曲率线

The paper deals with curvature line and curvature characteristic of developable surface based on differential invariant of developable surface and it details curvature line and curvature characteristic of cone and tangent surface .

本文通过可展曲面的微分不变量，导出可展面的曲率线与曲率特征，并以锥面和切线曲面为例阐明这些特性的几何意义。

The equations of the curvature, curvature radius, main curvature and main curvature radius on hypocycloid抯 and epicycloid抯 theoretical tooth shape and practical tooth profile are deduced respectively.

根据微分几何知识，分别推导出内、外摆线理论齿形和实际齿廓的曲率、曲率半径、主曲率及主曲率半径的方程式，并绘制了内、外摆线理论齿形和实际齿廓曲线及理论齿形的曲率半径变化曲线。

A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface, resulting in accelerating the Euler iteration process in solving the differential equation of curvature line. Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance.

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线。

Some properties of inversions are proved, It indicates that the inversion is conformal, the image of line of curvature is still the line of curvature of the inversion S of the hypersurface S, the principal curvature, the total curvature, and mean curvature of S are the functions...

在n-1维超曲面的反图变换中，示明反图变换为保角表示法，曲率线系的反影仍为反超曲面的曲率线系，反超曲面的主曲率，全曲率与平均曲率为原超曲面的主曲率的函数等。 3。最后导出公式(1)在四维空间与通常空间之特殊形式

B- spline Expression of Integral Curvature Line on NURBS Surface.

李宏坤，王国瑾，刘利刚， NURBS 曲面上积分曲率线的 B 样条表示，计算机辅助设计与图形学学报，2006， 18(3)：

Type IB: Isocline is convergent towards inner arc at a right angle to the fold.

根据等斜线的收敛层度，再细分为三个亚型：IA型：等弧线向内弧强烈收敛，各线长短判别极大，内弧曲率远大于外弧曲率，为典型的顶薄褶皱；IB型：等倾斜线向内弧收敛，并与褶皱面垂直，各线长短大致相等，褶皱层真厚度不变，内弧曲率仍大于外弧曲率，为典型的平行褶皱；IC型：等斜线相内弧轻微收敛，转折端等倾斜线比两翼附近的要略长一些，反应两翼厚度有变薄的趋势，内弧曲率略大于外弧曲率。

The line of curvature isn't only a curve of space, but a special and a very important curve of surface.

曲率线不仅是一条空间曲线，而且是曲面上定义的一种特殊而重要的曲线。

The line of curvature is relation to many basic conception with curve and surface, by which normal curvature and principal curvature are easier.

曲率线将曲线与曲面中的许多基本概念有机地联系起来，使得法曲率和主曲率的求解简单化。

In this paper, we will study the definination of lines of curvature and the correlative conception, for example, normal curvature, principal direction and principal curvature and so on, the connection of lines of curvature and correlative conception, especially probe into the solution with the equation of lines of curvature and the equivalence with its determinant theorem.

本课题主要研究曲率线的定义及其相关概念如法曲率、主方向、主曲率等，曲率线与相关概念的关系，重点探讨了曲率线方程的求解及曲率线判定的等价定理。

Results indicate that radial distance of the bushing from the rotor center and the radius of the hemispherical bushing significantly affect wear rate,and minimzing both two values will result in lowest wear for micro-rotor systems in MEMS.However,it is noted that the bearing radius sets a lower limit on the hemispherical bushing radius since the bushings are located beyond the rotor inner radius.It is desirable to reduce their effects on friction and wear on micro-rotors by regulating the radius of the bushing and the radial distance of the bushing from the rotor center within permissive range of micro-fabrication.Severe wear exists with increasing applied load and rotating speed of the rotor.Stress distributions in the contact region are different from Hertz solutions due to the convergence stresses apearing on the uncontinuous curvature line and the contact pressures display symmetrical parabola in the contact region.

结果表明：在MEMS微转子系统中，微转子轴衬偏心距离和转子轴衬半径影响线磨损率，以两者减至最小为较理想，但须注意设计中轴承半径的限制，并使轴衬偏心距离大于轴承内半径；在转子加工制造许可的范围内，可以通过调整转子轴衬的半径和偏心距离来减少摩擦磨损对微电机的影响，随着转子所承受载荷和转子旋转速度的增加，其磨损严重；接触区的应力分布不同于经典Hertz解，这是由于应力集中出现在不连续的曲率线上，且接触区的接触压力呈现轴对称抛物线状分布。

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。