Geometric Modeling And Algebraic Geometry

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Algebraic Geometry and Geometric Modeling

Author : Mohamed Elkadi
Publisher : Springer Science & Business Media
ISBN 13 : 3540332758
Total Pages : 252 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Algebraic Geometry and Geometric Modeling by : Mohamed Elkadi

Download or read book Algebraic Geometry and Geometric Modeling written by Mohamed Elkadi and published by Springer Science & Business Media. This book was released on 2006-11-02 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer Science & Business Media
ISBN 13 : 3540721851
Total Pages : 227 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Geometric Modeling and Algebraic Geometry by : Bert Jüttler

Download or read book Geometric Modeling and Algebraic Geometry written by Bert Jüttler and published by Springer Science & Business Media. This book was released on 2007-12-24 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Geometry and Geometric Modeling

Author : Mohamed Elkadi
Publisher : Springer
ISBN 13 : 9783642069932
Total Pages : 0 pages
Book Rating : 4.0/5 (699 download)

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Book Synopsis Algebraic Geometry and Geometric Modeling by : Mohamed Elkadi

Download or read book Algebraic Geometry and Geometric Modeling written by Mohamed Elkadi and published by Springer. This book was released on 2010-11-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Algebraic Geometry and Geometric Modeling

Author : Ron Goldman
Publisher : American Mathematical Soc.
ISBN 13 : 0821834207
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topics in Algebraic Geometry and Geometric Modeling by : Ron Goldman

Download or read book Topics in Algebraic Geometry and Geometric Modeling written by Ron Goldman and published by American Mathematical Soc.. This book was released on 2003 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture. The NSF sponsored the four-day ''Vilnius Workshop on Algebraic Geometry and Geometric Modeling'', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, ''On the determination of the degree of an equations obtained by elimination'', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.

Computer Graphics and Geometric Modelling

Author : Max K. Agoston
Publisher : Springer Science & Business Media
ISBN 13 : 1846281229
Total Pages : 972 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Computer Graphics and Geometric Modelling by : Max K. Agoston

Download or read book Computer Graphics and Geometric Modelling written by Max K. Agoston and published by Springer Science & Business Media. This book was released on 2005-09-05 with total page 972 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: Mathematics, contains the mathematical background needed for the geometric modeling topics in computer graphics covered in the first volume. This volume begins with material from linear algebra and a discussion of the transformations in affine & projective geometry, followed by topics from advanced calculus & chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and finally algebraic geometry. Two important goals throughout were to explain the material thoroughly, and to make it self-contained. This volume by itself would make a good mathematics reference book, in particular for practitioners in the field of geometric modelling. Due to its broad coverage and emphasis on explanation it could be used as a text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential & algebraic).

Curves and Surfaces in Geometric Modeling

Author : Jean H. Gallier
Publisher : Morgan Kaufmann
ISBN 13 : 9781558605992
Total Pages : 512 pages
Book Rating : 4.6/5 (59 download)

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Book Synopsis Curves and Surfaces in Geometric Modeling by : Jean H. Gallier

Download or read book Curves and Surfaces in Geometric Modeling written by Jean H. Gallier and published by Morgan Kaufmann. This book was released on 2000 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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

Computer Graphics and Geometric Modelling

Author : Max K. Agoston
Publisher : Springer Science & Business Media
ISBN 13 : 9781852338176
Total Pages : 984 pages
Book Rating : 4.3/5 (381 download)

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Book Synopsis Computer Graphics and Geometric Modelling by : Max K. Agoston

Download or read book Computer Graphics and Geometric Modelling written by Max K. Agoston and published by Springer Science & Business Media. This book was released on 2005-02 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second book of a two-volume work in which the author presents an overview of computer graphics as seen in the context of geometric modeling and the mathematics required to understand the subject.

Computer Graphics and Geometric Modelling

Author : Max K. Agoston
Publisher : Springer Science & Business Media
ISBN 13 : 9781852338183
Total Pages : 960 pages
Book Rating : 4.3/5 (381 download)

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Book Synopsis Computer Graphics and Geometric Modelling by : Max K. Agoston

Download or read book Computer Graphics and Geometric Modelling written by Max K. Agoston and published by Springer Science & Business Media. This book was released on 2005-01-04 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modeling, this two-volume work covers implementation and theory in a thorough and systematic fashion. It covers the computer graphics part of the field of geometric modeling and includes all the standard computer graphics topics. The CD-ROM features two companion programs.

Model Theory and Algebraic Geometry

Author : Elisabeth Bouscaren
Publisher : Springer
ISBN 13 : 3540685219
Total Pages : 223 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Model Theory and Algebraic Geometry by : Elisabeth Bouscaren

Download or read book Model Theory and Algebraic Geometry written by Elisabeth Bouscaren and published by Springer. This book was released on 2009-03-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.

Computer Graphics and Geometric Modelling

Author : Max K. Agoston
Publisher : Springer Science & Business Media
ISBN 13 : 1846281083
Total Pages : 908 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Computer Graphics and Geometric Modelling by : Max K. Agoston

Download or read book Computer Graphics and Geometric Modelling written by Max K. Agoston and published by Springer Science & Business Media. This book was released on 2005-12-06 with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Computational Geometry

Author : Ioannis Z. Emiris
Publisher : Springer Science & Business Media
ISBN 13 : 1441909990
Total Pages : 244 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Nonlinear Computational Geometry by : Ioannis Z. Emiris

Download or read book Nonlinear Computational Geometry written by Ioannis Z. Emiris and published by Springer Science & Business Media. This book was released on 2009-10-28 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.

Geometric Modeling

Author : Michael E. Mortenson
Publisher :
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Geometric Modeling by : Michael E. Mortenson

Download or read book Geometric Modeling written by Michael E. Mortenson and published by . This book was released on 1997 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, up-to-date presentation of the indispensable core concepts of geometric modeling Now completely updated to include the most recent developments in the field, Geometric Modeling, Second Edition presents a comprehensive discussion of the core concepts of this subject. It describes and compares all the important mathematical methods for modeling curves, surfaces, and solids, and shows how to transform and assemble these elements into complex models. Written in a style free of the jargon of special applications, this unique book focuses on the essence of geometric modeling and treats it as a discipline in its own right. It integrates the three important functions of geometric modeling: to represent elementary forms (i.e., curves, surfaces, and solids), to shape and assemble these into more complex forms, and to determine concomitant derivative geometric elements (i.e., intersections, offsets, and fillets). With more than 300 illustrations, Geometric Modeling, Second Edition appeals to the reader's visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. An extensive bibliography lists many supporting works, directing the reader to more specialized treatments of this subject. Geometric Modeling, Second Edition serves as an invaluable guide to computer graphics and CAD/CAM specialists, applications designers, scientific programmers, teachers, and students.

Theory and Practice of Geometric Modeling

Author : Wolfgang Straßer
Publisher : Springer Science & Business Media
ISBN 13 : 3642615422
Total Pages : 534 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Theory and Practice of Geometric Modeling by : Wolfgang Straßer

Download or read book Theory and Practice of Geometric Modeling written by Wolfgang Straßer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a result of the lectures and discussions during the conference "Theory and Practice of Geometric Modeling". The event has been organized by the Wilhelm-Schickard-Institut fiir Informatik, Universitat Tiibingen and took place at the Heinrich-Fabri-Institut in Blaubeuren from October 3 to 7, 1988. The conference brought together leading experts from academic and industrial research institutions, CAD system developers and experien ced users to exchange their ideas and to discuss new concepts and future directions in geometric modeling. The main intention has been to bridge the gap between theoretical results, performance of existing CAD systems and the real problems of users. The contents is structured in five parts: A Algorithmic Aspects B Surface Intersection, Blending, Ray Tracing C Geometric Tools D Different Representation Schemes in Solid Modeling E Product Modeling in High Level Specifications The material presented in this book reflects the current state of the art in geometric modeling and should therefore be of interest not only to university and industry researchers, but also to system developers and practitioners who wish to keep up to date on recent advances and new concepts in this rapidly expanding field. The editors express their sincere appreciation to the contributing authors, and to the members of the program committee, W. Boehm, J. Hoschek, A. Massabo, H. Nowacki, M. Pratt, J. Rossignac, T. Sederberg and W. Tiller, for their close cooperation and their time and effort that made the conference and this book a success.

Algebraic Models in Geometry

Author : Yves Félix
Publisher : Oxford University Press
ISBN 13 : 0199206511
Total Pages : 483 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Algebraic Models in Geometry by : Yves Félix

Download or read book Algebraic Models in Geometry written by Yves Félix and published by Oxford University Press. This book was released on 2008 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.

Geometric Modelling, Numerical Simulation, and Optimization:

Author : Geir Hasle
Publisher : Springer Science & Business Media
ISBN 13 : 3540687831
Total Pages : 559 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Geometric Modelling, Numerical Simulation, and Optimization: by : Geir Hasle

Download or read book Geometric Modelling, Numerical Simulation, and Optimization: written by Geir Hasle and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume addresses the importance of mathematics for industry and society by presenting highlights from contract research at the Department of Applied Mathematics at SINTEF, the largest independent research organization in Scandinavia. Examples range from computer-aided geometric design, via general purpose computing on graphics cards, to reservoir simulation for enhanced oil recovery. Contributions are written in a tutorial style.

Future Vision and Trends on Shapes, Geometry and Algebra

Author : Raffaele de Amicis
Publisher : Springer
ISBN 13 : 144716461X
Total Pages : 166 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Future Vision and Trends on Shapes, Geometry and Algebra by : Raffaele de Amicis

Download or read book Future Vision and Trends on Shapes, Geometry and Algebra written by Raffaele de Amicis and published by Springer. This book was released on 2014-06-13 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Geometry Modeling in Information Theory

Author : Edgar Martinez-Moro
Publisher : World Scientific
ISBN 13 : 9814335762
Total Pages : 334 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Algebraic Geometry Modeling in Information Theory by : Edgar Martinez-Moro

Download or read book Algebraic Geometry Modeling in Information Theory written by Edgar Martinez-Moro and published by World Scientific. This book was released on 2013 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.