解析几何

The ellipse curre equation of circular image is derived based on the theory of spatial analytic geometry and rotation matrix s representation with unit quaternion then a mathematical model of the distortion error is established which relates the distortion error to the foca length of the used CCD camera,the radius as well as the position and the attitude of the inspected circle directly.

研究三维视觉检测中圆的中心经针孔摄像机成像后存在畸变误差的问题，首先基于空间解析几何理论和旋转矩阵的四元数表示法推导出像平面上投影椭圆的参数方程；然后根据参数方程建立圆中心成像畸变误差的数学模型；最后对影响畸变误差的主要因素进行分析。

During the process of the fore mentioned analyses, some tentative works as follows were done.(1)On the basis of the fundamental of spatial analytic geometry, the basic method for displaceable block searching was put forward and the relevant program was written. With this program one can easily search out all the displaceable blocks and omitting of blocks, which is very common in searching blocks manually, can be avoided.(2)The coefficient of stability of blocks with failure mode II-2(that is, sliding on a single sliding surface, but confined by near intersecting line )was deduced.(3)The multi-cavern effect of Laxiwa underground caverns was studied on the assumption that all of the caverns were full face tunneled at the same time.(4)The stability classification scheme of rock mass surrounding large scale underground caverns was established. In addition to inherit the merits of the method of engineering geological

在完成上述工作的过程中，本论文主要在以下几个方面进行了一些探索：①基于空间解析几何原理，提出了块体搜索的基本思路并编制出相应的程序，基本实现了块体搜索的自动化，既大大缩短了块体搜索时间，又能防止因人工搜索引起的遗漏；②推导出Ⅱ-2型(单滑面滑动，但受侧限面约束)块体的稳定性系数计算公式；③以数值模拟方法论证了拉西瓦地下厂房洞室群全断面一次开挖时群洞效应的具体特点；④以岩体质量、开挖效应、群洞效应和次生灾害效应为评价指标，建立了&大型地下洞室群围岩稳定性分类&方案；该方案既继承了水电行业规范&围岩工程地质分类&法的优点，又综合考虑了大型地下洞室群的工程特点。

At the same time,the knowledge embodying the same idea and research method was optimized and arranged.

通过以上改革，对经典的解析几何内容进行了教育学的再加工。

In this paper,an uniform and intuitional method is given to get the spatial distance including the distance between the space point and the plane,the distance between the space point and the beeline,and two beelines which are not in the same plane.

点到平面的距离、点到直线的距离以及两条异面直线间的距离是空间解析几何部分要解决的3个距离问题，一般教材[1~2]都采用向量方法推导相应的距离公式。

Anti-aircraft weapons positions configuration model, make best distance and sheltering sector as index, and use analytic geometry to establish.

防空武器阵地配置模型，以最佳距离、掩护扇区为指标，运用解析几何建立。

The distance equation form dot to straight line is a basic equation for analytic geometry. This paper presents some deductions form angles.

点到直线的距离公式是解析几何中的一个基本公式，本文从不同角度对这一公式给出了几种推证。

Using the principle of Projectiv e geometry and Analytic geometry,we have intact analysed about the cut and hand in line of taper and Geometry proved the form produced by the special-position -leve and the general-position-level.

利用射影几何和解析几何的原理对圆锥截交线进行了完整的分析，对特殊位置截平面与一般位置截平面产生的截交线的形状进行了几何证明，为截交线的形状判别与绘制提供了理论依据。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失