封闭

By applying closed principal curve learning algorithm,we can obtain a simple polydragon as an approach for every simple closed curve in plane.

本文首先将具有简单封闭曲线特征的闭主曲线学习算法应用于平面有界闭区域图形的边界提取，给出相应的算法。

A closed curve is a path that repeats itself, and thus encloses one or more regions. Simple examples include circles, ellipses, and polygons .

封闭曲线的路径是循环的，包围一个或更多区域，简单的例子如圆、椭圆、多边形。

"Closed curve, one of the conic sections of analytic geometry, consisting of all points whose distances from each of two fixed points add up to the same value."

解析几何中圆锥截线的一条封闭曲线，包含了与两个定点之距离呈等值增加的所有点。

A closed curve is a path that repeats itself, and thus enclose s one or more regions. Simple examples include circles, ellipses, and polygons.

封闭曲线的路径是循环的，包围一个或更多区域，简单的例子如圆、椭圆、多边形。

The Fary-Milnor theorem states that the total curvature of a knotted simple closed curve in R^3 is greater than 4π.

Fary-Milnor 定理：一条空间中的简单封闭扭结其总曲率必大於4π。

This study investigated the ant groups algorithm to solve the problem of traveling salesman. The target of the article is that on the map G detect the shortest length of the Hamilton Circle, namely one pair of C n cities and only visit one of the shortest closed curve.

论文主要是研究蚁群算法来解决旅游商问题，其目标是从无向图G中寻出长度最短的Hamilton 圈，此即一条对C中n个城市访问且只访问一次的最短封闭曲线。

The gravitational fields required to make such a closed time-like curve would have to be very strong,"on the order of what you might find close to a black hole," Ori told LiveScience."We don't have any way of creating such strong gravitational fields today, and we certainly have no way of manipulating any such gravitational fields."

要制造出这样一条封闭时间曲线的引力场非得要非常强，"大约和你在一个黑洞附近找到的那么大"Ori告诉LiveScience"我们现在没有任何办法来制造这么强大的引力场，而且，可以肯定地说，我们无法来控制任何一个这样的引力场"

As a result, the standard union, intersection and the defined minus operation are closed under the domain of the representation.

这样， 在复形的伴随多面体表示域上，标准的集合交、并运算和定义的非流形上的标准差运算封闭。

The noise control of closed three-dimension domain (such as the cabin, cab, workroom, etc) is practical significance.

三维封闭空间(如船舶舱室、汽车驾驶室、工作间等)的噪声控制具有重要的实用价值。

For genus zero closed surfaces,the parameter domain is sphere,so the cutting of the surface meshes in the parametrization process is avoided.

对于零亏格封闭网格曲面，以球面为参数域的参数化方法可以有效避免对网格的切割，是近年来的研究热点。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！