Dokken / Muntingh SAGA – Advances in ShApes, Geometry, and Algebra

Results from the Marie Curie Initial Training Network
2014
ISBN: 978-3-319-08635-4
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 10, 323 Seiten, eBook

Reihe: Geometry and Computing

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.

Zielgruppe

Research

Autoren/Hrsg.

Dokken, Tor

Muntingh, Georg

Inhaltsverzeichnis

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¨i 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.