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＜電子ブック＞
SAGA – Advances in ShApes, Geometry, and Algebra : Results from the Marie Curie Initial Training Network / edited by Tor Dokken, Georg Muntingh
(Geometry and Computing. ISSN:18666809 ; 10)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
大きさ	XIII, 323 p. 95 illus., 70 illus. in color : online resource
著者標目	Dokken, Tor editor Muntingh, Georg editor SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Algebra LCSH:Computer science—Mathematics LCSH:Computer-aided engineering LCSH:Mathematical models FREE:Geometry FREE:Algebra FREE:Mathematics of Computing FREE:Computer-Aided Engineering (CAD, CAE) and Design FREE:Mathematical Modeling and Industrial Mathematics
一般注記	1 Introduction to ShApes, Geometry, and Algebra: Tor Dokken and Georg Muntingh -- Part I Change of Representation: 2 Numerical methods for implicitisation and their applications: Oliver J. D. Barrowclough -- 3 Sparse implicitization via interpolation: Ioannis Z. Emiris, Tatjana Kalinka, and Christos Konaxis -- 4 The intersection problems of parametric curves and surfaces by means of matrix-based implicit representations: Thang Luu Ba -- Part II Geometric Computing – Algebraic Tools: 5 Singular Zeros of Polynomial Systems: Angelos Mantzaflaris and Bernard Mourrain -- 6 Plane mixed discriminants and toric jacobians: Alicia Dickenstein, Ioannis Z. Emiris and Anna Karasoulou -- 7 Topology of the intersection of two parameterized surfaces, using computations in 4D space: Stéphane Chau and André Galligo --  8 Rational Bézier Formulas with Quaternion and Clifford Algebra Weights: Rimvydas Krasauskas and Severinas Zubé -- Part III Algebraic Geometry for CAD Applications: 9 Algebraic spline geometry – some remarks: Ragni Piene -- 10 On the dimension of spline spaces on triangulations: Nelly Villamizar and Bernard Mourrain -- 11 Polynomial Interpolation Problems in Projective Spaces and Products of Projective Lines: Elisa Postinghel -- 12 Rational parametrizations of edge and corner blends for isogeometric analysis: Heidi E. I. Dahl -- Part IV Practical Industrial Problems: 13 Bisectors and Vorono¨ı diagram of a family of parallel half-lines: I. Adamou, M. Fioravanti, L. Gonzalez-Vega, and B. Mourrain -- 14 Generating an approximate trivariate spline representation for contractible domains: Thien T. Nguyen -- 15 Isogeometric analysis of Navier-Stokes flow using locally refinable B-splines: Peter Nørtoft and Tor Dokken This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis, and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design HTTP:URL=https://doi.org/10.1007/978-3-319-08635-4

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