查询词典 curvature of a curve

In Riemannian manifolds, one studies Riemannian metric, covariant derivative, Riemannian connection, basic properties of the Riemann curvature tensor, curvature forms etc.

黎曼流形部分主要涉及黎曼度量，黎曼流形的定义，切向量场的协变微分，黎曼联络，黎曼几何的基本定理，曲率张量，曲率形式等概念和理论。

Methods:According to the standard of Borden Ways and Seze Ways to measure the regular cervical and lumbar curvature, then use the sectorial area formula of mathematics geometry to calculate the regular curvature arch form area of cervical and lumbar.

按Borden法和Seze法的标准，测出正常颈曲和腰曲，然后按数学几何学扇形面积计算公式，即S弓形，计算出正常的颈曲、腰曲的弓形面积，并统计正常颈曲126例，正常腰曲114例，经统计学处理得出均值和标准差。

Based on the definitions of metric tensor and curvature tensor, the full expressions of their changes are put forward with asymptotic analysis, where the metric tensor change expression coincides with Ciarlet's, and the curvature tensor change expression is described more accurately than Ciarlet's.

提出的度量张量的改变量与Ciarlet给出的一致，而曲率张量的改变量比Ciarlet给出的更精确。

This paper proposes a robust filter function, called trilateral filter function, to filter the noises in the domains of surface curvature, normal and position at each sample point while the local surface is fitted in a quadratic form. By optimizing the filtering result of curvature tensor, our approach is capable of preserving the feature on the target model.

通过在扫描模型每个采样点处拟合一个二次型曲面，设计了一个鲁棒的滤波函数--三边滤波函数；应用该函数分别对模型表面上每个点的法线、曲率和位置进行滤波；通过对曲率的滤波结果进行优化，可有效地保持三维模型表面上的特征。

When the slope type is UF_CURVE_SLOPE_AUTO, only the magnitude of the curvature vector is used as the curvature's magnitude.

斜率是UF_CURVE_SLOPE_AUTO时，曲率矢量的大小被用作曲率数值，曲率和斜率的方向都是由UG决定～ 5。

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。

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。

The discrete curvature vector based method to fair mesh by modifying vertex positions We first low-pass filter the discrete curvature vector function to make it change more gradually and uniformly, and then modify the vertex positions according the resulted function to improve the fairness of mesh.

以此为基础，给出了两个算法：网格改点光顺的离散曲率向量法基本思想是先用低通滤波算子修匀曲率向量，并由此修改顶点的位置以改善网格的光顺性。具体算法吸取了优化问题中Zoutendijk可行方向法的基本思想。

Through comparing with the results by simulation to study the effects of theprojectile"s final velocity, the angle of rotation and the ballistic trajectory"s migration withdifferent projectile"s rotating speeds, different target"s moving speeds and differentpenetration angles.

通过比较数值模拟的结果来研究不同弹头转速、目标速度、侵彻角对侵彻过程中弹头最终速度、翻转角度和弹道偏移的影响。

I love stationery and all the accoutrement of writing.

我爱文具以及所有的书写的工具装备。