曲线的曲率

3D reconstruction is one of the most challenging problems in computer vision. This project uses CAD model to increase the accuracy,robustness and speed of 3D reconstruction and five different works are conducted: 1 research on space curve 3D reconstruction method based on high curvature point nad turning point; 2 free-form curve 3D reconstruction based on B-spline and BURBS; 3 Active surface affine reconstruction based on single frame; 4 Matching and reconstruction of 3D sparse points; Data fitting method based on the iteration of nearest point.

三维重建是计算机视觉中公认的难题，本项目使用CAD模型来提高三维重建的精度、稳健性和速度的思路，围绕着空间曲线和曲面的三维重建和匹配开展了以下五个方面的研究：1）基于高曲率点和拐点分割的空间曲线三维重建方法研究；2）基于B样条和NURBS表示的空间自由曲线三维重建方法研究；3）基于单帧图像的有源曲面仿射重建；4）三维离散数据的匹配与重建；5）基于迭代最近点的数据拟合方法。

When the centre line of road is spiral curve,the edge lines(equidistance lines of centre line) are not spiral curves,which makes it difficult for construction location.

在各种曲线组合当中，卵型曲线中的回旋线曲率半径不是从无穷大开始，最为复杂。

And then, in this part, following the idea of Topping [51, 52], we will show an isoperimetric inequality (6.3.1) on surfaces of non-positive Gaussian curvature by means of the curve shortening flow on surfaces, this inequality can be considered as a generalization of the Banchoff-Pohl inequality in the Euclidean plane.

然后，仿照Topping[51]和[52]利用平均曲率流证明等周不等式的想法，我们利用曲面上的曲线缩短流在Gauss曲率非正的曲面上证明了一个等周不等式(6.3.1)，它可以看成欧氏平面上Banchoff-Pohl [8]不等式在曲面上的推广。

The whole process of moment-curvature relationship for RC beam was analyzed with the relative depth of compressive zone of the beam about 0.15 using the strip integral method and computer programme. The relationships between moment and strain of concrete, strain of steel, depth of compressive zone were got.

采用条带积分法，应用计算机编程，对相对受压区高度为0.15左右的钢筋混凝土梁的弯矩－曲率关系进行全过程分析，得出弯矩－曲率关系曲线，并给出弯矩与混凝土应变、钢筋应变及梁的相对受压区高度的对应关系。

At the same time, the method which feed can be adjusted with curvature of curve to implement the control of interpolation error in high speed and high precision is found.

同时为了保证自由曲线插补精度要求，提出了进给速度能随曲线曲率自适应调整，实现高速高精度插补误差控制的方法。

If the length of the arc and chord of the initial pair segments is in the range of error permission,the two segments can be determined as the candidate matching pair.

最后应用候选匹配曲线段上曲率的Hausdorff距离来验证曲线段的匹配，如果该距离在一定的容差范围内，则该曲线段匹配。

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。

First, a smooth curve is obtained from the data by curve fitting with the method of non-linear least squares fit. Then the tangent vector and the radius of curvature of each point on the curve can be calculated for the error evaluation. With the fitted curve, the focusing state of the aspheric lens can be obtained by the method of ray tracing.

主要过程为首先采用非线性最小二乘拟合的方法进行曲线拟合，并计算出曲线上各点的切矢量和曲率半径，分析它们的误差，最后对拟合后的曲线用光线追迹的方法得到非球面镜的聚焦情况。

Sixthly, research on seismic performance of repaired HSC column after hightemperatures The nonlinear whole process analysis method of reinforced concrete is used.Programs of moment-curvature and shear force-displacement of repaired HSCcolumn are developed after exposed to four sides and two symmetrical sides fire.Seismic performance of repaired reinforced HSC column after fire is studied. Byanalyzing the calculating results, the corresponding formulas of characteristicparameters of their skeleton curves of repaired HSC column after fire are proposed,and it is compared with corresponding curve of unfired columns.

火灾后已修复高强混凝土柱的抗震性能研究利用钢筋混凝土非线性全过程分析方法，编制了火灾后(包括四面受火和双面对称受火)已修复高强混凝土柱截面弯矩一曲率关系和剪力—位移关系的计算程序，对火灾后己修复高强混凝土柱的抗震性能进行了研究，通过对计算结果的分析和整理，给出了火灾后已修复高强混凝土柱M-φ及P-△骨架曲线特征参数的回归计算公式，并将上述曲线与未受火柱的相应曲线进行了比较。

The maximum peak coordinates in curvature spectrum, which indicates the maximum turning point position of singular value, is used to determine the number of effective singular values.

进而提出了奇异值曲率谱的概念，利用它来描述含噪信号奇异值曲线上的转折点情况，并提出根据曲率谱最大峰值位置即奇异值最大转折点来确定有效奇异值个数。

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。