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Advances in Geometric Modeling and Processing [[electronic resource] ] : 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010, Proceedings / / edited by Bernard Mourrain, Scott Schaefer, Guoliang Xu
| Advances in Geometric Modeling and Processing [[electronic resource] ] : 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010, Proceedings / / edited by Bernard Mourrain, Scott Schaefer, Guoliang Xu |
| Edizione | [1st ed. 2010.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2010 |
| Descrizione fisica | 1 online resource (X, 315 p. 158 illus.) |
| Disciplina | 516.00285 |
| Collana | Theoretical Computer Science and General Issues |
| Soggetto topico |
Computer graphics
Computer programming Computer science Computer science—Mathematics Discrete mathematics Algorithms Pattern recognition systems Computer Graphics Programming Techniques Theory of Computation Discrete Mathematics in Computer Science Automated Pattern Recognition |
| ISBN |
1-280-38688-6
9786613564801 3-642-13411-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Global Solutions of Well-Constrained Transcendental Systems Using Expression Trees and a Single Solution Test -- Surfaces with Rational Chord Length Parameterization -- Support Function of Pythagorean Hodograph Cubics and G 1 Hermite Interpolation -- Piecewise Tri-linear Contouring for Multi-material Volumes -- An Efficient Algorithm for the Sign Condition Problem in the Semi-algebraic Context -- Constraints on Curve Networks Suitable for G 2 Interpolation -- Computing the Distance between Canal Surfaces -- A Subdivision Approach to Planar Semi-algebraic Sets -- Non-manifold Medial Surface Reconstruction from Volumetric Data -- Decomposing Scanned Assembly Meshes Based on Periodicity Recognition and Its Application to Kinematic Simulation Modeling -- Automatic Generation of Riemann Surface Meshes -- G 1 Bézier Surface Generation from Given Boundary Curve Network with T-Junction -- Efficient Point Projection to Freeform Curves and Surfaces -- Construction of Minimal Catmull-Clark’s Subdivision Surfaces with Given Boundaries -- Parameterization of Star-Shaped Volumes Using Green’s Functions -- Optimal Analysis-Aware Parameterization of Computational Domain in Isogeometric Analysis -- Construction of Subdivision Surfaces by Fourth-Order Geometric Flows with G 1 Boundary Conditions -- Efficient Computation of 3D Clipped Voronoi Diagram -- Selecting Knots Locally for Curve Interpolation with Quadratic Precision -- Eigenmodes of Surface Energies for Shape Analysis. |
| Record Nr. | UNISA-996465639803316 |
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Advances in geometric modeling and processing : 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010 : proceedings / / [edited by] Bernard Mourrain, Scott Schaefer, Guoliang Xu
| Advances in geometric modeling and processing : 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010 : proceedings / / [edited by] Bernard Mourrain, Scott Schaefer, Guoliang Xu |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | New York, : Springer, 2010 |
| Descrizione fisica | 1 online resource (X, 315 p. 158 illus.) |
| Disciplina | 516.00285 |
| Altri autori (Persone) |
MourrainBernard
SchaeferScott XuGuoliang |
| Collana |
LNCS sublibrary. SL 1, Theoretical computer science and general issues
Lecture notes in computer science |
| Soggetto topico |
Geometrical models
Computer-aided design Geometry - Data processing |
| ISBN |
1-280-38688-6
9786613564801 3-642-13411-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Global Solutions of Well-Constrained Transcendental Systems Using Expression Trees and a Single Solution Test -- Surfaces with Rational Chord Length Parameterization -- Support Function of Pythagorean Hodograph Cubics and G 1 Hermite Interpolation -- Piecewise Tri-linear Contouring for Multi-material Volumes -- An Efficient Algorithm for the Sign Condition Problem in the Semi-algebraic Context -- Constraints on Curve Networks Suitable for G 2 Interpolation -- Computing the Distance between Canal Surfaces -- A Subdivision Approach to Planar Semi-algebraic Sets -- Non-manifold Medial Surface Reconstruction from Volumetric Data -- Decomposing Scanned Assembly Meshes Based on Periodicity Recognition and Its Application to Kinematic Simulation Modeling -- Automatic Generation of Riemann Surface Meshes -- G 1 Bézier Surface Generation from Given Boundary Curve Network with T-Junction -- Efficient Point Projection to Freeform Curves and Surfaces -- Construction of Minimal Catmull-Clark’s Subdivision Surfaces with Given Boundaries -- Parameterization of Star-Shaped Volumes Using Green’s Functions -- Optimal Analysis-Aware Parameterization of Computational Domain in Isogeometric Analysis -- Construction of Subdivision Surfaces by Fourth-Order Geometric Flows with G 1 Boundary Conditions -- Efficient Computation of 3D Clipped Voronoi Diagram -- Selecting Knots Locally for Curve Interpolation with Quadratic Precision -- Eigenmodes of Surface Energies for Shape Analysis. |
| Record Nr. | UNINA-9910484061203321 |
| New York, : Springer, 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Polynomial Optimization, Moments, and Applications / / Michal Kocvara, Bernard Mourrain, and Cordian Riener, editors
| Polynomial Optimization, Moments, and Applications / / Michal Kocvara, Bernard Mourrain, and Cordian Riener, editors |
| Edizione | [First edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2023] |
| Descrizione fisica | 1 online resource (XIV, 266 p. 40 illus., 29 illus. in color.) |
| Disciplina | 519.3 |
| Collana | Springer Optimization and Its Applications Series |
| Soggetto topico |
Mathematical optimization
Polynomials |
| ISBN | 3-031-38659-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgments -- Contents -- Contributors -- Polynomial Optimization, Certificates of Positivity, and Christoffel Function -- 1 Introduction -- 2 Notation, Definitions and Preliminary Results -- 3 The Moment-SOS Hierarchy in Polynomial Optimization -- 3.1 A Moment-SOS Hierarchy of Lower Bounds -- 3.2 A Moment-SOS Hierarchy of Upper Bounds -- 4 The Christoffel-Darboux Kernel and Christoffel Functions -- 4.1 Christoffel-Darboux Kernel -- 4.2 Christoffel Function -- 4.3 Some Distinguishing Properties of the CF -- 5 CF, Optimization, and SOS-Certificates of Positivity -- 5.1 The CF to Compare the Hierarchies of Upper and Lower Bounds -- 5.2 The CF and Positive Polynomials -- 5.3 A Disintegration of the CF -- 5.4 Positive Polynomials and Equilibrium Measure -- 6 Conclusion -- Appendix -- References -- Relative Entropy Methods in Constrained Polynomial and Signomial Optimization -- 1 Introduction -- 2 From Relative Entropy Programming to the SAGE Cone -- 2.1 Cones and Optimization -- 2.2 The Exponential Cone and the Relative Entropy Cone -- 2.3 The Basic AM/GM Idea -- 2.4 The SAGE Cone (Sums of Arithmetic-Geometric Exponentials) -- 3 Conditional Nonnegativity Over Convex Sets -- 4 The Circuit View for Unconstrained AM/GM Optimization -- 5 Sublinear Circuits -- 6 Irredundant Decompositions -- 7 Further Developments -- References -- Symmetries in Polynomial Optimization -- 1 Introduction -- 2 Preliminaries on the Moment-SOS Hierarchy in Polynomial Optimization and Semidefinite Programming -- 3 Using Representation Theory in SDPs for Sums-of-Squares -- 3.1 Basic Representation Theory -- 3.2 Representation Theory of Sn -- 3.3 Using Representation Theory to Simplify Semidefinite Formulations -- 4 Invariant Theory -- 4.1 Basics of Invariant Theory -- 4.2 Invariant Theory and Sums of Squares -- 4.3 Symmetric Sums of Squares.
5 Miscellaneous Approaches -- 5.1 Orbit Spaces and Polynomial Optimization -- 5.2 Reduction Via Orbit Decomposition -- 5.3 Symmetries of Optimizers -- References -- Copositive Matrices, Sums of Squares and the Stability Number of a Graph -- 1 Introduction -- 1.1 Organization of the Chapter -- 1.1.1 Notation -- 2 Preliminaries on Polynomial Optimization, Nonnegative Polynomials and Sums of Squares -- 2.1 Sum-of-Squares Certificates for Nonnegativity -- 2.2 Approximation Hierarchies for Polynomial Optimization -- 2.3 Optimality Conditions and Finite Convergence -- 3 Sum-of-Squares Approximations for COPn -- 3.1 Cones Based on Pólya's Nonnegativity Certificate -- 3.2 Lasserre-Type Approximation Cones -- 3.3 Links Between the Various Approximation Cones for COPn -- 4 Exactness of Sum-of-Squares Approximations for COPn -- 4.1 Exactness of the Conic Approximations Kn(r) -- 4.2 Exactness of the Conic Approximations LAS(r)n -- 4.3 The Cone of 55 Copositive Matrices -- 5 The Stability Number of a Graph α(G) -- 5.1 The Hierarchy ζ(r)(G) -- 5.2 The Hierarchy (r)(G) -- 5.2.1 Some Key Ingredients for the Proof for Theorem 22 -- 6 Concluding Remarks -- References -- Matrix Factorization Ranks Via Polynomial Optimization -- 1 Introduction and Motivation for Matrix Factorization Ranks -- 1.1 Applications of Nonnegative Factorization -- 1.2 Commonly Used Notation -- 1.3 On Computing the Nonnegative Rank -- 1.4 Other Factorization Ranks -- 2 Bounding Matrix Factorization Ranks -- 2.1 A Brief Introduction to Polynomial Optimization -- 2.2 Generalized Moment Problems -- 2.3 Constructing a Hierarchy of Lower Bounds for CP-Rank -- 2.4 A Note on Computing Hierarchies of SDPs -- 3 Exploiting Sparsity -- 3.1 An Abbreviated Introduction to Ideal Sparsity -- 3.2 Ideal Sparsity in Approximating CP-Rank -- 3.3 Advantages of the Sparse Hierarchy -- 4 Summary -- References. Polynomial Optimization in Geometric Modeling -- 1 Geometric Modeling and Polynomials -- 2 Polynomial Optimization Problems and Convex Relaxations -- 2.1 Sum of Squares Relaxations -- 2.2 Moment Relaxations -- 2.3 Computing the Minimizers -- 3 Minimal Enclosing Ellipsoids of Semi-algebraic Sets -- 4 Parameterized Surfaces -- 4.1 Closest Point and Surface-Surface Intersection -- 4.2 Bounding Box and Enclosing Ellipsoid of Parametric Surfaces -- 5 Robots and Mechanisms -- 5.1 Direct Kinematic Problem -- 5.2 Bounding Box of Robot Workspace -- 5.3 Enclosing Ellipsoid of Robot Workspace -- 5.4 Trajectories of a Parallel Robot -- 6 Conclusion -- References -- Assessing Safety for Control Systems Using Sum-of-Squares Programming -- 1 Introduction -- 1.1 Organization -- 1.2 Notation -- 2 Safety in Control Systems -- 2.1 Relationship Between Invariance and Safety -- 2.2 Control Invariance for Continuous-Time Systems -- 2.2.1 Control Invariance with Set Representation -- 2.2.2 Control Invariance with Function Representation -- 2.3 Control Invariance for Discrete-Time Systems -- 2.4 Summary -- 3 Sum-of-Squares Programming -- 3.1 Sum-of-Squares Decomposition -- 3.2 Convex Optimisation for Safety -- 3.3 Safety for Continuous-Time Systems -- 3.4 Safety for Discrete-Time Systems -- 3.5 Summary -- 4 Safety for Linear Systems with Constrained Inputs -- 4.1 Unit Peak Input -- 4.2 Summary -- 5 Applications -- 5.1 Nonlinear Control Affine System -- 5.2 Linear System -- 6 Conclusion -- Appendix -- References -- Polynomial Equations: Theory and Practice -- 1 Polynomial Equations in Optimization -- 2 Systems of Equations and Algebraic Varieties -- 3 Number of Solutions -- 3.1 Bézout's Theorem -- 3.2 Kushnirenko's Theorem -- 3.3 Bernstein's Theorem -- 4 Computational Methods -- 4.1 Normal Form Methods -- 4.2 Homotopy Continuation. 5 Case Study: 27 Lines on the Clebsch Surface -- References -- Index. |
| Record Nr. | UNINA-9910799488503321 |
| Cham, Switzerland : , : Springer, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||