SAGA - Advances in ShApes, Geometry, and Algebra: Results from the Marie Curie Initial Training Network by Tor DokkenSAGA - Advances in ShApes, Geometry, and Algebra: Results from the Marie Curie Initial Training Network by Tor Dokken

SAGA - Advances in ShApes, Geometry, and Algebra: Results from the Marie Curie Initial Training…

byTor DokkenEditorGeorg Muntingh

Hardcover | November 13, 2014

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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.

Title:SAGA - Advances in ShApes, Geometry, and Algebra: Results from the Marie Curie Initial Training…Format:HardcoverDimensions:323 pagesPublished:November 13, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319086340

ISBN - 13:9783319086347

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Table of Contents

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¨Ä± 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 Nortoft and Tor Dokken.