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Generalized Curvatures
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2008.
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| Edición: | 1st ed. 2008. |
| Colección: | Geometry and Computing,
2 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-540-73792-6 | ||
| 003 | DE-He213 | ||
| 005 | 20220120030255.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2008 gw | s |||| 0|eng d | ||
| 020 | |a 9783540737926 |9 978-3-540-73792-6 | ||
| 024 | 7 | |a 10.1007/978-3-540-73792-6 |2 doi | |
| 050 | 4 | |a QA641-670 | |
| 072 | 7 | |a PBMP |2 bicssc | |
| 072 | 7 | |a MAT012030 |2 bisacsh | |
| 072 | 7 | |a PBMP |2 thema | |
| 082 | 0 | 4 | |a 516.36 |2 23 |
| 100 | 1 | |a Morvan, Jean-Marie. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Generalized Curvatures |h [electronic resource] / |c by Jean-Marie Morvan. |
| 250 | |a 1st ed. 2008. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2008. | |
| 300 | |a XI, 266 p. 107 illus., 36 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Geometry and Computing, |x 1866-6809 ; |v 2 | |
| 505 | 0 | |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. | |
| 520 | |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. | ||
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 0 | |a Mathematics-Data processing. | |
| 650 | 0 | |a Image processing-Digital techniques. | |
| 650 | 0 | |a Computer vision. | |
| 650 | 1 | 4 | |a Differential Geometry. |
| 650 | 2 | 4 | |a Computational Mathematics and Numerical Analysis. |
| 650 | 2 | 4 | |a Computer Imaging, Vision, Pattern Recognition and Graphics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783642093005 |
| 776 | 0 | 8 | |i Printed edition: |z 9783540848400 |
| 776 | 0 | 8 | |i Printed edition: |z 9783540737919 |
| 830 | 0 | |a Geometry and Computing, |x 1866-6809 ; |v 2 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-540-73792-6 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||