SAGA - Advances in ShApes, Geometry, and Algebra : Results from the Marie Curie Initial Training Network
Tor. Dokken
Bok Engelsk 2014 · Electronic books.
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| Utgitt | Cham : : Springer International Publishing, , 2014.
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| Omfang | 1 online resource (324 p.)
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| Opplysninger | Description based upon print version of record.. - ""Preface""; ""Contents""; ""Chapter 1 Introduction to ShApes, Geometry, and Algebra""; ""1.1 Motivation""; ""1.2 The SAGA Initial Training Network""; ""1.3 A Preview of This Book""; ""Part I: Change of Representation""; ""Part II: Geometric Computing: Algebraic Tools""; ""Part III: Algebraic Geometry for CAD Applications""; ""Part IV: Practical Industrial Problems""; ""References""; ""Part I Change of Representation""; ""Chapter 2 Numerical Methods for Implicitisation and Their Applications""; ""2.1 Introduction""; ""2.2 Implicitisation Methods for Low Degree Planar Rational Curves"". - ""2.2.1 Lines in the Plane""""2.2.2 Rational Quadratic Bézier Curves in the Plane""; ""2.2.3 Rational Cubic Bézier Curves in the Plane""; ""2.2.4 Rational Bézier Curves of Higher Degree""; ""2.3 Numerical Methods for Implicitisation of Higher Degree Curves, Surfaces and Hypersurfaces""; ""2.3.1 A General Method for Implicitisation and Approximation Using Linear Algebra""; ""2.3.2 Approximate Implicitisation""; ""2.3.3 Interpolation and Approximation of Point Data""; ""2.3.4 Sparse Implicitisation""; ""2.4 Implicitisation of Envelope Curves, Surfaces and Hypersurfaces"". - ""2.5 Applications of Methods for Implicitisation""""2.5.1 Intersection Algorithms in Computer Aided Design""; ""2.5.1.1 Self-Intersections""; ""2.5.1.2 Curve and Surface Intersection via Algebraic Substitution""; ""2.5.1.3 Surface Trimming""; ""2.5.2 Rendering Curves and Surfaces""; ""2.5.3 Robotics""; ""References""; ""Chapter 3 Sparse Implicitization via Interpolation""; ""3.1 Introduction""; ""3.2 Implicitization Reduced to Elimination""; ""3.3 Algorithm and Implementation""; ""3.3.1 Multidimensional Kernel""; ""3.3.2 Bernstein Basis""; ""3.3.3 Comparisons to Other Methods"". - ""4.5 Matrix-Based Implicit Representations of Parametric Curves in Space""""4.5.1 Construction of the Representation Matrix""; ""4.5.2 Points on Curves and Inversion Problems""; ""4.5.3 Rank of a Representation Matrix at a Singular Point""; ""4.5.4 Curve/Curve Intersection""; ""Conclusion""; ""References""; ""Part II Geometric Computing: Algebraic Tools""; ""Chapter 5 Singular Zeros of Polynomial Systems""; ""5.1 Introduction""; ""5.2 Preliminary Considerations""; ""5.2.1 Isolated Points and Differentials""; ""5.2.2 Quotient Ring and Dual Structure""; ""5.3 Computing Local Ring Structure"". - ""5.3.1 Macaulay's Dialytic Matrices"". - ""Conclusion and Future Work""""References""; ""Chapter 4 The Intersection Problems of Parametric Curves and Surfaces by Means of Matrix-Based Implicit Representations""; ""4.1 Introduction""; ""4.2 Matrix Based Implicit Representations of Parametric Surfaces""; ""4.2.1 Construction of Matrix Representations""; ""4.2.2 Points on Surface and Inversion Problem""; ""4.3 Curve/Surface Intersection""; ""4.3.1 Linearization of a Polynomial Matrix in the Monomial Basis""; ""4.3.2 Extracting the Regular Part of a Non-square Pencil of Matrices""; ""4.4 Surface/Surface Intersection"". - 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) transiti
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 9783319086347
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