曲面

A novel rendering technology based on surface reconstruction of points is presented,and through local surface analysis,surface parameter extraction and re sampling, fine rendering result at any viewing distance is generated.

提出了一种基于曲面点集重建的渲染技术，能够对输入点集作局部分析，提取曲面的参数，并通过重采样的方法，获得新的、密集的采样点，生成近景的高质量渲染结果。

Web-based application system of geometric error compensation aims to broaden error compensation technology by using network. SMART-CNC machine tool has been chosen as the object of experiment. Based on the kinematics of multi-body system, the movement equation for SMART-CNC machine tool has been built.Furthermore, web-based error compensation system has been implemented.

基于Web的数控曲面磨床几何误差补偿技术：以误差补偿技术的网络化应用为目的展开研究，选取SMART-CNC 数控曲面磨床为研究对象，运用多体理论，建立了磨床的运动模型，获得了与精密刀具轨迹相对应的逆变刀具路线或逆变数控指令的求解方法，在此基础开发了基于网络的误差补偿软件，构建了网络化误差补偿服务系统。

A deformable model is used to reconstruct the shape of the LV: first, the dynamic equation governing the surface deformation is deduced; secondly the image planes are mapped to the reconstruction coordinate system. From the slices data, the external force exerted on the surface is defined and the elastic force of the surface is constructed by mean curvature of the deformation surface. Finally, a level set method is applied to solve the dynamic equation for LV shape.

为了重建左心室的形状，使用基於形变模型的方法：首先建立变形曲面的动力学方程；再将成像坐标系中的图像平面映射到重建坐标系，根据图像数据构造外力，使用平均曲率构造变形曲面的弹性力，然后用水平集数值解法求解动力学方程以重建左心室的表面。

We prove that the compact hypersurfaces and the hypersurfaces with constant mean curvature must be totally geodesic.

紧致超曲面以及常平均曲率超曲面的全测地性质。

Then, the first and second fundamental forms, Gaussian curvature and mean curvature of the surfaces are directly calculated according to the principles of differential geometry.

首先，根据微分几何中的基本知识，得到了该种度量形式下的平移曲面的第一、第二基本形式以及高斯曲率和平均曲率；然后，主要利用高斯曲率和平均曲率之间的线性关系和平方关系，得到了这类平移曲面的分类定理。

A new weighted mean algorithm according to angle vector is presented for modifying multipoint interference of tool axis.

该算法采用投影法，计算负梯度方向的搜索步长，快速计算出刀具中心线与曲面、刀具端面与曲面之间的最短距离。

Moreover, to get more effective control over the mesh size in the interior of the surfaces, an interactive control approach is adopted.

同时，为了加强对曲面内部单元的尺寸控制，采用了交互控制曲面内部单元尺寸的方法。

This paper begin with a review of curves and surfces modeling, then we discuss the parametric polynomial minimal surface. This is followed by a discussion of the representations of catenoids and helicoids. Next, we discuss the numeric approximations to the minimal surfaces with piecewise polygons and B-Spline surfaces.

全文安排如下首先，我们简要回顾曲面造型历史和发展现状在第二和第三章，讨论参数多项式极小曲面；在第四章讨论悬链面和螺旋面的表示；在第五章讨论极小曲面的分片线性逼近；在第六章讨论极小曲面的B-样条逼近；最后，我们对全文做简单的总结。

The Enneper's minimal surface is the unique cubic parametric polynomial minimal surface one can find and one can not find any high order polynomial minimal surface in the differential Geometry literatures.

极小曲面被广泛应用于建筑设计，飞机轮船制造业，在结构化学，材料科学，植物学，动物学等领域被用作各种模型，在这些应用领域已有很多文献出现，但是，在CAGD领域几乎还没有关于极小曲面造型方面的工作。

We can costruct an exterior n-form ξ for every hypersurface M in Euclidean space Rn+1. The submanifold M is minimal if and only if is closed (dξ= 0), then ξ is calibration and M is ξ-submanifold.

我们证明了对于欧氏空间R~(n+1)中每一超曲面M，可以构造η-微分式ζ，而超曲面极小的条件恰是ζ为闭形式，即dζ=0的条件。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。