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Applicable and Robust Geometric Computing

2001
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Release : 2001
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Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Applicable and Robust Geometric Computing by :

Download or read book Applicable and Robust Geometric Computing written by . This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt: This research project is aimed at aimed at facilitating an effective technology transfer from computational geometry to the various applied fields to which it is relevant. Our technical contributions include algorithmic foundations, practical methodologies, emerging technologies, and applications.

Robust and Error-Free Geometric Computing

2021-02-27 Computers
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Release : 2021-02-27
Genre : Computers
Kind : eBook
Book Rating : 627/5 ( reviews)

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Book Synopsis Robust and Error-Free Geometric Computing by : Dave Eberly

Download or read book Robust and Error-Free Geometric Computing written by Dave Eberly. This book was released on 2021-02-27. Available in PDF, EPUB and Kindle. Book excerpt: This is a how-to book for solving geometric problems robustly or error free in actual practice. The contents and accompanying source code are based on the feature requests and feedback received from industry professionals and academics who want both the descriptions and source code for implementations of geometric algorithms. The book provides a framework for geometric computing using several arithmetic systems and describes how to select the appropriate system for the problem at hand. Key Features: A framework of arithmetic systems that can be applied to many geometric algorithms to obtain robust or error-free implementations Detailed derivations for algorithms that lead to implementable code Teaching the readers how to use the book concepts in deriving algorithms in their fields of application The Geometric Tools Library, a repository of well-tested code at the Geometric Tools website, https://www.geometrictools.com, that implements the book concepts

Robust Algebraic Methods for Geometric Computing

2012-06
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Release : 2012-06
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Kind : eBook
Book Rating : 436/5 ( reviews)

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Book Synopsis Robust Algebraic Methods for Geometric Computing by : Angelos Mantzaflaris

Download or read book Robust Algebraic Methods for Geometric Computing written by Angelos Mantzaflaris. This book was released on 2012-06. Available in PDF, EPUB and Kindle. Book excerpt: Geometric computation in computer aided geometric design and solid modelling calls for solving non-linear polynomial systems in an approximate-yet-certified manner. We introduce new subdivision algorithms that tackle this fundamental problem. In particular, we generalize the univariate so-called continued fraction solver to general dimension. Fast bounding functions, unicity tests projection and preconditioning are employed to speed up convergence. Apart for practical experiments, we provide theoretical bit complexity estimates, as well as bounds in the real RAM model, by means of real condition numbers. A man bottleneck for any real solving method is singular isolated points. We employ local inverse systems and certified numerical computations, to provide certification criteria to treat singular solutions. In doing so, we are able to check existence and uniqueness of singularities of a given multiplicity structure using verification methods, based on interval arithmetic and fixed point theorems. Two major geometric applications are undertaken. First, the approximation of planar semi-algebraic sets, commonly occurring in constraint geometric solving. We present an efficient algorithm to identify connected components and, for a given precision, to compute polygonal and isotopic approximation of the exact set Second, we present an algebraic framework to compute generalized Voronoï diagrams, that is applicable to any diagram type in which the distance from a site can be expressed by a bi-variate polynomial function (anisotropic, power diagram etc.) In cases where this is not possible (eg. Apollonius diagram, VD of ellipses and so on), we extend the theory to implicitly given distance functions.

Handbook of Computational Geometry

1999-12-13 Mathematics
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Release : 1999-12-13
Genre : Mathematics
Kind : eBook
Book Rating : 682/5 ( reviews)

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Book Synopsis Handbook of Computational Geometry by : J.R. Sack

Download or read book Handbook of Computational Geometry written by J.R. Sack. This book was released on 1999-12-13. Available in PDF, EPUB and Kindle. Book excerpt: Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

Geometric Computations with Interval and New Robust Methods

2003-12-15 Computers
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Release : 2003-12-15
Genre : Computers
Kind : eBook
Book Rating : 976/5 ( reviews)

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Book Synopsis Geometric Computations with Interval and New Robust Methods by : H Ratschek

Download or read book Geometric Computations with Interval and New Robust Methods written by H Ratschek. This book was released on 2003-12-15. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes them rounding error free. Familiarises the reader with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations Provides two effective methods for obtaining correct results in interval arithmetic and ESSA

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