曲面

Properties of bi quadratic B spline surface are investigated by the subdivision approach, and the control mesh of bi quadratic B spline surface is constructed by employing Doo Sabin subdivision to derive the parametric representation of interpolation surface.

文中利用子分曲面理论研究双二次 B样条曲面的性质，在此基础上利用 Doo- Sabin子分模式构造插值顶点位置和法向的双二次 B样条曲面控制网格，得到插值曲面的参数表示。

Proposed surface geometric operations and the improved data structure can be applied for a general parametric surface and for representing solid bounded by other parametric surface.

所提出的曲面几何处理的算法，改进的可统一表示曲面、实体模型的数据结构亦可应用于一般的参数曲面几何处理与曲面实体模型的表示。

Secondly, the key technology of how to align point cloud with surface feature model of human body, analyze error, adjust position are researched and the algorithms of calculating center of mass, inertia axis, and symmetry plane are successfully introduced.

然后，研究了对齐后的模型，如何将点云投影到曲面，识别出曲面特征，并对点云进行参数化和采用基于约束及能量优化法算法进行曲面重构，快速的建立不同人体的光滑G~1连续的B样条参数曲面模型。

The adhesion region between two adjacent teeth on the 3D dental model is first detected by exploiting the minimum principal curvature information. Then, the adhesion region is cut off and the tooth profile opening caused by the removal of the adhesion region is filled with triangular patches adopting a local optimization scheme, it is then refined to form an intermediate restoration surface patch. The final restoration result is obtained by minimizing the surface energy to reflect the bio-characteristics of the single tooth.

根据三维牙颌模型的形态特征，采用基于曲面最小主曲率的方法对粘连区域进行准确的检测提取；对删除齿间粘连区域后生成的齿间开口利用局部最优化权值规则进行剖分并细分优化，生成"中间"恢复曲面；根据牙齿的生理医学特征，以齿间开口的边界信息为约束条件，采用基于最小化曲面能量函数的方法对"中间"恢复曲面进行变形调整，实现单颗牙齿缺失形状的准确恢复。

Firstly, using quadric surface to fit with given surface and calculate the error metric to identify free surface and general quadric surface.

首先用一般二次曲面方程拟合测量数据并计算曲面的拟合误差，比较拟合误差与阈值的大小来识别自由曲面和一般二次曲面。

In relation to the feature extracting, the first step is to extract the "simple" surfaces such as planes, natural quadric surfaces and tori. Planes considered as degenerated quadric surfaces, the quadric surface feature extracting should be more important in RE.

而在点云的特征提取中，首先提取的是包括平面、自然二次曲面(包括球面、圆柱面、圆锥面)和圆环面的"简单"曲面，我们认为平面是一种退化了的二次曲面，因此研究二次曲面特征的提取是其中首要的课题。

Firstly, the quadric surface with three points which doesn't on one line is fitted, and then the tangent plane of this fitting surface is got. Meanwhile, the random tangent plane of surface patch subdivided is got also. Finally, the distance can be obtained through iteration between two tangent planes.

首先对点云数据中邻域不在同一直线的三个点进行局部二次曲面拟合，并求取该拟合曲面的切平面，同时求得细分曲面片任意一点处的切平面，最后在两个切平面上进行点对迭代运算，得到点到曲面片的最短距离。

For 5-Axis Cut Line Surface milling and Swarf milling, the alues are: USE_SURF_NORMS—The surface normal is used in determining the tool axis orientation, that is, any user-specified axis definition proides a localized lead and tilt angle that is applied to the normal of the surface being machined.

对于"5 轴切削线曲面"铣削和"刀侧铣削"，值为：使用曲面法向-曲面法向用于确定刀具轴方向，即，任何用户指定的轴定义都提供应用到加工曲面的法向的定位导引角和倾角。

The control mesh representations of the minimal surfaces are given by tensor product Bézier surface and triangular Bézier surface. Finally, we presented their application in modeling of tensioned membrane structure.

利用张量积Bézier曲面和三角Bézier曲面给出了该曲面的控制网格表示，并研究了该类极小曲面在张拉膜结构设计中的应用。

Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.

本文结合微分几何学，基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上，得到了参数化曲面上的图像处理框架，并给出了边缘检测和形态学运算的算例；在已知给定曲面的隐式表达时，探讨了定义在任意曲面上的偏微分方程，解决了任意曲面上数据场的扩散问题。

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％。