Polyhedral And Algebraic Methods In Computational Geometry

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Polyhedral And Algebraic Methods In Computational Geometry

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Author : Michael Joswig
language : en
Publisher: Springer
Release Date : 2013-01-04

Polyhedral And Algebraic Methods In Computational Geometry written by Michael Joswig and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-04 with Mathematics categories.

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Polyhedral And Algebraic Methods In Computational Geometry

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Author : Michael Joswig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-04

Polyhedral And Algebraic Methods In Computational Geometry written by Michael Joswig 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 2013-01-04 with Mathematics categories.

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Polyhedral And Algebraic Methods In Computational Geometry

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Author : Nik Pachis
language : en
Publisher:
Release Date : 2016-04-01

Polyhedral And Algebraic Methods In Computational Geometry written by Nik Pachis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-01 with categories.

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with history stretching back to antiquity. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry are classical in nature, and may come from mathematical visualization. Other important applications of computational geometry include robotics, geographic information systems, integrated circuit design, computer-aided engineering, and computer vision. Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. This book is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Algorithmic And Experimental Methods In Algebra Geometry And Number Theory

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Author : Gebhard Böckle
language : en
Publisher: Springer
Release Date : 2018-03-22

Algorithmic And Experimental Methods In Algebra Geometry And Number Theory written by Gebhard Böckle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-22 with Mathematics categories.

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Handbook Of Discrete And Computational Geometry

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Author : Csaba D. Toth
language : en
Publisher: CRC Press
Release Date : 2017-11-22

Handbook Of Discrete And Computational Geometry written by Csaba D. Toth and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Computers categories.

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Computational Geometry In C

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Author : Joseph O'Rourke
language : en
Publisher: Cambridge University Press
Release Date : 1998-10-13

Computational Geometry In C written by Joseph O'Rourke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-13 with Computers categories.

This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.

Computational Geometry

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Author : Mark de Berg
language : en
Publisher: Springer Science & Business Media
Release Date : 2000

Computational Geometry written by Mark de Berg 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 2000 with Computers categories.

For students this motivation will be especially welcome.

Principles Of Computational Geometry

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Author : Devang Patil
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Principles Of Computational Geometry written by Devang Patil and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

"Principles of Computational Geometry" delves into the intersection of mathematics, algorithms, and computer science to solve geometric problems using computational methods. We cover a wide range of topics, from fundamental geometric concepts to advanced algorithmic techniques. Our book explores geometric data structures and algorithms designed to efficiently tackle issues like geometric modeling, spatial analysis, and geometric optimization. We introduce readers to key concepts like convex hulls, Voronoi diagrams, and Delaunay triangulations, which serve as building blocks for solving complex geometric problems. Additionally, we discuss techniques for geometric transformation, intersection detection, and geometric search, providing the tools needed to analyze and manipulate geometric data effectively. Throughout the text, we highlight practical applications of computational geometry, ranging from computer graphics and image processing to robotics and geographic information systems. We also explore the theoretical underpinnings of computational geometry, offering insights into the mathematical foundations of algorithms and their computational complexity. Overall, "Principles of Computational Geometry" serves as a comprehensive guide for students, researchers, and practitioners interested in leveraging computational methods to solve geometric problems efficiently and effectively. With its blend of theory and practical applications, our book offers a valuable resource for anyone exploring the rich and diverse field of computational geometry.

The Computer Algebra System Oscar

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Author : Wolfram Decker
language : en
Publisher: Springer Nature
Release Date : 2025-01-30

The Computer Algebra System Oscar written by Wolfram Decker and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Mathematics categories.

This book presents version 1.0 of the new Computer Algebra System OSCAR. Written in Julia, OSCAR builds on and vastly extends four cornerstone systems: ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry. It offers powerful computational tools that transcend the boundaries of the individual disciplines involved. It is freely available, open source software. The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.

Semidefinite Optimization And Convex Algebraic Geometry

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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21

Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.

An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.