查询词典 curvature of a curve

In addition, we made account for the selection of inverted bending curvature of pipe axis and the length of equal curvature region, and pointed out that we can only equalize the curvature in the equal region and carrying out straightening really is in the region of unequal curvature. This is the development and perfect of bending straightening theory and this method can spread to bar straightening machine.

此外，还对反弯曲线曲率和等曲率区长度的选取作了说明，指出在等曲率弯曲区只能使曲率均匀化，而真正实现矫正是在后部的非等曲率弯曲区，这是对矫正理论的深入和完善，并且这一研究方法也可推广到棒材矫正机。

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。

Chapter 2 introduces some propaedeutics of classic differential geometry, which include the first basic form, the second basic form, normal curvature, main curvature, mean curvature, Gauss curvature, unit normal vector, main vector, etc.

第二章介绍一系列的预备知识，主要是关于古典微分几何中第一，第二基本形式的定义，法曲率，主曲率，平均曲率，Gauss曲率，单位法向量，主方向等的定义。

In this paper, a "rigid bar relative movement model" was established to illustrate the traces of the helices in wire ropes. The angular speed of a moving particle of the model was relatives to curvature tensor to derive the curvature components and torsion of helices in multi-layer wire ropes. According to long and thin rod theory of Love and Yen-Chen's theoretical model considered the contact force and frictional force, the force-deformation or force-strain relative of wire in curved wire ropes subjected axial force is derived from the curvature components and curvature increment.

本研究改以刚杆相对运动模型，直接描述钢索中钢绞线轨迹，并且透过角速度类比曲率张量之概念，推导圆弧型多层钢索内部之钢铰线之曲率分量与扭率；之后再依据Love的细长杆理论，辅以Yen-Chen在考虑接触力及摩擦力下所修正之理论模型，以曲率及曲率增量来探讨圆弧型钢索受静态荷重作用下，钢绞线之受力与变形或应变关系。

Researches the submanifolds in nested space,for constant curvature Riemannian submanifold in quasi-constant curvature manifold and pseudo-umbilical submanifold with parallel mean curvature vector in constant curvature Riemannian submanifold,presents three sufficient conditions for this pseudo-umbilical submanifold to be total-umibilical submanifold,generalizes the result of JI Yongqiang.

对于拟常曲率流形中的常曲率黎曼子流形以及常曲率黎曼子流形中具有平行中曲率向量的紧致伪脐子流形，给出了这种伪脐子流形是全脐子流形的3个充分条件，推广了纪永强的相关结果。

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。

The computer software is worked out to calculate numerically the geometric drive properties: normal curvature, geodesic curvature, induced normal curvature, induced geodesic curvature, lubrication angle, contact line and meshing area, etc.

本文首次建立了在双自由度运动状态下，用直线型切刀包络加工圆柱蜗杆传动的啮合原理数学模型；并编制了相应的计算机软件，对其几何传动特性：法曲。。。

Its implementation processes include:①to perform wavelet transform and frequency decomposition and reconstruction to gain the seismic data with high quality;②to adopt least square method to approach and fit the local secondary curved face, and compute the fit coefficients of the secondary curved face, then use these coefficients to gridding mapping bed plane to compute the average curvature and Gauss curvature, then, obtain other curvatures through the various linear combinations of the two curvatures above;③to generalize the curvature of the bed layer to compute and reconstruct the curvature volume.

其实现过程为：①对地震资料进行小波变换、分频重构，获得高质量的地震资料；②采用最小二乘法一次逼近，对局部二次曲面进行拟合，求取二次曲面拟合系数，并利用这些系数对网格化成图层面计算平均曲率和高斯曲率，再从两个曲率的不同线性组合，获取其他曲率；③将层面曲率推广，计算和重构曲率数据体。

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。

From this viewpoint, we fulfilled to control the step-size with the curvature of integral curve. The step-size is smaller in calculating these points that the value of the curvature is bigger and the step-size is bigger in calculating these points that the value of the curvature is smaller, which is rather reasonable choice and is also a creative point in this paper.

从这个想法出发，在文中实现了以积分曲线的曲率控制步长大小的作法，在曲率大的点步长小，而在曲率小的点步长大，这是非常合理的选择，也是本文的一个创新点。

The production moved off-Broadway to New York City, where she won the Joseph E. Calloway award for her performance, and was profiled in American Theater Magazine as one of ten young theater artists to watch.

生产提出过百老汇的新的纽约市，在那里她赢得了约瑟夫calloway奖，她的表现，并于异型在美国的战区杂志之一， 10战区的青年艺术家观赏。

It's a risk tradeoff, and I believe that adding test support code usually wins.

这是一个风险的权衡，我相信添加测试代码通常会占上风。