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In a routine test, these points are marked by center punch, but, if a more detailed test is to be carried out, the extension is measured by an instrument called an extensometer, which produces the gauge points when it is attached to the test-piece.

在常规测试中，这些点用中心穿孔机标记但是，如果要进行更仔细的测试，延伸量要用名叫引伸计这种仪器进行测量，当引伸计连接试样时，它产生标距点。

In the fourth chapter we discuss the set of chain equivalent points of chain recurrentpoints,the set of unilateral γ-limit points and topological entropies of tree maps.

在第四章，我们讨论树映射的链等价集、单侧〓-极限集和拓扑熵。

According to that characteristic and based on the differential equation of the deformed surface of the orthotropic plate, with one principal direction size fixed, changing another principal direction size linearly, maintaining elasticity coefficient the same as in the first principal direction and Poisson ratio equal to the geometric mean of two principal Poisson ratios, the original orthogonal plate is equivalent to an isotropic plate. Results obtained show that the deflections of the equivalent isotropic plate are the same as the deflections of the original orthotropic plate at the corresponding points, the forces of the correspondent points have simple relations.

根据这一特性、从正交各向异性板挠曲面的偏微分方程出发，保持一个主方向尺寸不变，另一主方向的尺寸做线性缩放，保持弹性模量与第一主方向相同，泊松比取2个主方向泊松比的几何平均值，将这类正交各向异性板等效为一块各向同性板；通过分析得到：各向同性板任意点的挠度就是原正交各向异性板对应点的挠度，各对应点内力之间存在简单的比例关系，该文的方法将为工程技术人员提供方便，同时可以更加直观的认识正交各向异性板的受力。

"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。

And then, we prove the coincidence relation between one skyline point of high dimensional space and the most mild points of one subset, thus enabling it to transform skyline computing in high dimensional space to figuring out the most mild points in all subsets.

为此，本文首先提出了高维数据集上"平和点集"的概念，它由各属性值中的最小值比数据集中其他点对应最小值"好"的那些点组成；然后，论证了"平和点集"中最大平和点和skyline点的对应关系，从而转化高维数据集上skyline计算为其任意子空间上的最大平和点计算。

In this paper, cross ratios of the four collinear points and five coplanar points were analyzed first, then some affecting factors were concluded, and some constraints were proposed on constructing model-based object recognition system.

首先对共线4点和共面5点构成的交比不变量的稳定性进行了分析，得出了影响稳定性的因素，然后提出在构造目标识别系统的模型时应注意的约束条件，实验表明：在这些条件下构造模型的抗噪声能力大大提高。

The conventional Hough transform can only count the number of feature points which are collinear, and can't record the end points of a line segment and its length. Thereby, this paper present an improved Hough transform to overcome these two shortcomings. The algorithm is parallelized and implemented in MCC. What's more, we give a parallel algorithm to identify and eliminate overlapping line segments. These advantages are very useful in the real applications.

本文针对传统Hough变换只能统计直线上黑色象素个数，不能记录线段的两端点坐标及长度的缺点，介绍了一种改进Hough变换算法，并在网孔处理机阵列中实现，还给出了能够识别并消除重复线段的并行算法，这些在实际问题中是很有用的。

This paper proposes a flexible and reliable camera calibration of stereo vision measurement system based on unit quaternions with optical reference bar, which has three small collinear infrared LED feature points and the lengths between these feature points have been precisely calibrated.

提出了一种利用光学参考棒，基于单位四元数法的灵活、有效的立体视觉测量系统现场校准技术。

The proof of some propositions on points collinear in elementary geometry with vector mothod;2. The last we proof points of intersection being collinear .

文章首先证明了巴卜斯定理的特殊情况，然后利用此特殊情况及巴卜斯定理作了四个推广应用，最后将巴卜斯定理的原来三点共线推广到了六点共线，再推广到12n(n-1)个交点共线。

A calibration model was established by introducing a planar target that could move freely with three collinear and known mutual location points. The calibration point coordinates in a camera coordinate system could be calculated by using the imaging information of three points and the light stripes on image plane of the camera.

引入一个可自由移动的平面靶标，靶标上只需要共线且相互位置确定的3个特征点，利用共线三点建立三点透视数学模型，根据3个特征点以及光条纹在摄像机像面的成像信息，获取了光平面上标定点在摄像机坐标系下的坐标。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。