SAGA – Advances in ShApes, Geometry, and Algebra (eBook)

Results from the Marie Curie Initial Training Network

Tor Dokken, Georg Muntingh (Herausgeber)

eBook Download: PDF

2014 | 2014
XIII, 323 Seiten
Springer International Publishing (Verlag)
978-3-319-08635-4 (ISBN)

Infos

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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 24.10.2014
• Reihe/Serie: Geometry and Computing
• Reihe/Serie: Geometry and Computing
• Zusatzinfo: XIII, 323 p. 95 illus., 70 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Informatik ► Weitere Themen ► CAD-Programme
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• Schlagworte: Algebra • computing • Geometry • Representation • Splines
• ISBN-10: 3-319-08635-9 / 3319086359
• ISBN-13: 978-3-319-08635-4 / 9783319086354