查询词典 curvature of a curve

Besides common geometric measurements such as distances and angles,a new measurement of average curvature energy defined for boundary curve segment is included in the set to describe curve feature.

除了常见的几何测量外，提出了一种平均曲率能量的测量方法来描述边界曲线特征。

This paper used a method of curvature circle replacing general curve,the authors obtain twouniversal formulas calculating the inherent frequency of relative oscillation in miniamplitude be-tween columns that have general section curve.

本文应用曲率圆弧近似一般曲线的方法，导出了具复杂截面曲线的等截面柱体在另一柱体上微幅摆动时固有频率的一般计算式。

A new curvature-based algorithm in free-form curve fitting was proposed to fit a 2D NURBS profile with an arc spline ,where a new form of curvature formula with matrix representation was also proposed,and then the arc spline tool path with G~(1) continuity was generated.

给出了一种平面曲线轮廓的圆弧样条拟合及刀具路径生成算法，该算法面向零件轮廓的光顺性刀具路径生成，通过应用曲线的曲率关系，对以NURBS表示的被拟合自由曲线按参数递增的方向用G1连续的圆弧或直线段逐段拟合，并生成相应的圆弧样条刀具路径，从而实现零件曲线轮廓表面的光顺加工。

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。

If we consider a space uniformly filled with masses, as, for example, our space is filled with stars, galaxies and clusters of galaxies, we must conclude that, apart from localized large curvatures near particular stars or galaxies, space should possess an overall curvature due to the combined effect of all the masses- a regular tendency to curve uniformly over large distances.

如果我们考虑一个空间，被不均匀的质量块填充着，比如说，像我们的空间，被恒星、星系、和星系团填满，我们得出这样一个结论：除了局部在特殊的恒星或星系附近曲率很大的地方外，由于所有的质量块共同作用，空间应该有一个总曲率-一个在远距离上连续而不均匀的弯曲的趋势。

Based on this definition, the curvature、regular and integral properties of the general offset curve are discussed. As a result, J.steiners celebrated theorem of the oval is developed.

并在此基础上做相应的讨论，研究其正则性、曲率和积分性质，推广了J.steiner关于卵形线的外等距线所围面积的一个著名定理。

Depending on the axis being spacelike, timelike or null, there are three types of screw motions, the third case, i.e., cubic screw motion, is most particular because it is not a rotation together with a translation along the null axis, but a rotation together with a translation along a null curve with non-zero curvature.

依据旋转轴的向量类型，三维Minkowski空间中的螺旋运动可分为三类，其中第三类螺旋运动，即三次螺旋运动，是最特殊的。

As for the ovalization-curvature curve, it can be observed that the ovalization increases in a ratcheting manner with the number of the bending cycle. When the magnitude of the ovalization reaches a critical value, the tube buckles.

至於在椭圆化－曲度的曲线图中显示，椭圆化会随著循环弯曲的圈数渐增且呈现对称棘齿的变化，当椭圆化值增加到某一极限时，薄壁圆管便会发生皱曲破坏。

For the ovalization-curvature curve, the ovalization exhibits the unsymmetric-increasing ratcheting manner with the number of cycles. It is shown that the width does not affect the aforementioned curve, however, the deeper the sharp-notch, the larger amount of the ovalization to bend the tube to a certain magnitude of curvature.

至於椭圆化-曲度的曲线图中显示，椭圆化会随著循环圈数呈现非对称棘齿状的增加，而凹槽宽度对上述曲线没有太大的影响，但尖锐凹槽的深度越深，弯曲至某固定曲度时所产生的椭圆化量就越大。

The first case is the variable depth with a fixed notch-width and the second case is variable width with a fixed notch-depth. It can be observed fromthe moment-curvature curve of the first case that the magnitude of the moment is larger for the deeper depth than that for the shallow depth.

由有限元素ANSYS 分析结果可以观察出，在控制固定曲度做循环弯曲负载时，弯矩－曲度曲线图显示出，在固定凹槽的宽度，当深度较浅时，达到设定的控制曲度所需施加的弯矩相对於凹槽深度较大的圆管要大的多。

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。