二次曲面

So it is not easy to turn this idea into reality. We creatively give our parameterization by using the expression of the blending surface in affine coordinate system ([9]) and the plane pencil together.

在仿射坐标系下，二次有轴曲面的表达式相对简单，我们基于厉玉容[9]给出仿射坐标系下拼接曲面的表达形式、不分块直接对混合拼接曲面进行参数化。

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。

A frame to construct a blending surface among quadrics with the algebraic tensor-product B-spline surfaces was presented. A C^1 continuous algebraic spline surface was obtained that very smoothly joined the given quadrics.

给出了一种应用代数张量积B样条曲面构造blending曲面的框架并详细讨论了二次代数曲面间blending曲面的构造方法。

On the basis of OCM, segmentation based on curvature radium is presented in the paper, in which curvature radium is calculated using parametric-surface fitting, and detecting edge points is realized from orthogonal direction, which ensure the integrality of edge points. Since the data is organized by cross-line in OCM, a new arithmetic, Double-direction Angle Difference arithmetic, is brought forward, which can pick up edge points more quickly.

物体的表面一般由多个曲面相交组成，要建立完整的几何模型，需要对测量数据进行区域分割——区分不同曲面的数据，现有的区域分割大多是对单视图的图像式测量数据进行的，但完整的CAD模型需要联合多个视图产生，本文在上面提出的三维正交模型的基础上，提出了三种区域分割方法：第一种方法是基于曲率半径的数据分区方法，通过二次参数曲面拟合计算局部曲率半径，从正交的多个方向进行检测，保证了边点提取的完整性。

Based on study of relationship between the average quadric error and the surface curvature, a variable resolution surface reconstruction algorithm was proposed.

在研究平均二次误差与曲面曲率关系的基础上，提出了变分辨率的曲面重建算法。

The present thesis will adopt some of these methods to study on conjugation including the conjugate chord, Conjugate Direction and conjugate diameter of Conics as well as the Conjugate Direction, Conjugate net, Harmonic conjugate and Conjugate minimal surfaces of surfaces.

本文利用到了其中的某一些方法，讨论了这个问题，其中包括二次曲线的共轭弦、共轭方向，共轭直径。曲面上的共轭方向，共轭网，调和共轭，共轭极小曲面等。

For improving the quality of Chinese tradition frozen flour food,providing processing informa- tion for frozen flour food industry,standard wheat flour in market was selected as the material,second re- gress correctitude was performed with forceand tractilityas target,two second order quadratic equations for frozen dough sheet processing were built.

以市售标准粉为材料，利用二次回归正交旋转试验设计，分别以冷冻面片质构特性参数破碎力和延展性为响应值建立了冷冻面片制作的二次多项数学模型，验证了模型的有效性，采用响应曲面法(response surface methodology，RSM)考察了交互作用的影响，并根据方程求解出稳定点的水平值，从而确定出冷冻面片制作工艺的优化参数为：和面速度240 r/min，和面时间5 min，和面加水量40%，静置时间30 min，冷冻温度-30℃，冷冻时间5h。

It involves a spherical primary mirror and the secondary mirror with profile given by computer.lt is not necessary for the new optical system to obtain the on-axis solar image,so the secondary mirror may have a simpler profile.

一种由球面主镜和由计算机算出曲面型线的二次镜组成的新型二次反射聚光系统，可以减少制造困难，当这种光学系统用于太阳能聚光器时，由于不需要得到轴上的太阳像，其二次镜型线可更为简单。

Theory; the spatial meshing theory includes comparative motion, comparative differential and conjugative curved surface; and the application of meshing theory includes gear drive and worm drive. The spatial meshing theory is the main part of the course.

课程的重点讲解内容有曲线的参数方程、切线、法面、弧长、曲率、空间曲线的基本公式、挠率及平面曲线的基本公式等；曲面第一和第二基本公式，法曲率、主方向和主曲率、欧拉公式、短程挠率、欧拉公式和贝特朗公式推广、相对法曲率和相对短程挠率等；刚体的绝对和相对运动速度、相对微分和绝对微分、相对速度和相对微分、轨迹曲面的法曲率和短程挠率等；空间共轭曲面的啮合条件、诱导法曲率、两类界限点、等距共轭曲面、空间啮合的二次接触原理等；蜗杆传动的数学模型建立及啮合特性分析方法等。

This paper put forward the optimized methods include reconstructing the characteristic curve by reasonable use of the adjust tools and analyse tools of the modeling software, admeasuring the automotive model surface correctly, simulating the breaking surface and creating the surface in the right turns which is good for modeling a smooth and exactitude surface.

本文通过合理利用反求软件中的造型工具和分析工具，正确划分反求模型的造型区域，使用正确的曲面造型方法，对反求曲面的特征网格线进行二次优化，并对突变曲面进行拟合再生成处理及建立合理的曲面生成顺序等方法，最终获得了仿型度和光顺度都很高的反求曲面。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新