测地线

This paper presents a geodesic-based constrained deformation method for polygonal mesh models.

提出了一种基于测地线的多边形网格模型的约束变形方法。

Then, based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the principal normal surfaces of curves, the curves with constant Gaussian curvature and the two curves of which the ratio of their functions is constant can all be obtained, as well as the properties of geodesic curve and lumbar curve.

再根据平均曲率、高斯曲率及主曲率函数，能得到曲线的主法线曲面的极小轨迹、常高斯曲率曲线及两个主曲率函数之比为常数的曲线。还给出曲面上测地线和腰曲线的性质。

Secondly,for nonlinear vibratory systems,the relationship between a class of stationary geodesics of the Riemannian manifold and the nonlinear normal modes is found.

进而，将类似的对应关系推广应用到非线性振动系统中，得到了非线性模态与 Riemann 流形上的极值测地线之间的对应关系。

Newton's method; Riemannian manifold; Smale's point estimate theory; section of a vector bundle; geodesic; Lie group; one-parameter subgroup

基础科学，数学，几何、拓扑Newton法； Riemann流形； Smale点估计理论；向量丛的截面；测地线；李群；单参数子群

They've understood there is a generalized concept of straightness.

他们已经知道有一个广义概念的直线，它被称为测地线。

In 1898, Hadamard produced a specific example of geodesics on a surface of constant negative curvature which had this property of chaos.

在1898年， Hadamard 构造了一个在常负曲率表面关于测地线的特别例子，这个例子具有上述混沌特性。

The method avoids triangulating or reconstructing the point cloud to be a surface model so that it is practicable for dealing with the point cloud with a huge number of scattered points.

对点云模型的处理已成为近年来研究的热点，如研究针对点云数据的曲面重建、分割、布尔操作等。点云模型上2点间的测地线计算作为点云模型处理的基础之一，受到越来越多的关注。

Its level set methods are investigated in detail, and a fast initialization method for level set based on the threshold over interframe difference is proposed.

正是由于测地线主动轮廓模型的这些优点，我们对它的Level Set方法进行了研究，提出了基于帧间差的快速Level Set初始化算法。

Today, high resolution structures of virus capsids reveal the basis of this genetic economy as a highly symmetrical structure, much like a geodesic dome composed of protein subunits.

今天，高分辨率的病毒衣壳结构揭示出这遗传的经济性的基础是一个高度对称的结构，非常类似于一个由蛋白质二级单位组成的测地线状的穹丘。

The theory of surfaces made a slow start. It began with the subject of geodesics on surfaces.

曲面理论也经历了一个漫长的开端，曲面理论是从曲面上的测地线的研究开始的。

I bought a nice wrist watch as a surprise for my wife's birthday.

我买了一个漂亮的手表想要给我妻子的生日一个惊喜。

We don t expect students to be sponges. You can t expect to absorb everything and not have any questions to ask.

我们并不期待我们的学生是一块海绵，你没可能接收所有的东西而不提出任何问题。