曲线

For designing free curves, the continuity condition of the two-piece curves is discussed. Finally, some application examples of the curve in the curve design are presented.

为方便自由曲线的设计，还讨论了两段曲线的拼接条件，给出了该曲线在曲线设计中的实例应用。

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。

Under this flow, the convex initial curve will preserve its perimeter, enlarge the enclosed area and make its curvature to be positive definitely. And as the time lasts, it will become more and more circular, and finally, as the time goes to infinity, the curve will converge to a circle in the Hausdorff metric.

本文证明在这种新的曲线流之下，闭凸曲线周长保持不变、所围区域的面积不断增大而曲率保持恒正，并且，随着时间的推移曲线变得越来越圆，最终当时间t趋向于无穷大时，曲线在Hausdorff度量意义下收敛到一个圆周。

The properties of the new method are that (1) the equations that the quartic Bézier curve has to satisfy for being C 2 continuous are strictly row diagonally dominant;(2) the discontinuous points of the curve are at the given data points;(3) the curve is locally adjustable;(4) if the given data points are convex, the constructed quartic Bézier curve is convex.

用样条函数方法构造插值样条曲线曲面，曲线曲面的精度和形状是由给定的数据点和端点条件唯一确定的。在有些情况下，例如，对文献 [7～ 9]中的数据点集，由样条函数方法构造的C2 插值曲线是不可接受的，但由于没有额外自由度，无法调整曲线的形状。

A human model using polynomial convolution surface is presented which is modeled by articulated skeletons convolved with some kernel function. The convolution surface and curve correspondence theorem under orthogonal projection is presented. The human contour is approximated with a convolution curve and 3D human pose can be estimated using a nonlinear optimization algorithm.

首先建立了一种新颖的多项式密度卷积曲面人体模型，该模型由连接体线骨架与某种卷积核卷积而成，整个曲面是一张连续曲面，调节多项式和半径参数可以让人体任意变形；给出了正交投影下卷积曲面和曲线对应的概念和相关定理，为二维的图像轮廓和三维人体模型之间建立对应关系；根据正交投影下卷积曲面与曲线对应定理，用卷积曲线去逼近人体的图像轮廓曲线，从而估计和恢复出三维人体运动姿态。

Taking the unknown coordinate in curved surface and curve as design variables, the equation of curved surface as constrained condition, and the distance between unknown coordinate as objective function, optimization is proposed to minimize the distance between curved surface and curve.

建立以曲面、曲线上未知，点坐标设计变量，以曲面和曲线方程为约束条件，以曲线和曲面距离为目标函数的约束优化方法来精确地确定曲面和曲线之间最短距离，同时确定获得最短距离对应的坐标点。

To satisfy the requirements of fast producing,low cost manufacture and large thickness preforming in the field of non-resin winding cylinder composite,the equation of retracing cosine curve was deduced based on the section principle.

最后基于对余弦折回曲线的分析，利用数值模拟证实余弦折回曲线在干纱缠绕圆柱壳体预成型中有利于高速加工；在缠绕厚度相对不大且需要高速缠绕加工情况下，可采用余弦曲线作为端部区段的折回曲线。

Then, a modifiable cubic polynomial curve is presented based on the basis functions, and the relation between the curve and the classical Bézier curves is discussed.

然后，基于该调配函数生成了一类可调控的三次多项式曲线，并讨论了该曲线与二次Bézier曲线及三次Bézier曲线之间的关系。

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。

In this paper,We define the notions of lightcone Gauss map ,lightcone pedal curve and lightcone height function of a spacelike curve in Minkowski 4-space, and established the relationships between singularities of these objects and geometric invariants of curves under the action Lorentz group ,and as an applications of standard techniques of singularity theory classified singularities of a spacelike curve in this space .

在本文中我们定义了四维Minkowski空间内类空曲线的光锥高斯映射，光锥垂足曲线，光锥高度函数的概念，建立了这些对象的奇点与在洛仑兹群作用下曲线的几何不变量之间的关系，并且运用奇点理论的标准工具对该空间中类空曲线的奇点进行分类。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。