曲率

Through studying some fundamental properties of the curved surface in differential geometry , a method of linear feature extraction based on differential geometry is introduced.

通过研究微分几何理论中曲面的一些基本性质，本文介绍了一种基于微分几何的线状地物提取方法，首先在局部区域内拟合一个二次曲面函数，然后通过该函数来估算灰度曲面的梯度和曲率，设定合适的梯度和曲率阈值来检测线状地物，最后进行后处理，消除许多噪声颗粒及小块区域。

For the timelike surfaces with constant positive Gaussian curvature (K=1) in R〓, we construct the correspondence between R〓 and sl (2, R), and deduce the fundamental equations for a special choice of the velocity of motion of time-like surfaces in asymptotic coordinates under suitable conditions, meanwhile, we give the B〓cklund transformation and one soliton solution of the evolution equations, then in terms of a gauge transformation we obtain the explict expression of the motion of surfaces.

对于三维Minkowski空间R〓中具有正常高斯曲率（K=1）的类时曲面，取定特定速度，在以渐近线作为坐标曲线的情况下，曲面运动满足两个基本方程，即sinh-Gordon方程和θ随时间演化的方程（其中θ表示两条渐近线之间的夹角），同时给出两个基本方程的B〓cklund变换和单孤子解，并通过规范变换给出相应的正常高斯曲率曲面的显式表达式。

In fact, the mean curvature and Gauss curvature of any helicoidal surface are independent on rotation parameter.

事实上，三维Minkowski空间中任意螺旋面的平均曲率和Gauss曲率都与旋转参数无关。

And then, we gain some definitions that in relation to regular surfaces which include discrete Gauss curvature and discrete mean curvature.

由此获得了一系列的相对于光滑曲面的离散定义，如离散平均曲率，离散Gauss曲率等。

Unlike Gauss curvature, the mean curvature depends on the embedding, for instance, a

不象高斯曲率，平均曲率依赖于嵌入，例如，一个

Applying this rule, a kind of the definition of the discrete estimated value on the quadrilateral net is given. It includes the definition of discrete Gauss curvature and discrete mean curvature.

应用该方法，给出了一种四边形网格上任意顶点处的离散估计值的定义方法，主要包括离散的Gauss曲率和平均曲率的定义。

Thus, combining this work with Benekis work, we prove that there exist any type of helicoidal surface with mean curvature or Gauss curvature being any smooth function.

这样结合Beneki等人的工作，本文证明：三维Minkowski空间中，平均曲率或Gauss曲率为任意给定光滑函数的任意一类螺旋面都是存在的，并给出了具体的参数表达式。

But it operates on the triangle mesh of 3-D objects surface retrieved from range images, and calculates the value and sign of Gauss curvature according to the geometrical meaning of Gauss curvature in differential geometry, which merits are its accuracy and speed.

该方法在理论上没有从拟合表面、求表面偏导的传统思路出发，它使用从深度图像得到的三维物体表面的格网表示，直接根据高斯曲率的几何意义计算高斯曲率的大小和符号。

Gauss curvature method ; principal curvature method ; reservoir fracture ; Biyang Depression

高斯曲率法；主曲率法；储层裂缝；泌阳凹陷

Emphases are put on solving the problem of repeating searching extreme points in contours of Gauss curvature drawing,and the improved Bulirsch Stoer contour curve searching method is used in extreme points searching to speed up the searching efficiency.

提出了一种针对非均匀有理 B样条自由曲面的高斯曲率等值线的光顺检测方法，重点解决绘制高斯曲率等值线时出现的极值点的重复搜索问题，并将改进的Bulirsch-Stoer等值线搜索法用于极值搜索中，提高了搜索效率。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。