn Rockwood,Peter Chambers Pdf

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.

Shape Interrogation for Computer Aided Design and Manufacturing

Nicholas M. Patrikalakis,Takashi Maekawa
Shape Interrogation for Computer Aided Design and Manufacturing Book PDF

Author : Nicholas M. Patrikalakis,Takashi Maekawa
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 44,6 Mb
Release : 2002-02-14
Category : Computers
ISBN : 3540424547

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Shape Interrogation for Computer Aided Design and Manufacturing by Nicholas M. Patrikalakis,Takashi Maekawa Pdf

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.

Geometric Modeling with Splines

Elaine Cohen,Richard F. Riesenfeld,Gershon Elber
Geometric Modeling with Splines Book PDF

Author : Elaine Cohen,Richard F. Riesenfeld,Gershon Elber
Publisher : CRC Press
Page : 638 pages
File Size : 42,7 Mb
Release : 2001-07-18
Category : Computers
ISBN : 9781439864203

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Geometric Modeling with Splines by Elaine Cohen,Richard F. Riesenfeld,Gershon Elber Pdf

Written by researchers who have helped found and shape the field, this book is a definitive introduction to geometric modeling. The authors present all of the necessary techniques for curve and surface representations in computer-aided modeling with a focus on how the techniques are used in design. They achieve a balance between mathematical rigor

Geometric Modeling

Hans Hagen,Dieter Roller
Geometric Modeling Book PDF

Author : Hans Hagen,Dieter Roller
Publisher : Springer Science & Business Media
Page : 291 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642764042

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Geometric Modeling by Hans Hagen,Dieter Roller Pdf

This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.