查询词典 curvature of curve

Hausdorff convergence; almost nonnegative Ricci curvature; Betti number; harmonic 1-form; nilpotency; splitting theorem; positive sectional curvature; gradient curve

基础科学，数学，几何、拓扑Hausdorff收敛；几乎非负Ricci曲率；贝蒂数；调和1-形式；幂零指标；分裂定理；正截面曲率；梯度曲线

Curvature is 100 feet long curve corresponding to the central angle, curvature and inversely proportional to the radius.

驾驶员所能看到的前方行车道上最大距离称为视距。

Degree B-Spline curve is chosen to fit the longitudinal settlement curves, which solves the problem of curvature continuum for joint notes due to its continuous second derivative vector and overcomes the efficiency and accuracy of computing curvature with 3 points by hand.

选取三次B样条方法对隧道纵向累计沉降曲线进行拟合，利用三次B样条曲线二阶导矢连续的特性，解决了拟合曲线在曲线连接点处曲率的连续性问题，克服了以往人工计算隧道曲率半径在效率和准确性方面的缺陷；并在此基础上，推导了隧道纵向变形曲率与纵向螺栓拉应力、相对弯曲与纵向螺栓剪应力之间的关系； 3。

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。

Here, we will give an independent proof of the existence for inequality (2.1.3), and by the way, give an estimate on the width of the bi-enclosing annulus of closed convex curves in the plane. Secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature.

其次，对双曲平面上的曲线引入平均测地曲率的概念，并讨论双曲平面上凸曲线的嵌入性与它的平均测地曲率之间的关系，其目的是为了将双曲平(来源：ABC论84文网www.abclunwen.com)面上曲线的性质与欧氏平面中曲线的性质作一些对比；最后，我们利用Minkowski支撑函数构造了一类新的非圆的光滑常宽曲线，其目的是想回答有关常宽曲线的一些未解决问题如是否存在非圆的多项式常宽曲线？

We decompose curvature signal with wavelet at first and then extract itslow frequency coefficients as new smooth curvature signal, which is used to constructa G~2 continuous piecewise rational cubic Bezier curve with GHI method subsequently.

本文首先对估算得到的离散曲率进行小波分解，提取其低频部分作为新的曲率，然后利用几何Hermite插值方法，重建出光顺的截面线。

We decompose curvature signal with wavelet at first and then use its low frequency coefficients as new smooth curvature signal, which is used to construct a G^2 continuous piecewise rational cubic Bezier curve with (Geometric Hermite Interpolation, GHI) GHI method subsequently.

针对在逆向工程的实践中常见的轮廓线的光顺问题，给出了一种先对曲率图进行小波分解，提取其低频部分作为新的曲率图，并利用几何Hermite插值方法，生成G^2连续的分段三次有理Bézier曲线，从而重建出光顺的产品轮廓曲线的新方法。

The weakness of fixed step-size is that step-size is not variable regardless the curvature of each point of the integral curve change or not, which will affirmatively bring serious error in these points that the value of curvature is bigger. And, this kind of error will accumulate in calculating process.

定步长的缺点在于不管是积分曲线的各个点的曲率如何都取一样的步长，这样肯定会在曲率大的一些点带来比较严重的误差，这种误差将在每一步的计算中积累。

The interpolate algorithms of three-order NURBS curve and double three-orders NURBS surface are presented. The expressions of partial derivative and normal curvature of NURBS surface are derived by the theory of differential geometry. The geometric characteristics of different curvature area of the free-form surfaces are analyzed in detail. All these work lays a theoretical foundation for constructing the cutter location calculating model of free-form surfaces NC machining. 2 On the basis of analyzing the methods of cutter path generation, the standard of evaluating the various methods of cutter path generation is presented. The method of generating cutter path with constant scallop height is presented for the first time.

本文以提高复杂曲面多坐标数控加工精度和加工效率为目的，在对国内外研究现状进行深入分析的基础上，对数控编程中各环节的关键技术问题进行了深入研究，主要内容包括以下几方面： 1 分析了复杂曲面各种造型方法的优缺点，给出了根据各种边界条件所确定自由曲面的NURBS表示方法以及三次NURBS曲线曲面反算算法；用微分几何理论推导了NURBS曲面的偏导矢及法曲率计算表达式；对曲面不同曲率特性区域的几何特征进行了深入分析，为建立复杂曲面的数控加工刀位计算模型奠定了理论基础。

The large curvature of the Earth appearing in the visor reflection is not the true curvature of our spherical Earth, but rather an artifact of the curve of the space helmet.

头盔反射看到的巨大的地球弯曲度并不是我们球形地球真正的弯曲度，而恰恰反映的是太空中头盔弯曲度。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。