曲线坐标

The paper introduces the concept of curve following turnout branch line and some relevant regulations,discussing maintenance method of mini-typed curve on railway with coordinate method based on original curve following turnout branch line at Rolling Line No.

介绍道岔附带曲线概念及其有关规定，结合中3条原有附带曲线的特点，阐述用坐标法对铁路线路上小型曲线的维修方法。

Firstly, some basic concepts about ECC are introduced;then the scalar multiplication under affine coordinate is discussed, we make a research and analysis of the side channel attack of scalar multiplication used in portable device, give out a new scalar multiplication algorithm which has the advantage of efficiency over other protected algorithm; and an improvement of the standard scalar multiplication algorithm proposed by IEEE1363 is made with the efficiency increasing by about 10%; at last, we deal with the using of complex multiplication in scalar multiplication algorithm, we generalize the methods and deduce a complete computing procedure, with proposing a new method which used several different fast endomorphism ,we give out an approach to boost the scalar multiplication with fast endomorphism.

本文首先介绍了椭圆曲线密码的有关基本概念；其次介绍了椭圆曲线上点的标量乘法在仿射坐标下的计算，对一般便携设备上的椭圆曲线点的标量乘法的边信道攻击做了研究与分析，给出了一种在效率上优于其它可抵抗边信道攻击的标量乘法的新算法，并对IEEE P1363 标准给出的标量乘法做了改进，使得标量乘法的运算效率提高了近10%；最后介绍了利用复乘计算标量乘法的方法，对已有的方法进行总结归纳，得出完整的计算过程，并针对两类超奇异椭圆曲线给出了一种利用多个可快速计算的复乘的标量乘法，得出一类普遍的结果，并给出了进一步用复乘加快标量乘法的思路。

In inner action domain, the local coordinate of each point related to test feature curve need to be calculated, and then the point is deformed by finding the position with the same coordinate related to reference feature curve.

在内部作用范围内，通过计算每一点相对于测试特征曲线的局部坐标，然后在参考特征曲线坐标系下找到相同的坐标位置，完成该点的交换过程。

Taking the unknown coordinate in curved surface and curve as design variables, the equation of curved surface as constrained condition, and the distance between unknown coordinate as objective function, optimization is proposed to minimize the distance between curved surface and curve.

建立以曲面、曲线上未知，点坐标设计变量，以曲面和曲线方程为约束条件，以曲线和曲面距离为目标函数的约束优化方法来精确地确定曲面和曲线之间最短距离，同时确定获得最短距离对应的坐标点。

Through to the road grade separation circular route mathematical model's research, has based on this compiled the road grade separation circular route coordinate computational procedure; Each kind of curve linear on the one hand pile computation general formula's establishment, is advantageous in the programming solves on the other hand any curve the pile coordinate.

通过对公路立交匝道数学模型的研究，在此基础上编写了公路立交匝道坐标计算程序；各种曲线线形边桩计算通用公式的建立，有利于编程以解决任何曲线边桩坐标。

An optical system with refraction and total internal reflection was proposed according to the luminous characteristic of LED and the law of energy conservation. The ordinary differential equations satisfying the spots on the contour curve of TIR refractive and reflective planes were established. The coordinates of points on profile curves were obtained by solving these ordinary differential equations using Runge-Kutta method. The profile curves were acquired by curve fitting of the coordinate spots with software UG, and then TIR model of the projector and data of the surface shape suitable for NC manufacture were obtained.

根据LED的发光特性以及能量守恒定律选择采用折射全反射光学系统，通过建立TIR折射面及全反射面轮廓曲线上的点所满足的常微分方程，利用RungeKutta求解常微分方程得到轮廓曲线上点的坐标，再在UG中对坐标点进行曲线拟合得到轮廓曲线，进而得到TIR模型及适合数控加工的面形数据。

Study on geometry theory and engagement characteristics of scroll profiles Aiming as the limitations of scroll profiles in existence, the whole characteristics and local characteristics of plane curve instinct equation were studied. Analyzed the equidistant curve of envelope principle, normal equidistant curve creating method and envelope equidistant curve creating method were gained.

针对现有表征方式的局限性和不足之处，从微分几何角度出发，研究了平面曲线固有方程的局部特性和整体特性，分析了通用涡旋型线等距曲线和包络原理，得到了法向等距曲线生成及包络法等距曲线生成方法，推导了通用涡旋型线的坐标变换方法，得到了通用涡旋型线的平面啮合理论。

The concept of exponential transformations of rectangular Cartesiancoordinates is introduced, showing that a plane curve is more frequently expressed by a unionof four or fewer quadrantal equations defined uniquely in the respective quadrants whichthe curve covers and are therefore quadrant invariant, then the Fermat curve s with someof their geometric properties are formulated.

引入直角笛卡儿坐标幂变换的概念，说明一平面曲线是较经常地用4个或更少的象限方程的并集来表示的；这些象限方程是在曲线所在的各个象限中惟一定义的，因而是象限不变的。然后列出费马曲线的方程，并简述了费马曲线的一些几何性质

Firstly got the sequence of the contour points with one pixel width of the image to be assembled.

首先求出待匹配图像单像素宽的轮廓曲线上像素点的坐标序列，然后利用轮廓上各点和与其相差六个点的像素点之间的位置关系及行列坐标差的平方代数和对轮廓进行表示，得到两轮廓曲线的表示序列后；接着采用寻找两轮廓表示序列的最长公共子序列的方法进行匹配，并在匹配过程中引入了"断点续配"的概念，有效提高了算法的容错性。

General procedures for measuring highway as follows: First check the correctness of the original data, including principal point coordinates, distance, azimuth,桩号miles, round curves, relaxation curves and vertical curve elements of the curve, more than longitudinal slope and the slope design of high, ultra high and wide, and draw good draft for field use.

公路测量的程序一般为：首先校核原始资料的正确性，主要包括主点坐标、距离、方位角、里程桩号、圆曲线、缓和曲线和竖曲线的曲线要素、纵坡和边坡坡比、设计高、超高和加宽等，并画好草图以备外业使用。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。