| 書(shū)目名稱 | Generalized Curvatures | | 編輯 | Jean-Marie Morvan | | 視頻video | http://file.papertrans.cn/383/382195/382195.mp4 | | 概述 | First coherent and complete account of this subject in book form | | 叢書(shū)名稱 | Geometry and Computing | | 圖書(shū)封面 |  | | 描述 | 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 g | | 出版日期 | Book 2008 | | 關(guān)鍵詞 | Gaussian curvature; Riemannian geometry; Riemannian manifold; computational geometry; computer graphics; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-540-73792-6 | | isbn_softcover | 978-3-642-09300-5 | | isbn_ebook | 978-3-540-73792-6Series ISSN 1866-6795 Series E-ISSN 1866-6809 | | issn_series | 1866-6795 | | copyright | Springer-Verlag Berlin Heidelberg 2008 |
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