曲面

A method of the surface combination based on classification or Euler Operation and the computation of the surface boundaries of a surface is offered to finish the geometry mapping of surfaces between half-edge model and the closed_shell branch of manifold surface model. Moreover, the concepts of conformal-shape geometrical mapping and topological mapping are given. The bi-directional conformal-shape topological mapping between half-edge model and the closed_shell branch of manifold surface model is proved.

提出了一种基于等价分类和欧拉操作的面片合成和曲面边界计算方法，完成了半边模型到流形曲面模型closed shell枝的曲面几何映射；给出了保形几何和保形拓扑映射概念，证明了半边模型到流形曲面模型的closed_shell分枝的双向保形拓扑映射。

According to this process, the key technology which including the characteristic measurement of surface, the pretreatment of data getting by line scan, the character expression and fitting of curve and surface, the characteristic identify of surface and translation from the model of surface to CAD.

对实物反求过程中的各关键技术作了研究，包括：曲面的特征测量、逐行扫描测量数据的预处理、曲线曲面的特征表示及其拟合、曲面的特征识别以及曲面模型向CAD模型的转化。

When you create skin surfaces in CoCreate Surfacing, you can store the properties for the 3D curve mesh and surface conditions defining the skin as part of the model.

当您使用CoCreate Surfacing 曲面模组建立一个网格曲面时，您可以将曲面的条件及参考线储存在曲面零件内。

With CoCreate Modeling 2008, you can analyze both imported and native skin surfaces to automatically create 3D curve meshes that you can store as surface properties.

曲面编辑：定义曲面属性( Surface Editing： Assign Surface Properties )在CoCreate 2008，您可以分析汇入的或自行产生的网格曲面来自动产生3D架构线，并可将其储存为该曲面的属性资料。

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。

To eliminate the information of the surface model, thus improving the modeling speed and enhancing precision, an algorithm based on digital image processing for generating self-adaptive density mesh from measured dense scatted points is also introduced.

模型采用离散拓扑结构，无须进行曲面分片，因此不存在子曲面片之间的拼接问题；不采用解析函数表达曲面，因此不存在复杂组合曲面的参数域界定困难的问题；模型去噪能力强，特别适合大噪声场合。

In the CAGD field, Coons surface, B-spline surface and NURBS surface are mainly used.

唐泽圣 ，左万利，王拉柱Coons类曲面、B样条曲面和NURBS曲面是CAGD中主要的曲面表达形式。

These surfaces not only inherit the most properties of Coons surfaces,but also can adjust their shape through changing the values of parameters.The effect of two parameters λ1 and λ2 on the interior concavity and convexity of the generated surfaces is also discussed.

这些曲面不仅具有Coons曲面的良好边界插值性质，还可以通过调整参数λ的值来改变曲面内部的形状，并讨论了参数λ1，λ2对曲面内部凹凸的影响。

In this paper, we consider the n-dimensional hypersurfaces (n≥3) with vanishing Mbius form Φ.

本文考虑了S(上标 n+1)(n≥3)中具有消失Mbius形式Φ的超曲面：对具有调和曲率张量的超曲面进行分类，进而，在Mbius度量的意义下，对Einstein超曲面和具有常截面曲率的超曲面也进行了分类。

With the boundary point and the known adjacent relations, an overall marching procedure can go on and the iteration process stops until the intersection curve is self-closed or reaches the border of the composite surface. In the later case, the marching must be repeated from the starting point in the reverse direction until the intersection curve reaches the other border of the composite surface.

由一个交点出发，通过计算跟踪方向和跟踪步长，迭代计算出下一个精确的交点；利用边界点和近曲面点计算方法，根据曲面片的拓扑关系找到交线所经过的下一张曲面片，从而使跟踪过程继续下去，直至形成封闭交线环而停止该交线段的跟踪，或到达复合曲面的边界后由首交点反向跟踪到达复合曲面的另一边界。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。