作者: 胰臟 時(shí)間: 2025-3-21 22:18 作者: 鴿子 時(shí)間: 2025-3-22 02:18 作者: mastoid-bone 時(shí)間: 2025-3-22 06:10 作者: Wordlist 時(shí)間: 2025-3-22 12:24
Riemannian Submanifoldsect generalization in any dimension and codimension of curves and surfaces in E3. Their extrinsic curvatures generalize the Gauss and mean curvatures of surfaces. We review (without proof) some fundamental notions on the subject. Classical books on Riemannian submanifolds are [26, 27].作者: AROMA 時(shí)間: 2025-3-22 13:12 作者: AROMA 時(shí)間: 2025-3-22 19:55 作者: 傲慢人 時(shí)間: 2025-3-23 01:11
The Steiner Formula for Convex Subsetshat the convexity of .implies that this volume is polynomial in ε, the coefficients (Φ.(.),0.) depending on the geometry of .[77]. Up to a constant, these coefficients (called the . of Minkowski) are the valuations, which appear in Definition 23 and Theorem 28 of Hadwiger. Moreover, these coefficien作者: 提升 時(shí)間: 2025-3-23 05:00 作者: Mortar 時(shí)間: 2025-3-23 05:35
Motivation: Curvesese invariants can be done. Our goal is to investigate a framework in which a geometric theory of both smooth and discrete objects is simultaneously possible. To motivate this work, we begin with two simple examples: the length and curvature of a curve.作者: 戰(zhàn)役 時(shí)間: 2025-3-23 09:45 作者: Conscientious 時(shí)間: 2025-3-23 15:19
R. F. Bishop,J. B. Parkinson,Yang Xianiant forms described in Chap. 19 have a typical Riemannian flavor. That is why we give a brief survey of Riemannian geometry. The reader interested in the subject can consult [10], [29], [76], [57, Tome 1, Chaps. 4 and 5], or [67].作者: FIS 時(shí)間: 2025-3-23 20:42
https://doi.org/10.1007/978-3-0348-0843-9rea of a sequence of triangulations inscribed in a fixed cylinder of E. may tend to infinity when the sequence tends to the cylinder for the Hausdorff topology. We give here a general . by adding a suitable geometric assumption: we assume that the tangent bundle of the sequence tends to the tangent bundle of ., in precise sense.作者: Euthyroid 時(shí)間: 2025-3-24 00:04
Book 2008calar 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 re作者: 激怒某人 時(shí)間: 2025-3-24 02:26
Background on Riemannian Geometryiant forms described in Chap. 19 have a typical Riemannian flavor. That is why we give a brief survey of Riemannian geometry. The reader interested in the subject can consult [10], [29], [76], [57, Tome 1, Chaps. 4 and 5], or [67].作者: 無孔 時(shí)間: 2025-3-24 09:36 作者: 幻想 時(shí)間: 2025-3-24 11:40 作者: 完整 時(shí)間: 2025-3-24 16:07
Introduction a circle is geometric for . but not for ., while the property of being a conic or a straight line is geometric for both . and .. This point of view may be generalized to any subset . of any vector space . endowed with a group . acting on it..In this book, we only consider the group of rigid motions作者: 獨(dú)輪車 時(shí)間: 2025-3-24 21:04 作者: pineal-gland 時(shí)間: 2025-3-25 00:35 作者: 結(jié)構(gòu) 時(shí)間: 2025-3-25 05:42
Stefan M. Duma Ph.D.,Steven Rowson Ph.D. a circle is geometric for . but not for ., while the property of being a conic or a straight line is geometric for both . and .. This point of view may be generalized to any subset . of any vector space . endowed with a group . acting on it..In this book, we only consider the group of rigid motions作者: FLINT 時(shí)間: 2025-3-25 10:16
M. A. Rao,D. A. Rao,K. R. D. Royevaluation of these curvatures cannot be done by differentiations of a parametrization of the boundary, because of the lack of differentiability. We shall directly evaluate them for convex polyhedra. All these techniques will be generalized in the next chapters to objects which are not convex, but w作者: 忍受 時(shí)間: 2025-3-25 15:37
https://doi.org/10.1007/978-3-540-73792-6Gaussian curvature; Riemannian geometry; Riemannian manifold; computational geometry; computer graphics; 作者: 疏遠(yuǎn)天際 時(shí)間: 2025-3-25 17:53
978-3-642-09300-5Springer-Verlag Berlin Heidelberg 2008作者: 刺耳 時(shí)間: 2025-3-25 20:58 作者: Restenosis 時(shí)間: 2025-3-26 03:43 作者: Curmudgeon 時(shí)間: 2025-3-26 07:16 作者: visceral-fat 時(shí)間: 2025-3-26 09:02 作者: expire 時(shí)間: 2025-3-26 16:28 作者: 盡責(zé) 時(shí)間: 2025-3-26 17:43 作者: brother 時(shí)間: 2025-3-27 00:47
Currentsrt introduction to this subject. We end this chapter with important theorems used in the approximation and convergence results proved in the succeeding parts of the book. A nice introduction to this subject can be found in [63].作者: disrupt 時(shí)間: 2025-3-27 03:29
Jean-Marie MorvanFirst coherent and complete account of this subject in book form作者: 維持 時(shí)間: 2025-3-27 05:24
https://doi.org/10.1007/978-1-4612-4772-2Our goal in this chapter is to point out the difficulties arising when one evaluates the area and the curvatures of a surface by approximation.作者: agenda 時(shí)間: 2025-3-27 10:29
K. E. Kürten,M. L. Ristig,J. W. ClarkThere is an abundant literature on convexity, crucial in many fields of mathematics. We shall mention the basic definitions and some fundamental results (without proof), useful for our topic. In particular, we shall focus on the properties of the volume of a convex body and its boundary. The reader can consult [9, 71, 74, 79] for details.作者: 鍍金 時(shí)間: 2025-3-27 17:06 作者: ALLAY 時(shí)間: 2025-3-27 18:12
J. N. Herrera,L. Blum,Fernando VericatLet us introduce the concept of . on a .-manifold . of dimension . with or without boundary ?. (.≥1,.≥2). The goal is to use suitable differential forms to construct measures, with which one can define the notion of ., fundamental in our context. Chapter 3 of [11] gives a complete introduction to the subject.作者: 不透明性 時(shí)間: 2025-3-28 00:03
Situation, Jetztsein, Psychose,We have seen in Chap. 13 that the length of a curve is classically defined as the supremum of the lengths of polygonal lines inscribed in it. Our purpose here is to compare the length of a given smooth curve with the length of a curve close to it, or more precisely with the length of a polygonal line inscribed in it.作者: Indelible 時(shí)間: 2025-3-28 04:07 作者: MAOIS 時(shí)間: 2025-3-28 07:20
Hédi Hamdi,Charfeddine Mrad,Rachid NasriIn previous chapters, we have seen that it is possible to define . which describe the global shape of two classes of subsets of E., namely the convex bodies and the smooth submanifolds. A good challenge is to find larger classes of subsets on which a more general theory holds. In 1958, Federer [43] made a major advance in two directions:作者: 本能 時(shí)間: 2025-3-28 13:19 作者: 神圣不可 時(shí)間: 2025-3-28 16:22 作者: CLASH 時(shí)間: 2025-3-28 20:00
Convex SubsetsThere is an abundant literature on convexity, crucial in many fields of mathematics. We shall mention the basic definitions and some fundamental results (without proof), useful for our topic. In particular, we shall focus on the properties of the volume of a convex body and its boundary. The reader can consult [9, 71, 74, 79] for details.作者: Scintillations 時(shí)間: 2025-3-29 00:35
Differential Forms and Densities on ECurvature measures will be defined by integrating .. Let us introduce their definitions, beginning with exterior algebra in a vector space and continuing with the smooth category. We only give here a brief survey. See [59] for a complete one.作者: GUEER 時(shí)間: 2025-3-29 04:14 作者: 沒有準(zhǔn)備 時(shí)間: 2025-3-29 07:42
Approximation of the Length of CurvesWe have seen in Chap. 13 that the length of a curve is classically defined as the supremum of the lengths of polygonal lines inscribed in it. Our purpose here is to compare the length of a given smooth curve with the length of a curve close to it, or more precisely with the length of a polygonal line inscribed in it.作者: 殺菌劑 時(shí)間: 2025-3-29 14:50
Tubes FormulaIn Chap. 16, we have seen that the volume of the parallel body of a convex body with smooth boundary is a polynomial whose coefficients depend on the second fundamental form of the boundary. This formula has been generalized by Weyl [82] for the volume of tubes around any smooth submanifold in E., with or without boundary.作者: wall-stress 時(shí)間: 2025-3-29 15:34
Subsets of Positive ReachIn previous chapters, we have seen that it is possible to define . which describe the global shape of two classes of subsets of E., namely the convex bodies and the smooth submanifolds. A good challenge is to find larger classes of subsets on which a more general theory holds. In 1958, Federer [43] made a major advance in two directions:作者: 影響深遠(yuǎn) 時(shí)間: 2025-3-29 22:50 作者: 評論性 時(shí)間: 2025-3-30 03:55
Stefan M. Duma Ph.D.,Steven Rowson Ph.D.ate precisely what we mean by a geometric quantity. Consider a subset . of points of the .-dimensional Euclidean space E., endowed with its standard scalar product < ., . >. Let . be the group of rigid motions of E.. We say that a quantity .(.) associated to . is . if the corresponding quantity .[.(作者: Cytology 時(shí)間: 2025-3-30 06:14 作者: trigger 時(shí)間: 2025-3-30 09:38 作者: Conduit 時(shí)間: 2025-3-30 13:04 作者: RALES 時(shí)間: 2025-3-30 16:43
Oriol T. Valls,Zlatko Tesanovicect generalization in any dimension and codimension of curves and surfaces in E3. Their extrinsic curvatures generalize the Gauss and mean curvatures of surfaces. We review (without proof) some fundamental notions on the subject. Classical books on Riemannian submanifolds are [26, 27].作者: Petechiae 時(shí)間: 2025-3-30 22:18
E. Krotscheck,J. L. Epstein,M. Saarelart introduction to this subject. We end this chapter with important theorems used in the approximation and convergence results proved in the succeeding parts of the book. A nice introduction to this subject can be found in [63].作者: Ganglion-Cyst 時(shí)間: 2025-3-31 02:29 作者: murmur 時(shí)間: 2025-3-31 06:25
M. A. Rao,D. A. Rao,K. R. D. Royhat the convexity of .implies that this volume is polynomial in ε, the coefficients (Φ.(.),0.) depending on the geometry of .[77]. Up to a constant, these coefficients (called the . of Minkowski) are the valuations, which appear in Definition 23 and Theorem 28 of Hadwiger. Moreover, these coefficien
