参数曲线

The cubic algebraic curves (the Bezier curve and B style curve, etc belong to the parameter curve) is apter to realize the curve transition and fitting to dispersed data than the cubic parametric curves.

比如参数曲面与平面的交线就是一条平面代数曲线；平面参数曲线的等距曲线也是一条代数曲线。

For a general parametric curve/surface, we usually cannot compute its exact implicit form. Even though its exact implicit form can be computed, the curve/surface implicitization involves relatively complicated computation and the degree is higher. Moreover, it may have unexpected components and self-intersections. All these unsatisfied properties limit the applications of the exact implicitization. So finding curve/surface approximate implicitization has become a practical problem. In this paper, we present an algorithm to solve the approximate implicitization of a given parametric curve by using a quadratic algebraic spline curve.

由于精确隐式化过程不一定可以实现，即使可以实现隐式曲线曲面的阶数高计算复杂，并且具有不希望的自交点和奇异分支，从而限制了隐式化的运用，所以寻求参数曲线曲面的近似隐式化问题成为很实际又重要的问题，提出利用二次代数样条曲线来实现一般平面参数曲线近似隐式化的一种算法。

The interpolation algorithm of introduced error compensation for complex parametric curve in space is proposed for the high precision interpolation of parametric curve on the basis of studying the first, second order taylor expression parametric curve interpolation algorithm and the plane parametric curves interpolation algorithm.

以一、二阶泰勒展开式参数曲线插补算法和平面参数曲线插补算法研究为基础，提出引入误差补偿值的复杂空间参数曲线高精度插补算法以实现空间曲线的高精度插补。

In the last part of the paper, we construct a family of 2 parameter cubic algebraic curves interpolating two given endpoints and two given tangent lines and two given curvatures at these two endpoints with different initial cases in detail.

引 言三次参数曲线在计算机辅助几何设计与计算机图形学领域一直扮演着十分重要的角色，这主要是由于三次参数曲线是具有奇异性的次数最低的曲线，这些奇异性包括尖点、拐点和闭圈。

Aimed at the characteristic of multiple types of faults possibly happened in nuclear power plant, large scale of training sample, and requirement of quick and accurate diagnosing, after the analysis of large sample number generated by large fault type exceeds limitation of 64K paragraph in DOS and large number of local minmum in error surface, measurements of same format of data file, Win95/NT operating system platform, resetting weight learning rate, dynamic training set in quick learning algorithm and improvement on quick learning algorithm using homotopy method which can avoid local minmum points in error surface have been adopted to ensure quickly and effective process of the course of neural network's training and testing.

针对核动力装置可能发生的故障种类多，训练样本规模大，故障诊断需要快速准确的特点等，分析了样本多和故障种类多产生的训练样本量超出DOS段大小和网络误差曲面上局部极小值多的情况，采取了使用相同格式数据文件、Win95/NT操作系统平台，对快速学习算法采用重置神经网络权值学习率和动态训练集、并采用能够有效克服网络误差曲面上局部极小点的同伦方法对学习算法进行改进等措施保证神经网络训练测试过程的快速、有效地进行；针对装置发生的故障须快速、准确诊断的需要，分析了故障的产生对装置参数变化的影响及操纵员对故障诊断的基础，在核动力装置发生故障时参数曲线的变化量与正常运行时参数曲线的变化量存在明显差异的基础上，提出采用参数曲线的变化量作为神经网络的输入，并围绕参数变化量的方法采用二次曲线拟合滤波求变化量和阈值技术来保证神经网络得到精确的装置参数变化量，从而得到准确的诊断结果。

On the traditional electrical property parameter apparent resistivity curves, besides compact fine sandstone, igneous rock and limestone have obvious high-ohmic anomaly, there are no obvious electrical property difference between coal and wall rocks, the curve almost show itself a straight line; self-potential log also can hardly to reflect regularities.

常规的电性参数视电阻率曲线除致密的细砂岩、火成岩及灰岩有明显的高阻异常反映外，煤与围岩无明显的电性差异，曲线几乎呈一条直线；自然电位参数曲线反映规律性也较差。

It is composed of a deformable parametric curve and corresponding energy function.

主动轮廓模型是一种基于高层信息的目标轮廓特征提取算法，它由一条可变形的参数曲线及其相应的能量函数组成，以最小化能量函数为目标，控制参数曲线变形，具有最小能量的闭合曲线就是目标轮廓。

In computer-aided manufacturing, the processed parametric curve and surface should be regular, so the parametric curve and surface generated by computer-aided design should be regular first.

在计算机辅助制造过程中，要求所处理的参数曲线曲面是正则的，前提是计算机辅助设计得到的参数曲线曲面是正则曲线曲面。

Introduced is a kind of space uniform rational spline curve, which possesses tension parameters and is based on hyperbolic spline functions.

引入了基于双曲样条函数的、具有张力参数的空间有理等距节点样条参数曲线，给出了这种曲线在每个样条子区间上为挠曲线段的充分必要条件；分析了这种挠曲线段没有尖点、重结点和泛拐点的特性；因而在用于空间曲线几何造型时可避免奇异性。

Further, it is found that the limit curve is a uniform rational cubic B-spline curve or the curve's control polygon when its tension parameters tend to zero or infinity respectively.

Barsky[4 ] 将具有张力参数样条的双曲样条曲线引入CAGD ，称之为张力样条参数曲线，并证明了这种曲线是一类泛函问题的极小解。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。