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Medial/Skeletal Linking Structures for Multi-Region Configurations.
The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions \{ \Omega_i\} in \mathbb{R}^{n+1} which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries \mathcal{B}_i in a...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2018.
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| Colección: | Memoirs of the American Mathematical Society.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction; Part 1 . Medial/Skeletal Linking Structures; Chapter 2. Multi-Region Configurations in \Râ#x81;¿â#x81;ð¹; Local Models for Regions at Singular Points on Boundary; The Space of Equivalent Configurations via Mappings of a Model; Configurations Allowing Containment of Regions; Chapter 3. Skeletal Linking Structures for Multi-Region Configurations in \Râ#x81;¿â#x81;ð¹; Skeletal Structures for Single Regions; Skeletal Linking Structures for Multi-Region Configurations; Linking Between Regions and Between Skeletal Sets.
- Chapter 4. Blum Medial Linking Structure for a Generic Multi-Region ConfigurationBlum Medial Axis for a Single Region with Smooth Generic Boundary; Structure of Maxwell Set Described by \cRâ#x81;ð-Versal Unfoldings; Addendum to Generic Blum Structure for a Region with Boundaries and Corners; Spherical Axis of a Configuration; Blum Medial Linking Structure; Existence of a Blum Medial Linking Structure; Addendum: Classification of Linking Types for Blum Medial Linking Structures in \R³; Chapter 5. Retracting the Full Blum Medial Structure to a Skeletal Linking Structure.
- Example of Evolving Skeletal Linking Structure for Simple Generic TransitionRetracting Full Blum Linking Structure via Smoothing; Part 2 . Positional Geometry of Linking Structures; Chapter 6. Questions Involving Positional Geometry of a Multi-Region Configuration; Chapter 7. Shape Operators and Radial Flow for a Skeletal Structure; The Radial Flow; Radial and Edge Shape Operators; Curvature Conditions and Nonsingularity of the Radial Flow; Evolution of the Shape Operators Under the Radial Flow; Chapter 8. Linking Flow and Curvature Conditions; Nonsingularity of the Linking Flow.
- Special MÃœbius Transformations of Matrices and OperatorsEvolution of the Shape Operators Under the Linking Flow; Chapter 9. Properties of Regions Defined Using the Linking Flow; Medial/Skeletal Linking Structures in the Unbounded Case; Medial/Skeletal Linking Structures for the Bounded Case; Chapter 10. Global Geometry via Medial and Skeletal Linking Integrals; Defining Medial and Skeletal Linking Integrals; Computing Boundary Integrals via Medial Linking Integrals; Computing Integrals as Skeletal Linking Integrals via the Linking Flow.
- Skeletal Linking Integral Formulas for Global InvariantsChapter 11. Positional Geometric Properties of Multi-Region Configurations; Neighboring Regions and Measures of Closeness; Measuring Positional Significance of Objects Via Linking Structures; Properties of Invariants for Closeness and Positional Significance; Tiered Linking Graph; Higher Order Positional Geometric Relations via Indirect Linking; Part 3 . Generic Properties of Linking Structures via Transversality Theorems; Chapter 12. Multi-Distance and Height-Distance Functions and Partial Multi-Jet Spaces.