查询词典 plane curve

Shaped like a hump or an arching curve .A plane cubic curve having a single loop, a node, and two ends asymptotic to the same line.

平面立方曲线平面的立方曲线，具有一个拱形、一个交点和逐渐接近同一条线的两个端点

The basic idea is as follows: first, a kind of plane α-B-spline interpolation curve with a shape control parameter a is constructed; then, by converting the first derivatives of the curve into Bernstein polynomial, the positive conditions of Bernstein polynomial can be used to get the necessary and sufficie nt conditions for the monotonicity of α-B-spline interpolation curves, i.e., the range of the parameter a. Therefore, monotone-preserving interpolating curves can be obtained succinctly.

其基本思想是：首先构造带有形状可调参数的一类平面(-B样条插值曲线，再把其一阶导矢的两个分量分别转化为Bernstein多项式，从而利用Bernstein多项式的正性条件，得到此曲线为单调的充要条件，即形状参数的取值范围，简单、快捷地实现此参数样条曲线的保单调插值。

By applying closed principal curve learning algorithm,we can obtain a simple polydragon as an approach for every simple closed curve in plane.

本文首先将具有简单封闭曲线特征的闭主曲线学习算法应用于平面有界闭区域图形的边界提取，给出相应的算法。

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. Finally, we will employ the Minkowskis support function to construct a new kind of non-circular smooth constant breadth curves in order to attack some open problems on the constant width curves for example, whether there is a non-circular polynomial curve of constant width, etc.

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？

Curve traced on an imaginary sphere with the source at its center and joining all the points corresponding to those directions in which the luminous intensity is the same, or a plane projection of this curve.

在一个以光源为圆心的虚拟的球面上，将光源射向球体上光强相同的各方向的点用线连接起来，就成为等光强曲线。

The general formula to calculate the rotating surface area which is shaped by rotating the curve c in xoy plane around the L-axis by using curve integral.

依据所证得的通用计算公式推证得到，在某些特定情形下利用定积分计算旋转曲面面积的具有针对性的公式。

Based on the Guldin's first theorem, it was deduced that the general formula to calculate the rotating surface area which is shaped by rotating the curve Г in a plane around the L-axis in the space by using curve integral.

依据古鲁金第一定理推证，得到利用曲线积分计算空间某一平面上的曲线Г绕直线L旋转而成的旋转曲面面积的通用公式；利用曲线积分计算xoy面上的曲线c绕直线L旋转而成的旋转曲面面积的通用公式。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r"‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

The whole multi-Agent system runs based on the continuous communication among agents. The architecture of the cloverleaf is variable, the beeline, the round curve and the convolute curve is the basic elements for the plane curves,the longitudinal gradient reflects the change of the vertical section. We consider sufficiently these specific factors in building road Agent. The different parameters are set to describe the geometrical characteristic and traffic characteristic.

立交枢纽的线形多变，直线、圆曲线与缓和曲线为平面线形组成的三个基本要素，坡度反应纵断面的路线起伏，本文在建立路段智能体中充分考虑了这些立交枢纽的特有要素，为每个智能体设置了不同的几何特性及交通特性，并在决策单元中加入对车辆驶入、换道、超车、限速等的智能控制模型，使得车辆智能体能够在由路段智能体相互连接组成的立交枢纽上正常行驶。

For each patient, a 3D reconstruction of the spine was obtained from calibrated biplanar radiographs.3 The reconstructed models were then used to compute 4 indices of the thoracic segment: the Cobb angle, thoracic kyphosis (measured from T4–T12), axial rotation of the apical vertebra, and the orientation of the plane of maximum curvature with respect to the sagittal plane.22,2 Measurements of coronal and sagittal plane curvature were based on a curve fitted mathematically through the centers of the vertebrae.

对冠状面和矢状面的角度测量基于通过椎体中心的合适的曲度数学计算。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。