平面曲线

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。

We analyze the boundary structure of interval Bézier curves in detail. Efficient and reliable algorithms for evaluating the boundaries of the interval Bézier curve in 2D and 3D are presented.

作者对区间Bézier曲线的边界结构作了精细的分析，详细地给出了计算平面区间Bézier曲线边界的编程算法，并将边界曲线表示为B样条。

Its shape, known as a 'tri-plane curvature', comprises three curves, or planes, rather than being a continuous curve.

它的造型称为"三翼式曲线"，由三道曲线或平面组成，而不是一条连续的曲线。

In the first part of the paper, we construct a family of 1 parameter cubic algebraic curves interpolating four given points and two tangent lines at the endpoints, and one can manipulate the shape of cubic algebraic curves by controlling the points or the tangent line directly.

该文提出的代数曲线的结构有两种，一种是插值平面上四点及两端点切线的三次代数曲线；另一种是插值两端点、两切线及两曲率的三次代数曲线。

Geodesic curvature of the pitch curve on spherical surface was introduced as a medium,through which the pitch curve on spherical surface can be changed into equivalent planar pitch curve by numerical computation method.

以曲面上曲线的短程曲率为媒介，导出了球面节曲线伸展成平面当量节曲线的算法。

This bicubic Pythagorean hodograph curves can deal with the inflexion flexibly and two cubic Pythagorean hodograph curves reaches C 1 continuous at the connection point.

引 言PH曲线是一类特殊的平面多项式曲线，1 990年由 Farouki和 Sakkalis[1]在研究等距曲线的过程中提出。

Firstly, the average equation under first,and second order of Van der pol-Mathieu-Duffing system are obtained through theatric methods. According to the stability criteria, the physical parameter plane is divided into different regions, associated with different types of steady state solutions, which are proved by employing numerical methods.

本文首先通过理论分析得到了Van der pol-Mathieu-Duffing方程在一、二阶近似下的定常解，分析了平均方程在不同参数平面内的幅值响应曲线，根据解的稳定性判据得到了物理参数平面上的分岔集以及定常运动在相应平面的分布情况，详细分析了该系统在各个区域内的动力学特性。

Based on the tooth profile plane model's boundary scope and the geometry dimension of the transmission gear, the paper calculates every point's Cartesian coordinate in all parts of tooth profile, such as addendum arc, involute, dedendum easement curve, axle hole arc and other boundary line section.

最后根据齿廓的几何尺寸和五类齿廓平面模型的边界范围，计算齿廓各部分，即齿顶圆圆弧段、渐开线段、齿根过渡曲线段、轴孔圆圆弧段和齿廓平面模型上其他边界线段上点的坐标，并连接这些点生成各部分线段，从而生成齿廓平面模型。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

The reservoir rock types in the region of interest are grain limestone, algal limestone, cryptite, siltstone, muddy limestone and mudstone. The thesis identified as a result of changes in the deposition causing the heterogeneity in plane, and then the geological oil reserves have been calculated in accordance with the areal heterogeneity.3、Based on the data of core analysis, bore logging, array induction imaging log and FMI, porosity and permeability model were built using regression analysis. Through testing 45 rock samples, a, b, m, n value were obtained and used to calculate single-layer oil saturation value using the Archie formula. According to the theory of laterolog and inductolog, resistivity ratio and cross plot were used to identification effective thickness. Effective thickness was identified delicately in 103 wells. Based on the over work, active porosity and oil saturation was calculated accurately.4、According to observation of 100 pieces of the thin slices, cast thin slices and 383m core in three wells, the chief diagenesis in this area were compaction, cementation, denudation and cataclasis. Cementation and denudation were universally influenced active porosity this area. The intergranular pores, residual pores and secondary pores were formed in thin carbonated reservoir of lacustrine facies.5、The influence of reservoir heterogeneity to reservoir calculation was analyzed systematically using actual data. And the conclusions were as follows:①The principal reason leading to oil distribution unequal is interior structural feature of reservoir in structural hydrocarbon reservoir.

确定了由于沉积微相的变化而导致的平面非均质性，进而在平面上按照平面非均质单元计算了石油地质储量。3、利用岩心分析、常规测井曲线与阵列感应、成像测井资料相结合，分岩性利用回归分析方法建立了储层孔隙度、渗透率模型；通过对45块岩样进行岩电试验，获取了a、b、m、n值，利用阿尔奇公式计算了各单层含油饱和度值；根据侧向电阻率和感应电阻率串并联特性，利用电阻率比值法与常规交会图法相结合重建了有效厚度图版，对全区103口井目的层段进行了有效厚度精细划分，通过以上工作，准确求取了储量计算单元内有效厚度参数、有效孔隙度参数以及含油饱和度参数。4、通过对研究区3口井383m岩心观察，100余块薄片、铸体薄片镜下鉴定得出：油泉子油田上、下油砂山组储层主要成岩作用是压实作用、胶结作用、溶蚀作用和破裂作用，其中溶蚀作用、胶结作用最普遍，这两种作用对有效孔隙度影响最大，以上成岩作用形成了原生粒间孔、粒间残余孔和次生孔隙(如粒间溶孔、粒内溶孔、铸模孔、晶间孔等)为主的薄层湖相碳酸盐岩储层。5、利用实际资料，系统分析了油藏非均质对储量计算的影响，认为：①对于构造油气藏而言，油气藏构造及断裂特征是造成油气分布不均的首要原因，储集条件相同的条件下，构造高部位有利于储存油气，油气在垂向的重力分异体现了油气藏内部构造的不均一特征。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了