Librería Samer Atenea
Librería Aciertas (Toledo)
Kálamo Books
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Librería Kolima (Madrid)
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1 Arrangements Efi Fogel, Dan Halperin, Lutz Kettner, Monique Teillaud, Ron Wein, Nicola Wolpert 1.1 Introduction1.2 Chronicles1.3 Exact Construction of Planar Arrangements 1.3.1Construction by Sweeping 1.3.2 Incremental Construction1.4 Software for Planar Arrangements1.4.1 The Cgal Arrangements Package1.4.2 Arrangements Traits 1.4.3 Traits Classes from Exacus 1.4.4An Emerging Cgal Curved Kernel1.4.5 How To Speed UpYour Arrangement Computation in Cgal 1.5 Exact Construction in 3-Space 1.5.1 Sweeping Arrangements of Surfaces 1.5.2Arrangements of Quadricsin 3D1.6 Controlled Perturbation: Fixed-Precision Approximation of Arrangements1.7 Applications 1.7.1 Boolean Operations for Conics 1.7.2 Motion Planning for Discs 1.7.3 Lower Envelopes for Path Verification in Multi-Axis NC-Machining1.7.4 Maximal Axis-Symmetric Polygon Containedin a Simple Polygon 1.7.5 Molecular Surfaces1.7.6 Additional Applications 1.8 Further Reading and Open problems2 Curved Voronoi Diagrams Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec2.1 Introduction2.2 Lower Envelopes and Minimization Diagrams 2.3 Affine Voronoi Diagrams 2.3.1 Euclidean Voronoi Diagrams of Points2.3.2 Delaunay Triangulation2.3.3 PowerDiagrams2.4 Voronoi Diagrams with Algebraic Bisectors 2.4.1 Möbius Diagrams2.4.2 Anisotropic Diagrams 2.4.3Apollonius Diagrams2.5 Linearization 2.5.1Abstract Diagrams2.5.2 Inverse Problem 2.6 Incremental Voronoi Algorithms2.6.1 Planar Euclidean diagrams2.6.2 Incremental Construction2.6.3 The Voronoi Hierarchy 2.7 Medial Axis 2.7.1 Medial Axis and Lower Envelope 2.7.2 Approximation of the Medial Axis 2.8 Voronoi Diagrams in Cgal 2.9 Applications 3 Algebraic Issues in Computational Geometry Bernard Mourrain, Sylvain Pion, Susanne Schmitt, Jean-Pierre Técourt, Elias Tsigaridas, Nicola Wolpert 3.1 Introduction3.2 Computers and Numbers3.2.1 Machine Floating Point Numbers: the IEEE 754 norm........1193.2.2 Interval Arithmetic ......................................1203.2.3 Filters..................................................1213.3 Effective Real Numbers .......................................1233.3.1 Algebraic Numbers ......................................1243.3.2 Isolating Interval Representation of Real Algebraic Numbers 3.3.3 Symbolic Representation of Real Algebraic Numbers .........1253.4 Computing with Algebraic Numbers ............................1263.4.1 Resultant...............................................1263.4.2 Isolation................................................1313.4.3Algebraic Numbers of Small Degree ........................1363.4.4 Comparison.............................................1383.5 Multivariate Problems ........................................1403.6 Topology of Planar Implicit Curves.............................1423.6.1 The Algorithm from a Geometric Point of View .............1433.6.2 Algebraic Ingredients.....................................1443.6.3 How to Avoid Genericity Conditions .......................1453.7 Topology of 3d Implicit Curves.................................1463.7.1 Critical Points and Generic Position........................1473.7.2 The Projected Curves ....................................1483.7.3 Lifting a Point of the Projected Curve......................1493.7.4 Computing Points of the Curve above CriticalValues.........1513.7.5 Connecting the Branches .................................1523.7.6 The Algorithm ..........................................1533.8 Software ....................................................1544 Differential Geometry on Discrete Surfaces David Cohen-Steiner, Jean-Marie Mo
