曲面的平均曲率

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。

Firstly, the method fits each vertex and its local neighborhood of the clothing and human models by constructing the biquadratic Bezier surface. It can estimate the Gaussian curvature and the mean curvature of each vertex. Then, the feature points of two mesh models are extracted according to curvatures.

该方法基于双二次Bezier曲面局部拟合服装模型和人体模型的网格顶点及其邻近点，估算出人体和服装模型网格顶点的高斯曲率和平均曲率，然后提取出人体和服装模型两点集的特征匹配点。

And then, in this part, following the idea of Topping [51, 52], we will show an isoperimetric inequality (6.3.1) on surfaces of non-positive Gaussian curvature by means of the curve shortening flow on surfaces, this inequality can be considered as a generalization of the Banchoff-Pohl inequality in the Euclidean plane.

然后，仿照Topping[51]和[52]利用平均曲率流证明等周不等式的想法，我们利用曲面上的曲线缩短流在Gauss曲率非正的曲面上证明了一个等周不等式(6.3.1)，它可以看成欧氏平面上Banchoff-Pohl [8]不等式在曲面上的推广。

And then, we gain some definitions that in relation to regular surfaces which include discrete Gauss curvature and discrete mean curvature.

由此获得了一系列的相对于光滑曲面的离散定义，如离散平均曲率，离散Gauss曲率等。

In Chapter 6, by using the matrix models of 3-dimensional Minkowski space R〓, first we study deformation properties and integrablilities on spacelike surfaces with a harmonic inverse mean curvature and timelike surfaces with a Lorentz harmonic inverse mean curvature.

在第六章中，首先借助三维Minkowski空间R〓的矩阵模型，研究了R〓中具有调和逆平均曲率的类空曲面和洛伦兹调和逆平均曲率类时曲面的可积性及其形变。

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。

There have been many good results when M is minimal sub manifold. In the first section we will introduce the context and make a general description on the recent researches. In the second we will introduce the complexion of the development for this problem. In the fourth we\'ll discuss the second gap on special conditions using similar methods when the mean curvature is constant, and find the second gap.

关于极小子流形的间隙问题已经有了很多好的结果，第一节引言中我们将介绍本文的研究背景及这些主要结果，第二节中我们来介绍具有常平均曲率情形的间隙问题的发展现状，在第四节中我们用类似的方法讨论平均曲率为常数的紧致超曲面的第二间隙问题，得到了第二间隙δ=？

The normal and curvature are significant geometry information for 3D point clouds.

差分坐标以其相关之拉普拉斯运算子在三维数位几何模型上已有许多的研究及应用，顶点的差分坐标计算是由顶点与拓扑上之相邻点的相对位置关系所求得，因此顶点之差分坐标代表了区域曲面起伏变化情况，差分坐标其方向会近似於区域法线方向而其长度会近似予区域平均曲率，此两项资讯为点云资料重要几何资讯。

Let x be an immersion of a compact Willmore surface M into the n-dimensional unit sphere Sn. In this thesis we first consider the Willmore surfaces in the unit 3-sphere, and establish an integral inequality for the square of the length of the trace free part of the second fundamental form and the mean curvature.

令x是一个从紧致威尔摩曲面M到n 维单位球面Sn的浸入，在本论文中我们首先考虑3维单位球面中的威尔摩曲面并建立一个包含第二基本型式迹为零部份的张量长度平方与平均曲率之积分不等式。

The author used this intrinsic connection to give the notion of horizontal mean curvatures of hypersurfaces in sub-Riemannian manifolds.

作者应用这个内在的联络给出了超曲面的水平平均曲率的几何定义。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。