闭曲面

Harvey证明了在亏格为g，g≥2的可定向闭曲面上，保定向周期自同胚的最大阶是4g+2。

Harvey that the maximal order of an orientation preserving Periodic map on an orientable closed surface of genus g. g ≥ 2 , is 4g + 2 . In this paper , we investigate the uniqueness of such maps .

闭曲面有限元网格生成的边界预调整方法

Boundary Pre-Adjustment Method for Finite-Element Mesh Generation of Closed Surface

做为应用给出了不定向闭曲面上具有伪轨跟踪性质的Cr流的特征。

Then we give the characterization of Cr flows with the pseudo orbit tracing property on nonorientable closed surfaces .

著名的Ros不等式的一个重要推论就是关于著名的Alexandrov定理的精彩证明：嵌入E~3中的平均曲率为常数的紧致闭曲面一定是球。采用什么标准评价？

We will use the Ros ' inequality to reprove the theorem of Alexandov : the only compact embedded surfaces of constant mean curvature in E ~ 3 are the standard spheres .

闭曲面上的C~0流的几类局部结构

Some local structures of C 0 flows on closed surfaces

二维有限亏格的可定向闭曲面上的拓扑传递性与度量传递性

Topological Transitivity and Metric Transitivity in Closed Directed Two-dimensional Surface of Finite Genus

可定向闭曲面上最大阶保定向周期映射的唯一性

Uniqueness of Orientation Preserving Periodic Maps of Maximal Order on Orientable Closed Surfaces

d轨道各瓣闭曲面的旋转对称性

Rotational symmetry of closed surfaces of D obitals

有限群在可定向闭曲面上反向自由作用的等价性（英文）

Equivalence of the Orienation-Reversing Free Actions on Closed Orientable Surfaces by Finite Groups ;

本文建立关于三维空间型中的可定向闭曲面的某些公式。

This paper establishes some formulas on orientable closed surfaces in 3-dimensional space forms .

在较弱条件下研究了凸闭曲面的调和映射问题。

We have discussed the harmonic mappings of closed convex surfaces under some weak conditions .

引入积分绝对平均曲率来描述可定向闭曲面的平均弯曲程度。

Integral absolute mean curvature is introduced to describe average curving of an orientable closed surface .

高中数学欧拉公式与闭曲面分类教学设计研究

Instruction Design Studies of " Euler 's Formula and the Classification of Closed Surfaces " for High School Mathematics

散度定理为我们提供了一种，计算向量场通过闭曲面的通量的方法。

So , the divergence theorem gives us a way to compute the flux of a vector field for a closed surface .

经过曲面切片、型值点提取、点列排序、一维插值、数据融合，得到闭曲面四边形网格图。

The quadrilateral grid graph of closed surfaces was obtained through surface slicing , offset point picking up , ordering of point array , 1D interpolation , and data merging .

而且探讨了空间型中超平面的性质，这对构造体现空间型中闭曲面整体弯曲程度的例子是有帮助的。

Some properties of the super plane in space forms are investigated , which is helpful to construct the example showing the banding properties of the closed surfaces in space forms .

当所给点集是闭曲面集的局部分离样本或已知采样空洞半径的全局分离样本时，本算法将给出正确的重建结果；

When the given point set is a local separate sample of a closed surface set or an overall separate sample with known radius of sampling hole , the algorithm will reconstruct a correct result ;

曲面上的（拓扑）地图是一个闭曲面的胞腔分解，0-胞腔称做顶点，1-胞腔称做边，2-胞腔称做面，顶点和边形成地图的基图。

A map on a surface is a cellular decomposition of closed surface into O-cells called vertices , 1-cells called edges and 2-cells called faces . The vertices and edges of a map form its underlying graph .

该算法首先对数据点进行参数化；然后利用张量积曲面的性质，将曲面反算问题化解为一系列曲线反算问题，分别反求闭曲面和开曲面的控制点。

The algorithm first parameterizes data point ; then using the nature of the tensor product , surface of inverse problem will be resolved as a series of curves of inverse problem , namely , reverse closed surface and open surface of the control points .

欧氏空间中凸闭超曲面的唯一性定理的推广

Generalization of a uniqueness theorem on closed convex Hypersurfaces in Euclidean space

开闭式曲面屋盖体系分析中与结构移动有关的若干问题

Some Issues About Roof Moving in Analysis for Retractable Roof Structures with Curved Surface

本文研究欧氏空间中凸闭超曲面的唯一性，得到了S.S.Chern，J.Hano＆C.C.Hsiung（1960）关于欧氏空间中凸闭超曲面的唯一性定理的一个推广。

In this paper , we study the uniqueness on closed convex hypersurfaces in Euclidean space . S. S.

在众多光顺方法中能量法仍是一种应用非常广泛的曲线曲面光顺方法，可以处理约束问题，并适用于大挠度和闭曲线曲面的光顺。

Energy optimization is still widely used among a lot of the methods in the faring of B-spline curves and surfaces . Energy optimization can deal with the problems of constraints , and can be used in large flexibility and close B-spline curves and surfaces .

多材料结构中材料界面的变形运动在几何上可以抽象为闭曲线或闭曲面随时间的演化。

In a structure of multi-materials , the motion of material interlaces can be abstracted as the evolvement of closed curve or curved surfaces with respect to time .

并讨论了在放开或删除一个控制点后，不再生成该控制点邻域内的所有曲面片，从而开放闭多面体的边界，将闭曲面造型算法延伸为开曲面造型的算法；

The paper also discussed removing one of the control vertex of control polyhedron and the adjacent domain of the removing vertex was not considered again , so that the algorithm was reformed to be one of the unclosed surface modeling .