Geometric Modeling

The Mathematics of Shapes

Author: Nikolay Golovanov

Publisher: CreateSpace

ISBN: 9781497473195

Category: Computer-aided design

Page: 348

View: 5261

"The book outlines methods used to construct curves, surfaces, and solids. It describes composition, principles of manipulation, and applications of geometric models. It has been written for university students and specialists in computer-aided design."--Abstract, p. 3.

Designing Fair Curves and Surfaces

Shape Quality in Geometric Modeling and Computer-Aided Design

Author: Nickolas S. Sapidis

Publisher: SIAM

ISBN: 9781611971521

Category: Computer-aided design

Page: 318

View: 2773

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 for product realization

selected and expanded papers from the IFIP TC5/WG5.2 Working Conference on Geometric Medeling, Rensselaerville, NY, U.S.A., 27 September-1 October 1992

Author: Peter R. Wilson,Michael J. Wozny,Michael J. Pratt

Publisher: North Holland

ISBN: 9780444816627

Category: Art

Page: 325

View: 451

State-of-the-art research and development in geometric and product modeling is reflected in this publication. The papers have been organized into five main topic areas - geometry, shape modeling, feature-based modeling, applications, and data interfaces - though many contributions inevitably cross the artificial boundaries implied by such partitioning.The first group of papers deal with particular aspects of the problem of curve and surface representation under constraints. The second and largest section contains papers addressing the topic of describing the shape of a product. Advances achieved are acknowledged, including the development of work on representing imprecisely defined shapes, which signifies a movement from the detailed product design stage towards the more conceptual design application. The third section continues this theme with consideration of higher levels of design abstraction beyond the traditional shape models. Specific design and manufacturing applications are discussed in the fourth chapter. The final section provides an overview of the problems and solutions related to the transfer and manipulation of geometric and product data between and within CAX systems.

Geometric modeling

Author: Michael E. Mortenson

Publisher: John Wiley & Sons Inc


Category: Mathematics

Page: 763

View: 8221

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.

Advances in Multiresolution for Geometric Modelling

Author: Neil Dodgson,Michael S. Floater,Malcolm Sabin

Publisher: Springer Science & Business Media

ISBN: 3540268081

Category: Mathematics

Page: 436

View: 3398

Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and rendering as well as coding, compression, and digital transmission of 3D geometric objects. This book marks the culmination of the four-year EU-funded research project, Multiresolution in Geometric Modelling (MINGLE). The book contains seven survey papers, providing a detailed overview of recent advances in the various fields within multiresolution modelling, and sixteen additional research papers. Each of the seven parts of the book starts with a survey paper, followed by the associated research papers in that area. All papers were originally presented at the MINGLE 2003 workshop held at Emmanuel College, Cambridge, UK, 9-11 September 2003.

Geometric Modeling

Algorithms and New Trends

Author: Gerald E. Farin

Publisher: Society for Industrial & Applied

ISBN: 9780898712063

Category: Mathematics

Page: 399

View: 4258


An Integrated Introduction to Computer Graphics and Geometric Modeling

Author: Ronald Goldman

Publisher: CRC Press

ISBN: 1439803358

Category: Computers

Page: 574

View: 8946

Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics. Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques. Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.

From Geometric Modeling to Shape Modeling

IFIP TC5 WG5.2 Seventh Workshop on Geometric Modeling: Fundamentals and Applications October 2–4, 2000, Parma, Italy

Author: Umberto Cugini,Michael Wozny

Publisher: Springer

ISBN: 0387354956

Category: Computers

Page: 244

View: 1326

IFIP Working Group 5.2 has organized a series of workshops aimed at presenting and discussing current issues and future perspectives of Geometric Modeling in the CAD environment. From Geometric Modeling to Shape Modeling comprises the proceedings of the seventh GEO workshop, which was sponsored by the International Federation for Information Processing (IFIP) and held in Parma, Italy in October 2000. The workshop looked at new paradigms for CAD including the evolution of geometric-centric CAD systems, modeling of non-rigid materials, shape modeling, geometric modeling and virtual prototyping, and new methods of interaction with geometric models. The seventeen included papers provide an interesting overview of the evolution of geometric centric modeling into shape modeling. Also included is an invited speaker paper, which discusses the foundation of the next generation of CAD systems, where shape and function enhance geometric descriptions. The main topics discussed in the book are: Theoretical foundation for solids and surfaces; Computational basis for geometric modeling; Methods of interaction with geometric models; Industrial and other applications of geometric modeling; New paradigms of geometric modeling for CAD; Shape modeling. From Geometric Modeling to Shape Modeling is essential reading for researchers, graduate and postgraduate students, systems developers of advanced computer-aided design and manufacturing systems, and engineers involved in industrial applications.

Algebraic Geometry and Geometric Modeling

Author: Mohamed Elkadi,Bernard Mourrain,Ragni Piene

Publisher: Springer Science & Business Media

ISBN: 3540332758

Category: Mathematics

Page: 252

View: 4429

This book spans the distance between algebraic descriptions of geometric objects and the rendering of digital geometric shapes based on algebraic models. These contrasting points of view inspire a thorough analysis of the key challenges and how they are met. The articles focus on important classes of problems: implicitization, classification, and intersection. Combining illustrative graphics, computations and review articles this book helps the reader gain a firm practical grasp of these subjects.

Geometric Modeling and Algebraic Geometry

Author: Bert Jüttler,Ragni Piene

Publisher: Springer Science & Business Media

ISBN: 9783540721857

Category: Mathematics

Page: 231

View: 9884

Geometric Modeling and Algebraic Geometry, though closely related, are traditionally represented by two almost disjoint scientific communities. Both fields deal with objects defined by algebraic equations, but the objects are studied in different ways. In 12 chapters written by leading experts, this book presents recent results which rely on the interaction of both fields. Some of these results have been obtained from a major European project in geometric modeling.

Advances in geometric modeling

Author: Muhammad Sarfraz

Publisher: John Wiley & Sons Inc

ISBN: 9780470859377

Category: Mathematics

Page: 320

View: 4493

"Advances in Geometric Modeling" illustrates the significance of Geometric Modeling in construction, design and manufacture, in not only the traditional industries such as automobile and aircraft manufacturing, but also in modern industry. This includes CAD/CAM, Computer Art, Entertainment, Education and Training, Visualization, robotics, medical imaging, visualisation, painting and media, and others. This volume willProvide a valuable source focusing on interdisciplinary methods and affiliate research in the area of geometric modeling.Provide the user community with a variety of advanced geometric modeling techniques and their applications.Collate and disseminate information from various disciplines such as; Curve and Surface Fitting, Geometric Algorithms, Visualization, Computational Geometry, Solid Modeling, Computer Graphics, Computer Aided Geometric Design, Splines, Deformation of Objects, Virtual Reality, Mesh Simplification, Multi-resolution, Texture Mapping, Reverse Engineering, etc.Provide a source for researchers and practitioners who are looking for the latest developments in the field of geometric modeling. This in-depth and well-illustrated book is an excellent reference for researchers, computer scientists, practicing engineers and those who seek state-of-the-art techniques and applications in geometric modeling.

Geometric Modeling With Splines

An Introduction


Publisher: A K Peters Ltd

ISBN: 9781568811376

Category: Computers

Page: 616

View: 6123

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 and broad applicability. Appropriate for readers with a moderate degree of mathematical maturity, this book is suitable as an undergraduate or graduate text, or particularly as a resource for self-study.

Advances in Geometric Modeling and Processing

5th International Conference,GMP 2008, Hangzhou, China, April 23-25, 2008, Proceedings

Author: Falai Chen

Publisher: Springer Science & Business Media

ISBN: 3540792457

Category: Computers

Page: 606

View: 8567

This book constitutes the refereed proceedings of the 5th International Conference on Geometric Modeling and Processing, GMP 2008, held in Hangzhou, China, in April 2008. The 34 revised full papers and 17 revised short papers presented were carefully reviewed and selected from a total of 113 submissions. The papers cover a wide spectrum in the area of geometric modeling and processing and address topics such as curves and surfaces, digital geometry processing, geometric feature modeling and recognition, geometric constraint solving, geometric optimization, multiresolution modeling, and applications in computer vision, image processing, scientific visualization, robotics and reverse engineering.

Geometric Modelling

Theoretical and Computational Basis towards Advanced CAD Applications. IFIP TC5/WG5.2 Sixth International Workshop on Geometric Modelling December 7–9, 1998, Tokyo, Japan

Author: Fumihiko Kimura

Publisher: Springer Science & Business Media

ISBN: 9780792375388

Category: Computers

Page: 372

View: 976

Geometric modelling has been an important and interesting subject for many years from the purely mathematical and computer science viewpoint, and also from the standpoint of engineering and various other applications, such as CAD/CAM, entertainment, animation, and multimedia. This book focuses on the interaction between the theoretical foundation of geometric modelling and practical applications in CAD and related areas. Geometric Modelling: Theoretical and Computational Basis towards Advanced CAD Applications starts with two position papers, discussing basic computational theory and practical system solutions. The well-organized seven review papers give a systematic overview of the current situation and deep insight for future research and development directions towards the reality of shape representation and processing. They discuss various aspects of important issues, such as geometric computation for space search and shape generation, parametric modelling, feature modelling, user interface for geometric modelling, geometric modelling for the Next Generation CAD, and geometric/shape standard. Other papers discuss features and new research directions in geometric modelling, solid modeling, free-form surface modeling, intersection calculation, mesh modeling and reverse engineering. They cover a wide range of geometric modelling issues to show the problem scope and the technological importance. Researchers interested in the current status of geometric modelling research and developments will find this volume to be an essential reference.

Geometric Modeling for Scientific Visualization

Author: Guido Brunnett,Bernd Hamann,Heinrich Müller,Lars Linsen

Publisher: Springer Science & Business Media

ISBN: 3662074435

Category: Mathematics

Page: 488

View: 859

Geometric Modeling and Scientific Visualization are both established disciplines, each with their own series of workshops, conferences and journals. But clearly both disciplines overlap; this observation led to the idea of composing a book on Geometric Modeling for Scientific Visualization.

Geometric Modeling: Theory and Practice

The State of the Art

Author: Wolfgang Straßer,Reinhard Klein,Rene Rau

Publisher: Springer Science & Business Media

ISBN: 3642606075

Category: Computers

Page: 434

View: 7329

The Blaubeuren Conference "Theory and Practice of Geometric Modeling" has become a meeting place for leading experts from industrial and academic research institutions, CAD system developers and experienced users to exchange new ideas and to discuss new concepts and future directions in geometric modeling. The relaxed and calm atmosphere of the Heinrich-Fabri-Institute in Blaubeuren provides the appropriate environment for profound and engaged discussions that are not equally possible on other occasions. Real problems from current industrial projects as well as theoretical issues are addressed on a high scientific level. This book is the result of the lectures and discussions during the conference which took place from October 14th to 18th, 1996. The contents is structured in 4 parts: Mathematical Tools Representations Systems Automated Assembly. The editors express their sincere appreciation to the contributing authors, and to the members of the program committee for their cooperation, the careful reviewing and their active participation that made the conference and this book a success.

Shape Interrogation for Computer Aided Design and Manufacturing

Author: Nicholas M. Patrikalakis,Takashi Maekawa

Publisher: Springer Science & Business Media

ISBN: 3642040748

Category: Computers

Page: 408

View: 4401

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. This book provides a bridge between the areas geometric modeling and solid modeling. Apart from the differential geometry topics covered, the entire book is based on the unifying concept of recasting all shape interrogation problems to the solution of a nonlinear system. It 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, and geodesics.

Mathematical Tools for Shape Analysis and Description

Author: Silvia Biasotti,Bianca Falcidieno,Daniela Giorgi,Michela Spagnuolo

Publisher: Morgan & Claypool Publishers

ISBN: 1627053646

Category: Mathematics

Page: 138

View: 1028

This book is a guide for researchers and practitioners to the new frontiers of 3D shape analysis and the complex mathematical tools most methods rely on. The target reader includes students, researchers and professionals with an undergraduate mathematics background, who wish to understand the mathematics behind shape analysis. The authors begin with a quick review of basic concepts in geometry, topology, differential geometry, and proceed to advanced notions of algebraic topology, always keeping an eye on the application of the theory, through examples of shape analysis methods such as 3D segmentation, correspondence, and retrieval. A number of research solutions in the field come from advances in pure and applied mathematics, as well as from the re-reading of classical theories and their adaptation to the discrete setting. In a world where disciplines (fortunately) have blurred boundaries, the authors believe that this guide will help to bridge the distance between theory and practice. Table of Contents: Acknowledgments / Figure Credits / About this Book / 3D Shape Analysis in a Nutshell / Geometry, Topology, and Shape Representation / Differential Geometry and Shape Analysis / Spectral Methods for Shape Analysis / Maps and Distances between Spaces / Algebraic Topology and Topology Invariants / Differential Topology and Shape Analysis / Reeb Graphs / Morse and Morse-Smale Complexes / Topological Persistence / Beyond Geometry and Topology / Resources / Bibliography / Authors' Biographies

Geometric Modeling

Methods and Applications

Author: Hans Hagen,Dieter Roller

Publisher: Springer Science & Business Media

ISBN: 3642764045

Category: Computers

Page: 286

View: 3911

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.