Topics In Algebraic Geometry And Geometric Modeling

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Topics In Algebraic Geometry And Geometric Modeling

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Author : Ron Goldman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Topics In Algebraic Geometry And Geometric Modeling written by Ron Goldman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

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.

Algebraic Geometry And Geometric Modeling

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Author : Mohamed Elkadi
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-02

Algebraic Geometry And Geometric Modeling written by Mohamed Elkadi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Mathematics categories.

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.

Computer Graphics And Geometric Modelling

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Author : Max K. Agoston
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-09-05

Computer Graphics And Geometric Modelling written by Max K. Agoston and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-05 with Computers categories.

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).

Algebraic Geometry And Geometric Modeling

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Author : Mohamed Elkadi
language : en
Publisher: Springer
Release Date : 2010-11-19

Algebraic Geometry And Geometric Modeling written by Mohamed Elkadi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-19 with Mathematics categories.

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.

Future Vision And Trends On Shapes Geometry And Algebra

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Author : Raffaele de Amicis
language : en
Publisher: Springer
Release Date : 2014-06-13

Future Vision And Trends On Shapes Geometry And Algebra written by Raffaele de Amicis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-13 with Mathematics categories.

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.

Nonlinear Computational Geometry

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Author : Ioannis Z. Emiris
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-28

Nonlinear Computational Geometry written by Ioannis Z. Emiris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-28 with Mathematics categories.

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.

Topics In Surface Modeling

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Author : Hans Hagen
language : en
Publisher: SIAM
Release Date : 1992-01-01

Topics In Surface Modeling written by Hans Hagen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.

Contains recent ideas and results in three areas of growing importance in curve and surface design: algebraic methods, variational surface design, and some special applications. Leading researchers from throughout the world have contributed their latest work and provided several promising solutions to open issues in surface modeling.

Computer Graphics And Geometric Modelling

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Author : Max K. Agoston
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-04

Computer Graphics And Geometric Modelling written by Max K. Agoston and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-04 with Computers categories.

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.

Algebraic Geometry Modeling In Information Theory

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Author : Edgar Martinez-Moro
language : en
Publisher: World Scientific
Release Date : 2013

Algebraic Geometry Modeling In Information Theory written by Edgar Martinez-Moro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.

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.

Nonlinear Computational Geometry

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Author : Ioannis Z. Emiris
language : en
Publisher:
Release Date : 2009-10-29

Nonlinear Computational Geometry written by Ioannis Z. Emiris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-29 with categories.