参数曲线

Consider a plane curve with parametric equation.

设平面曲线的参数方程为，则曲率为

Based on the local parametric representation of a curve, the mathematical models of planar mechanism optimum synthesis for the local path generation are built. Objective functions are constructed generally and for some special cases as well.

在平面曲线局部参数表示的基础上建立平面机构局部轨迹优化综合的数学模型，构造了一般情况下及常见特殊情形的优化目标函数。

2D hairy brush model, 3D hairy brush model and parametric curve scheme are analyzed and various algorithms are compared.

把绘制方法分为2D，3D毛笔模型以及基于参数化曲线的纯几何图形学方法，对其中的典型算法进行了分析和比较。

Chapter 4 probes the approaches to draw out the graphs of conic sections with locus and parametric equation as well as the approaches to create the graphs of polynomials.

第四章探索利用轨迹及参数式作出圆锥曲线图形的方法，以及多项函数图形的作法。

The theory of cutting Bezier line apart is above all developed into Bezier surface whose parametric equation and separating caculation formula are coorespondingly concluded.

首次将Bezier曲线分割拓广到Bezier曲面分割，推导并给出了Bezier曲面的参数形式和它的分割计算公式。

In chapter 4, the case of risk asset allocation with allowed sell and restricted short sell is discussed, especially in case of restricted short sell, the efficient frontier piecewise partition is determined by using duality theory in parametric quadratic programming. And the concept of tripartition is introduced, economic meaning stated and algorithm to determine efficient frontier proposed.

特别对限制卖空的证券组合，应用参数二次规划对偶性理论解决了有效边缘曲线分片划分的问题，并引入了三元分割的概念，解释其经济意义，同时给出确定有效边缘的算法；对于协方差矩阵是奇异的情况，利用矩阵分块技术，得到不同情形下有效边缘的解析表达式，并用直观的几何图形描述，克服了M-V模型在实证分析中遇到的困难。

The quadratic patches is fixed,and its parametric representation method is gained.The cubic patches reduce to three local factors through reducing Bernstein coefficients to control shape of curve,two of them are used to join segments into G2- continuity approximating curves for given sequence data in space,and the other is used to adjust shape of segment.

先固定二次曲面片，并得到其参数形式，然后约简三次曲面片所对应的Bernstein系数，使之为带有三个形状调整的形状因子，其中两个分别代表曲线段端点处的曲率，另外一个作为形状的调整。

And boundary condition and parametrization of offset data points influencing on interpolating curve is discussed.

因此，正确地选择边界条件和型值点的参数化方法将会得到所需要的插值曲线。

The gamma function calculation of Pearson type III distribution is investigated,a new approximation method by using cone curve is put forward,and neither numerical integral nor series expansion may be used.

对皮尔逊Ⅲ型分布公式中伽玛函数的计算问题进行了研究，提出了一种新的数值逼近方法，在一定范围内对伽玛函数用圆锥曲线表示，利用递推公式扩大参数范围，免去了数值积分和用级数展开计算的麻烦。

The new method is given to design the optimum profile modification curve design The effects of optimum profile gear in improving the dynamic performance of gear transmission are verified in the Gear Dynamic Performance Test Rig In this dissertation, the main study contents and creative results are shown as following: The influences on the gear transmission system caused by the gear's accumulated error (periodic error and harmonic error) are theoretically studied. A new method is developed to simulate the gear's harmonic error by using the 2-order MARKOV process A simulated model of the dynamic performance which is excited by the gear's accumulated error is obtained.

本文在前人大量研究的基础上，结合作者承担的国家自然科学基金项目"齿轮传动动态系统辨识与三维修形研究"和山东省自然科学基金项目"齿轮传动动态性能仿真及结构参数、齿形的优化修形"，采用理论和试验相结合的新思路，系统地研究了齿轮传动的动态性能，建立了能正确描述齿轮传动系统动态性能的仿真模型和系统辨识模型，给出了确定齿轮传动轮齿修形曲线的优化设计方法，利用自行研制的齿轮传动动态性能试验装置，验证了优化修形齿轮对提高齿轮传动动态性能的突出作用。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。