SAGA – Advances in ShApes, Geometry, and Algebra
Springer International Publishing (Verlag)
978-3-319-08634-7 (ISBN)
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.
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.
| Erscheint lt. Verlag | 13.11.2014 |
|---|---|
| Reihe/Serie | Geometry and Computing |
| Zusatzinfo | XIII, 323 p. 95 illus., 70 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 672 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Informatik ► Weitere Themen ► CAD-Programme | |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Algebra • computing • Geometry • Representation • Splines |
| ISBN-10 | 3-319-08634-0 / 3319086340 |
| ISBN-13 | 978-3-319-08634-7 / 9783319086347 |
| Zustand | Neuware |
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