| Generalized Curvatures Contributor(s): Morvan, Jean-Marie (Author) |
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ISBN: 3642093000 ISBN-13: 9783642093005 Publisher: Springer OUR PRICE: $123.49 Product Type: Paperback - Other Formats Published: October 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Number Systems - Computers | Computer Vision & Pattern Recognition - Mathematics | Geometry - Differential |
| Dewey: 006.6 |
| Series: Geometry and Computing |
| Physical Information: 0.59" H x 6.14" W x 9.21" (0.87 lbs) 266 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |