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130626 ||| eng |
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|a 9783540737926
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|a Morvan, Jean-Marie
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| 245 |
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|a Generalized Curvatures
|h Elektronische Ressource
|c by Jean-Marie Morvan
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| 250 |
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|a 1st ed. 2008
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2008, 2008
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| 300 |
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|a XI, 266 p. 107 illus., 36 illus. in color
|b online resource
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|a 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
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Image processing / Digital techniques
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| 653 |
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|a Computer vision
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| 653 |
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|a Computational Mathematics and Numerical Analysis
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| 653 |
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|a Mathematics / Data processing
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| 653 |
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|a Computer Imaging, Vision, Pattern Recognition and Graphics
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| 653 |
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|a Differential Geometry
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Geometry and Computing
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| 028 |
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|a 10.1007/978-3-540-73792-6
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| 856 |
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|u https://doi.org/10.1007/978-3-540-73792-6?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 516.36
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| 520 |
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|a 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 , endowed with its standard N scalar product. LetG be the group of rigid motions of E . We say that a 0 quantity Q(S) associated toS is geometric with respect toG if the corresponding 0 quantity Q[g(S)] associated to g(S) equals Q(S), for all g?G . For instance, the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG . But the distance from the origin O to the closest point ofS is not, 0 since it is not invariant under translations ofS. It is important to point out that the property of being geometric depends on the chosen group. For instance, ifG is the 1 N group of projective transformations of E , then the property ofS being a circle is geometric forG but not forG , while the property of being a conic or a straight 0 1 line is geometric for bothG andG . This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on it
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