平面曲线

The characters of the singular point of the visible contour line of a concave rotative surface and its corresponding projection are analyzed on condition that the projection of the contour line is smooth near the singular point , the shape of the visible contour line of a concave rotative surface near the singular point is further studied.

对凹回转面可见轮廓线的投影在奇点附近仍光滑的情况下，分析了可见轮廓线本身与奇点对应点处的曲线特征以及可见轮廓线在其对称平面的投影图上与奇点对应的点的特征。对凹回转面可见轮廓线在奇点附近形状作了进一步的分析与研

Four main types of spatial binary links are investigated in details for kinematic synthesis both in precision-position synthesis and multi-position synthesis. In terms of the invariants of spherical curve and cylindrical curve, the mathematical models of adaptive fitting sphere and cylinder are constructed by means of the saddle-point programming.

再次，根据常见空间机构运动副组合的约束曲线与约束曲面的曲率理论，阐述了空间机构运动综合的基本要素及其不变量拟合理论与方法，研究了有限位置和多位置情况下，自适应综合方法在空间S-S、C-S、C-C和S-C四类二副杆组运动综合中的应用，实现了自适应综合方法从平面到空间的扩展。

And the tangent plane of three characteristic curves on the tire determines the spatial position of the tested wheel.

每个车轮使用3个线结构激光传感器，通过求取轮胎上3条特征曲线的切平面来确定车轮的空间位置。

Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.

本文结合微分几何学，基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上，得到了参数化曲面上的图像处理框架，并给出了边缘检测和形态学运算的算例；在已知给定曲面的隐式表达时，探讨了定义在任意曲面上的偏微分方程，解决了任意曲面上数据场的扩散问题。

Based on the analysis of the characteristics of triangular Bezier surface construction and surface/plane intersection, in chapter 4, the author puts forward a construction method of surface/plane intersection curves.

第四章针对三角Bezier曲面的构造特性以及平面与三角曲面求交的特点，提出了一种任意截面曲线的保形构造方法。

Research on fast algorithm of point inclusion query. From the point of view of computational geometry, winding number is extended from close curve to line segment, polygon, 2-dimensional object, plane subdivision, polyhedra, 3-dimensional object and 3D subdivision.

7，研究点查询的快速算法，从计算几何的角度将环绕系数扩展到一个除闭合曲线外的线段，多边形，二维对象，平面分割，多面体，三维对象，三维空间分割等，进而构造出各种情况下的点查询代数算法。

This conclusion corrects a mistaken resultIn the planar quadratic system there is not cubic algebraical saddle-nodeseparatrix-loop,in which the author asserrts that quadratic system has no the cubicalgebraical saddle-node separatrix cycle .

本文证明了平面二次系统的三次代数同宿轨线上可以存在鞍结点，并且二次系统可以存在含鞍结点的无返回映射三次曲线分界线环。

The Phase I tip has simple straight swept or tapered shape, the curve change of the platform is included during Phase Ⅱ, and the geometry of the Phase Ⅲ tip is extended to anhedral modification.

第一层次的桨尖形状为直线后掠或尖削，第二层次包括桨尖平面的曲线变化，而第三层次进入到下反桨尖这种三维变化。

Their adsorption rate on the molecular sieve catalysts surface and the stability of their carbonium ions were then obtained based on the molecular simulation on these molecules from their dipole moment, 2-dimensional electrostatic potential energy contours and 3-dimensional electrostatic potential energy isosurface.

采用半经验的AM1量子化学计算方法和静态理论，分别考察了噻吩、 3 甲基噻吩和 2 ，5 二甲基噻吩分子结构特性的不同，从偶极矩、各自垂直于芳香环平面的二维电势能分布曲线和整个分子周围三维电势能分布情况等方面分析了它们在分子筛催化剂表面吸附速度的快慢和生成正碳离子稳定性的高低，进一步比较了噻吩及其衍生物所生成的正碳离子进一步反应的能量变化，从而可判断噻吩及其衍生物裂化脱硫速度的快慢，噻吩及其衍生物裂化脱硫的速度由大到小分别为：2 ，5 二甲基噻吩、 3 甲基噻吩、噻吩。

On the basis of fivebar pantograph configurations with generating similar curves, the loop augmentation method is used to synthesize the configurations of movable planar seven-bar zero-degree-of-freedom and eight-bar negative-degree-of-freedom overconstrained chains with prismatic pairs.

文中以平面五杆缩放机构为基本架构，利用其产生相似运动曲线之特性，配合回路增殖法，分别合成出自由度为0之七杆与自由度为-1之八杆可动呆链之构形。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了