连续曲线

Based on Bezier curve continuance of first－order and second－order derivative, the characteristic vector equation of two Bezier curve is presented in point of intersection. The algorithm is not only of high accuracy with all of the interpolated points being on the curve theoretically, but also of very high speed in the real－time interpolation processes. The interpolation velocity does not change and the segment tolerance of interpolation can be control by selecting the parameter in cerement rationally every time.

为保证两段Bezier曲线在连接点处一阶导数、二阶导数连续，导出了两段Bezier曲线特征向量应满足的关系方程，Bezier插补法不仅在理论上可使所有的插补点落在曲线上，而且实时插曲补速度高，每次插补时可合理地选择参数增量，能使插补速度保证不变，也可控制弓高误差。

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 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。

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。

Also the constructed curve is a shape-preserving curve for the original curve. We can also adjust the shape of curves by parameters of trigonometric uniform polynomial curve to approach the polygon closer. The general trigonometric polynomial curves with m degree and C(superscript 2m-1)(m=1, 2, 3) continuity are further presented.

除了通过切点参数，还可以通过三角均匀多项式曲线参数来调整曲线形状，使所得曲线更加逼近多边形，并可进一步、类似地可构造与给定多边形相切的C(上标 2m-1)(m=1， 2， 3)连续的m次三角多项式曲线。

Ythagorean hodograph curves enjoy a number of remarkable properties, such as, its offset curves have exact rational representations; the arc length function of a Pythagorean hodograph curve is simply a polynomial function of the curve parameter; and the lower degree Pythagorean hodograph curves have intuitive geometrical interpretation.

H曲线具有诸如有精确的有理 Offset、弧长函数可由多项式函数表示以及几何解释优美等一系列优良性质。基于复分析方法，避免了实分析讨论中出现的复杂表示及繁琐计算，构造了满足给定 C1 Hermite插值条件且以C1拼接连续的三次 PH曲线偶。该曲线偶可灵活处理拐点，从而克服了一般三次 PH曲线因恒凸而无法处理拐点的缺陷。

Deformation greatly promoted carbonitride isothermal precipitation and made C-curve shift leftwards. The position and shape of C-curve depended on the content of Nb and N to a great extent, C-curve shifted leftwards a little when N content increased and its nose temperature was raised with Nb content increased. 3 when cooling rate increased, start temperature and finish temperature of continuous cooling precipitation decreased, full precipitation became difficult to take place, the volume fraction of carbonitride precipitation decreased, molar fraction of Nb and C dissolved in austenite increased, and the precipitation grain was further refined. Deformation shorten precipitation start time during continuous cooling, raised precipitation start temperature, accelerated precipitation kinetics of carbonitrides.

计算表明：1在Fe—Nb—C系统中，随着温度的降低，析出相的平衡体积分数增加，溶解在奥氏体中的Nb、C的摩尔分数降低，析出相中C和Nb的原子分数的比值v增加；2变形大大促进了碳氮化物的等温析出，使C曲线左移，Nb和N的含量与C曲线的位置和形状有一定的关系，N含量的增加，使C曲线略有左移，而Nb的含量的增加使得C曲线的鼻子区上移；3随着冷却速率的增大，连续冷却析出的开始温度和结束温度均有所降低，并且析出变得越来越不充分，析出相体积分数明显减小，溶解在奥氏体中Nb和C的摩尔分数增大，析出相粒子被明显细化，变形大大缩短了CCP过程碳氮化物析出的开始时间，提高了析出的开始温度，促进了析出动力学。

Constructing C 2 interpolation curve by quartic Bézier curve offers additional freedom degrees those can be used to adjust the shape of the curve.

用四次B？zier曲线构造C2 连续的插值曲线可提供额外的自由度，用于控制曲线的形状。新方法构造辅助曲线用于描述B？

For example, we study the properties of the"centroid curve" and the"auxiliary curve", and identify two planes in which these two curves are defined respectively; we also use the idea of homotopy method to prove a fact that the orbit of a differential system has no triple contact point with the line we considered. Another key technique, which we use several times, is deformation argument.

例如研究由Abel积分之比定义的"质心曲线"和"辅助曲线"的几何性质，并把这两条在不同平面上定义的曲线放在同一坐标系中考虑；利用拓扑中同伦的思想来证明微分系统的轨线不可能与某条直线三重相切；利用几何方法与分析计算相结合证明了某一曲线是正则的；以及连续变动参数的技巧。

Take DMSO swollen treatment and DEA-SO2-DMSO decrystallization treatment for example, the X-ray diffraction and the Tobolsky's intermittent stress relaxation of treated woods were determined during soaking in water, analyzed the effects of water on crystal degree and inter-cohesion of treated woods. According to these continuous relaxation curves measured in water with different temperatures, various thermodynamic quantities were obtained by using Eyring absolute rate theory, and reviewed the chemical reactions in wood which occur in different relaxation process. For the first time quantify these crosslinkings formed in the process of tensional relaxation by using the SMCIR intermittent stress relaxation way, and defined the cross-linking reaction types. In order to find out the contribute of drying to the fixation of deformation of chemically treated wood, stress relaxation of oven-dry untreated and treated wood was measured during the process of temperature elevation and descend, then analyzed the effect of temperature change on relaxation mechanism of treated oven-dry wood. According to continuous relaxation curves of oven-dry treated wood under various constant temperature, calculated the thermodynamics of relaxation process and discussed the mechanism of molecule change in wood, at the same time, also quantified these cross-linkings produced in wood by intermittent method and on the basis of which the model of molecular change during relaxation process of chemically treated was constructed.

以DMSO膨胀处理及DEA- SO2-DMSO非晶化塑化处理为例，测定了两种处理木材在水浸渍过程中的X射线衍射及Tobolsky间歇应力松弛，分析了水对处理木材结晶度及内部凝聚力的影响；通过未处理和两种处理木材在不同温度水中的连续应力松弛测定，应用Eyring的绝对速度反应理论计算并获得了松弛过程中的各热力学量，分析了在水中松弛过程中不同阶段木材内部发生的化学反应；并首次采用SMCIR连续·不连续双曲线应力松弛法定量了轴向拉伸应力松弛过程中木材内部产生的架桥量，明确了交联反应的类型；为了了解干燥对处理木材塑性变形固定的影响，测定了未处理和两种处理绝干木材在温度下降过程和上升过程中的应力松弛，分析了温度变化对处理绝干木材应力松弛的影响；根据多个温度水平下的连续应力松弛测定曲线，计算松弛过程的热力学量，考察了绝干木材在松弛过程中内部发生的分子变化机理，同时也用间歇法定量了木材内部新形成的架桥量，并在此基础上构筑处理木材在松弛过程中内部分子构造的变化模型。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。