Generalized Curvatures

• Κύριος συγγραφέας: Morvan, Jean-Marie (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Σειρά: Geometry and Computing, 2
• Θέματα: Mathematics.; Computer graphics.; Computer mathematics.; Differential geometry.; Differential Geometry.; Computational Mathematics and Numerical Analysis.; Computer Imaging, Vision, Pattern Recognition and Graphics.

The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space (E ,), endowed with its standard scalar product. Let us state precisely what we mean by a geometric quantity. Consider a subset N S of points of the N-dimensional Euclidean space E , e...

Πίνακας περιεχομένων:

• Motivations
• Motivation: Curves
• Motivation: Surfaces
• Background: Metrics and Measures
• Distance and Projection
• Elements of Measure Theory
• Background: Polyhedra and Convex Subsets
• Polyhedra
• Convex Subsets
• Background: Classical Tools in Differential Geometry
• Differential Forms and Densities on EN
• Measures on Manifolds
• Background on Riemannian Geometry
• Riemannian Submanifolds
• Currents
• On Volume
• Approximation of the Volume
• Approximation of the Length of Curves
• Approximation of the Area of Surfaces
• The Steiner Formula
• The Steiner Formula for Convex Subsets
• Tubes Formula
• Subsets of Positive Reach
• The Theory of Normal Cycles
• Invariant Forms
• The Normal Cycle
• Curvature Measures of Geometric Sets
• Second Fundamental Measure
• Applications to Curves and Surfaces
• Curvature Measures in E2
• Curvature Measures in E3
• Approximation of the Curvature of Curves
• Approximation of the Curvatures of Surfaces
• On Restricted Delaunay Triangulations.