查询词典 plane geometry

Firstly, This paper processes geometry filtration based on character of orbit's apogee and perigee after orbit model is analyzed and based. Secondly Space Debris is separated into two kinds, coplanar and not coplanar according as location interrelation of target and debris. In Dynamic filtration's processing, considering prediction time limit and orbit perturbation, secular effects which have increaser effect is considered so that some need catching danger time point is appeased, some law about time when target and debris pass intersectant line each other is inferred, when debris and object are in different plane and some similar law also is inferred otherwise. The time list is arithmetical progression. These laws can improve calculation efficiency remarkably; Lastly orbit predict is a course approaching least distance. Danger time point in the last step become beginning time point from which debris and object's position and velocity are calculated by SXP4 Model which is an analytic model.By result, determine that relative movement trend is closer or apart, farther calculate the interval apart from time when predictive least relative distance occurs. Least relative distance and time when least distance occurs is calculated finally. It is a fast approach course adopting varied interval.

本文在分析、建立轨道摄动计算模型的基础上，首先采用基于轨道远、近地点特征对大量编目在册的空间碎片进行初步几何静态筛选，然后根据碎片与目标轨道面的相对位置特点把碎片分为异面与准共面两种情况以进行动态筛选，在筛选过程中考虑到预报时限长度和轨道摄动影响，引入了轨道摄动中具有积累效应的长期项以满足危险时间点的捕捉要求，利用了长期项摄动变化线性的特点导出了碎片与目标异面情况下各自过交线的时间序列成准等差数列的规律性和准共面情况下类似的规律性，从而显著地提高了前期轨道筛选的计算效率；最后对剩余危险碎片和目标飞行器利用SXP4轨道预报模型在前期轨道筛选的基础上以各个危险探测时间点为预报的时间起点，并根据预报计算结果，分析目标和碎片在该时间点的运动趋势是相互远离还是相互接近，推出预计最小相对距离发生时刻相对此刻的时间长度，得到其随时间变化的局部最小相对距离以及危险距离发生的时刻和相对速度，这是一个采用变时间步长、快速逼近最小相对距离的过程。

First-principles plane-wave pseudopotential calculations were performed to study energetics , the geometry structures of intrinsic vacancies and interstitials on the anatase TiO2 (101) crystal surface.

采用平面波超软赝势方法计算了锐钛矿型TiO2(101)面存在本征空位和间隙点缺陷的几何结构以及缺陷形成能。

Proposed a representation scheme for 3D face -- Surface UnfoldingFor its irregular sampling in 3D space, 3D face surface cannot be processed by many orthogonal and subspace analysis toolkits directly, i.e. DFT, DCT, PCA, LCA. Surface Unfolding projects the 3D face to a 2D plane while retaining its intrinsic geometry properties of angle and area which issues a surface representation — Unfolded Image.

提出了一个三维人脸的平面表征方法——曲面开折模型不同于传统的数字生物特征，3D人脸数据是非规则采样的，传统的信号处理工具难以对3D数据进行直接处理。

So we can analyse the stability of lattice structure as solid web beam without change its geometry dimension. The out-of-plane stability of bending beam, which is made up with 2 beams and loaded by non-directional force, is studied.

对两节梁组成的弯曲梁在非保向力作用下的平面外失稳问题进行了研究，通过建立每节梁临界状态下弯曲和扭转变形微分方程，根据杆件变形的边界条件以及杆件之间的变形协调关系，得出了一端固定一端悬臂的弯曲梁在非保向力作用下平面外失稳的特征方程。

We know that functional biology also has structural analysis, which is like an analysis of points and lines of certain geometry at a plane level.

我们知道功能生物学的研究也进行结构分析，它就好比是在一个平面层次上，对一个特定几何图形中的点、线的分解。

Line segment intersection is one of the most important problems in computational geometry. Plane sweep algorithm is commonly used for this problem with bounding box filter.

平面线段相交是计算几何的基本问题之一，通常采用基于包围盒过滤规则的平面扫描方法求解。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r"‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

A non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane.

假设在平面中同一点上可以有两个或两个以上的平行线不交叉于一个给定直线的非欧几里得几何学。

Say for example, when discussing on parallel axiom, which is "given a point and a line on a plane, there exists a unique line on the plan that passes through the point and is parallel to the line", if we change the axiom as "there is not any or there are infinitely many lines that will pass through the point and be parallel to the line", then we have two kinds of non-Euclidian geometry.

就像对于平行公理的讨论一样，干脆规定：过已知直线外一个固定点可以作无数条与已知直线平行的直线；或者过已知直线外一个固定点的任何直线都不能与已知直线平行；这样还产生了两个版本的非欧几何。

The basic idea is as follows: with the help of the related results of differential geometry, the problem of interpolating curve on a parametric surface is converted to a similar one on its parametric plane.

基本思想是借助于微分几何的有关结论，曲面上曲线的插值问题被转化为其参数平面上类似的曲线插值问题。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。