向量

It is based on the discrete model of finite analysis to get curvature ,normal vector, direction and geodesic curve,then to analyze and design the structure.

基于有限元分析的离散模型，将离散微分几何领域的最新成果运用于膜结构设计，求解曲面曲率，法向量，主方向及测地线，进行结构分析设计。

Triangular mesh, normal vector, principal curvature, gaussian curvature, mean curvature

三角网格，法向量，主曲率，高斯曲率，平均曲率

Let be a compact pseudo-umbilical submanifolds with parallel mean curvature vector in the quasi constant curvature space.

设Mn是拟常曲率空间Nn+p中具有平行平均曲率向量的紧致伪脐子流形，论证得到了这种子流形的两个内蕴积分不等式，从而给出了Mn是全脐子流形的两个内蕴充分条件。

The shape-form analysis and load analysis were done by nonlinear FEM. On the basis of surface FEM grid nodes, geometry property research of structure curved surface was progressed, including normal vector, GAUSS curvature, mean curvature and principal direction vector. In this process, the approximate expression of surface didn't need to he known.

采用非线性有限元法进行了膜结构的形态分析和荷载分析，得到了曲面有限元网格；通过离散微分几何方法，研究了薄膜结构曲面的几何性质，包括曲面的法线向量、高斯曲率、平均曲率和主方向矢量，避免了复杂的曲面拟合过程。

Mesh fairness problem We propose the conception of discrete curvature vector for meshes, and suggest a new fairness criterion that a mesh is fair if changes in discrete curvature vectors of this mesh are gradual and uniform Based on this fairness criterion, two algorithms are presented.

网格的光顺问题本文提出了离散曲率向量的概念，并以其变化平稳均匀作为网格光顺的准则，这一准则兼顾了曲率大小及法向的变化。

A pinching theorem of compact pseudoumbilical submanifolds with parallel mean curvature vector in a locally symmetric conformally flat Riemannian manifolds

研究了复空间形式中具有平行法平均曲率向量的紧致全实伪脐子流形。

This paper develops methods for tangent direction continuous (G1) and both tangent direction and curvature continuous (G2) interpolation of a range of points on surface with specified tangent and either a curvature vector or a geodesic curvature at every point.

给出了数据点的切方向(切方向及曲率向量或测地曲率值)指定而G1连续(G2连续)插值曲面上任意点列的方法。

This pepediscusses compact submanifoldsoftheunit sphere Study is made on conditions ofsubmanifolds with parallel mean curvature vector,submanifolds with flat normal bundle and pseudo-umbilical submanifolds to be umbilical respectively.

本文讨论球的紧致子流形，研究具平行平均曲率向量的，具平坦法丛的、以及伪脐子流形成为全脐子流形的条件，得到几个关于第二基本形式长度千方S的pinching条件。

The Pinching problems are discussed on the sectional curvature of compact space-like pseudo-umbilical submanifolds M~n with parallel mean curvature vector in De Sitter space S~_p, and the theory of reduction of the codimension is obtained in De Sitter space through evaluating the Laplacian of square of the length.

讨论了De Sitter空间Snp+p中，具有平行平均曲率向量的紧致类空伪脐子流形Mn的截面曲率的拼挤问题，通过估计第二基本形式模长平方的Laplacian，得到了De Sitter空间中的余维数压缩定理。

We propose a unified method to approximate important geometric attributes, including normal vector, gauss curvature, mean curvature, principal curvatures and principal directions on point sampled surface. Based on MLS projection our method is robust to noise and stable to the sampling density.

曲面的微分性质包括法向量和切平面、高斯曲率、平均曲率、主曲率和主方向，在计算机图形学、机器视觉和计算机辅助设计等领域发挥了重要的作用，比如曲面绘制、内外测试、曲面重建、曲面简化、去除曲面噪声和模型分割等。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。