Geometric Modeling

The Mathematics of Shapes

Author: Nikolay Golovanov

Publisher: CreateSpace

ISBN: 9781497473195

Category: Computer-aided design

Page: 348

View: 6973

"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: 4027

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: 3035

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: N.A


Category: Computers

Page: 505

View: 1350

Completely updated to include the most recent developments in the field, the third edition like the two previous editions, emphasizes clarity and thoroughness in the mathematical development of its subjects. It is written in a style that is free of jargon of special applications, while integrating the three important functions of geometric modeling: to represent elementary forms (curves, surfaces, and solids), to shape and assemble these into complex forms, and to determine geometric properties and relationships. With hundreds of illustrations, this unique book appeals to the readers visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. Upper-division and graduate students, teachers, and professionals studying, teaching or practicing geometric modeling, 3D modeling, computational geometry, computer graphics applications, animation, CAD/CAM, and related subjects will find this to be a very valuable reference. Describes and compares all the important mathematical methods for modeling curves, surfaces, and solids. Prepares the reader for more advanced topics, such as 3D modeling, CAD/CAM, animation, and scientific visualization. Incorporates references throughout the text to direct the reader to more specialized treatments of the subjects. Carefully designed illustrations and exercises support each mathematical concept presented. Offers hundreds of exercises to test the readers comprehension.

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: 8279

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.

Algebraic Geometry and Geometric Modeling

Author: Mohamed Elkadi,Bernard Mourrain,Ragni Piene

Publisher: Springer Science & Business Media

ISBN: 3540332758

Category: Mathematics

Page: 252

View: 3391

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.

An Integrated Introduction to Computer Graphics and Geometric Modeling

Author: Ronald Goldman

Publisher: CRC Press

ISBN: 1439803358

Category: Computers

Page: 574

View: 2824

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.

Geometric Modeling With Splines

An Introduction


Publisher: A K Peters Ltd

ISBN: 9781568811376

Category: Computers

Page: 616

View: 3021

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.

Geometric Modeling and Algebraic Geometry

Author: Bert Jüttler,Ragni Piene

Publisher: Springer Science & Business Media

ISBN: 9783540721857

Category: Mathematics

Page: 231

View: 1112

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.

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: 1616

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.

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: 6578

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.

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: 1908

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.

Advances in geometric modeling

Author: Muhammad Sarfraz

Publisher: John Wiley & Sons Inc

ISBN: 9780470859377

Category: Mathematics

Page: 320

View: 3033

"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.

Future Vision and Trends on Shapes, Geometry and Algebra

Author: Raffaele de Amicis,Giuseppe Conti

Publisher: Springer

ISBN: 144716461X

Category: Mathematics

Page: 162

View: 3163

Mathematical algorithms are a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. This book provides a bridge between algebraic geometry and geometric modelling algorithms, formulated within a computer science framework. Apart from the algebraic geometry topics covered, the entire book is based on the unifying concept of using algebraic techniques – properly specialized to solve geometric problems – to seriously improve accuracy, robustness and efficiency of CAD-systems. It provides new approaches as well as industrial applications to deform surfaces when animating virtual characters, to automatically compare images of handwritten signatures and to improve control of NC machines. This book further introduces a noteworthy representation based on 2D contours, which is essential to model the metal sheet in industrial processes. It additionally reviews applications of numerical algebraic geometry to differential equations systems with multiple solutions and bifurcations. Future Vision and Trends on Shapes, Geometry and Algebra is aimed specialists in the area of mathematics and computer science on the one hand and on the other hand at those who want to become familiar with the practical application of algebraic geometry and geometric modelling such as students, researchers and doctorates.

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: 7394

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.

Geometric Modeling

Methods and Applications

Author: Hans Hagen,Dieter Roller

Publisher: Springer Science & Business Media

ISBN: 3642764045

Category: Computers

Page: 286

View: 2193

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.

Geometric Modeling

Algorithms and New Trends

Author: Gerald E. Farin

Publisher: Society for Industrial & Applied

ISBN: 9780898712063

Category: Mathematics

Page: 399

View: 843


Mathematical Aspects of Geometric Modeling

Author: Charles A. Micchelli

Publisher: SIAM

ISBN: 0898713315

Category: Mathematics

Page: 256

View: 2774

Examines concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies them.

Geometrie und Billard

Author: Serge Tabachnikov

Publisher: Springer-Verlag

ISBN: 3642319254

Category: Mathematics

Page: 165

View: 7369

Wie bewegt sich ein Massenpunkt in einem Gebiet, an dessen Rand er elastisch zurückprallt? Welchen Weg nimmt ein Lichtstrahl in einem Gebiet mit ideal reflektierenden Rändern? Anhand dieser und ähnlicher Fragen stellt das vorliegende Buch Zusammenhänge zwischen Billard und Differentialgeometrie, klassischer Mechanik sowie geometrischer Optik her. Dabei beschäftigt sich das Buch unter anderem mit dem Variationsprinzip beim mathematischen Billard, der symplektischen Geometrie von Lichtstrahlen, der Existenz oder Nichtexistenz von Kaustiken, periodischen Billardtrajektorien und dem Mechanismus für Chaos bei der Billarddynamik. Ergänzend wartet dieses Buch mit einer beachtlichen Anzahl von Exkursen auf, die sich verwandten Themen widmen, darunter der Vierfarbensatz, die mathematisch-physikalische Beschreibung von Regenbögen, der poincaresche Wiederkehrsatz, Hilberts viertes Problem oder der Schließungssatz von Poncelet.​