参数曲线

Regularity is an important algebraic property of parametric curve and surface, which depends on the parameterization of parametric curve and surface.

正则性是参数曲线曲面的重要代数性质，是由参数曲线曲面的参数化决定的。

This algorithm firstly translates arbitrary parameter curves into the piecewise cubic-degree Bezier curves, then using the properties of Bezier curve we can get the tangent vector and the normal vector of every point on the approximation curve, and calculate the approximating offset curve.

此算法先将任意形式的参数曲线转化成分段三次Bézier曲线，利用Bézier曲线的性质容易得到逼近曲线的切向量和法向量，从而计算出其等距逼近曲线。

However, no matter what free-form deformation based on extension factor for parametric curve or arbitrary partition will reduce smoothness of parametric curve.

然而，无论是基于伸缩因子的自由变形还是基于任意分割参数曲线的自由变形都会使参数曲线的光滑度降低。

For drawing the parameter curve by point to point it orde to the parameter t's step length of increased make the progress range of the curve can not large than the length of one pels, otherwise the curve may step over one middle pels and skip one point that it should be on the curve.

要逐点地生成参数曲线，就要求参数t每次增加的步长要使曲线前进的幅度不得超过一个象素长度，否则有可能跨过一个中间象素而产生断点。

For example, quadratic curve and quadric surface are used as primitive element in most modeling/CAD system. The implicit formulae for computing the intrinsic geometric invariant??

随着对参数曲线曲面研究的深入，早在80年代初苏步青教授等就将几何不变量的研究引入并应用到参数曲线、曲面的研究中，取得了重要的成果［1？

And then, by regarding the curve and surface as a map from differential manifold to topological manifold, we present the framework of GRPCS and discussed its basic properties in detail. GRPCS provides a unified framework for parametric curve and surface.

然后通过势函数来构造微分流形上的单位分解，将曲线曲面看作微分流形到拓扑流形的映射，给出了广义有理参数曲线曲面的整体理论框架，并对广义有理参数曲线曲面的基本性质进行了讨论。

And then, using Matlab, we give some examples on regular surfaces. For example, plane, helicoidal, 3-dimensional Gauss profile, etc.

最后利用数学软件Matlab，给出了一系列的由光滑曲面上的参数曲线网经过离散化得到的离散参数曲线网，如平面，正螺面，三维Gauss型分布图，由3dMax生成的一般曲面等。

The method of prediction on stochastical simulating 3D parameter field of rock mechanics is brought forward in this paper. Namely, rock mechanics parameters- curve obtained by known and limited conventional log materials is took as inputs of hard data;and seismic attribute data body, hydrating of mud shale and rock environmental parameters data is took as constraint of soft data. By simulating stochastically through optimizing algorithm of Sequential Gauss Simulation,dynamical data field of rock mechanics parameter of three-dimensional space are gotten, then log response of rock mechanics parameters in position of any point in space is predicted.

提出三维岩石力学参数场随机模拟预测的方法，即以已知有限的常规测井资料计算出来的岩石力学参数曲线作为硬数据输入，以已知地震属性数据体及泥页岩水化和岩石环境参数数据作为软数据约束，选择序贯高斯模拟方法，随机模拟得到动态规律变化的岩石力学参数的三维空间数据场，然后由岩石力学参数的三维空间数据场预测空间任一位置的岩石力学参数在井上的测井响应，并把该反映动态规律变化的测井响应按照油田勘探开发的要求输出成特定格式，供生产和工程上使用。

In many applications, it is desirable to analyze the parametric curves for undesirable features like cusps and inflection points.

为了便于对参数曲线段的形状控制和几何特征的进一步认识，在许多的实际应用中，需要分析参数曲线段上有无多余拐点和奇点，如果有就要消除它。

This software requires less input parameters, use-friendly, easy to operate, and can output the curve of rock mechanics parameters, stress curve, collapsing pressure and rupture pressure curve, and can guided the Air-drilling Well body structure design and the field practicals.

软件要求输入的参数少，界面友好，操作方便，能输出岩石力学参数曲线、地应力曲线、坍塌压力与破裂压力曲线，对空气钻井井身结构设计以及施工具有很强的现实指导意义。

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。