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Advanced and Innovative Models And Tools for the development of Semantic-based systems for Handling, Acquiring, and Processing knowledge Embedded in multidimensional digital objects. |
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The focus of this project is the solution of polynomial systems by matrix methods. Our approach leads naturally to problems in structured and sparse matrices. Real root isolation, either of one univariate polynomial or of a polynomial system, is of special interest, especially in applications in geometric modeling, CAD or computational geometry. We are interested in computational geometry, actually, in what concerns curves and surfaces. The framework of this work is the european project ECG. |
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The project "GAIA II - "Intersection algorithms for geometry based IT-applications using approximate algebraic methods" combines knowledge from Computer Aided Geometric Design (CAGD) and classical algebraic geometry to improve intersection algorithms for Computer Aided Design (CAD) types system. 2002-2005 |
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The overall objectives of the project are: - To take into consideration the multidisciplinary nature of the problem and to develop cooperative research in three main directions: computational geometry, computer algebra and numerical analysis. - To give Effective Computational Geometry for Curves and Surfaces solid mathematical and algorithmic foundations, to provide solutions to key problems and to validate our theoretical advances through extensive experimental research and the development of software packages that could serve as steps towards a standard for safe and effective geometric computing. - To promote collaborative research, the interchange between the partners (workshops), exchanges of Ph.D. students and research staff. - To disseminate our results through research reports, open source softwares, software packages and through a program of open activities including summer-schools and advanced courses intended to academia and industry. |
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