In the second part , we investigate the compact submanifolds m with the parallel isoperimetric section in the real space forms rm ( c ) and prove that if there exists a parallel isoperimetric section on m , and the sectional curvature of m is always greater than zero , then m is contained in a hyper - sphere ; and get that the gauss curvature of the compact surfaces m with constant mean curvature in constant curvature space r4 ( c ) is always greater than zero , then m is a totally geodesic surface or a sphere , where an isoperimetric on m means a unit normal vector field defined globally on m with m1 ( ) = constant ( 2 )研究了实空间形式r ~ m ( c )中具有平行等参截面的紧致子流形m ,证明了具有一平行等参截面的子流形m ,如果m的截面曲率恒正,则m包含在r ~ m ( c )的一个超球面内;对于常曲率空间及r ~ 4 ( c )中具有常平均曲率的紧致曲面m ,如果m的高斯曲率处处大于零,则m或为r ~ m ( c )中的全测地曲面或为一球面。这里m上的等参截面是m上整体定义的单位法向量场,使得m关于它的平均曲率m _ 1 ( )是常数。
Then i consider a correlative problem : where m , > 0 , s is a bounded domain with smooth boundary in ; v is outward normal vector on ; f ( s ) is continuous function and satisfies some increasing conditions ; u0 ( x ) is a positive function satisfying some compatibility conditions , to obtain the blow - up conditions of the positive solution using the method of subsolution and supersolution , extend the result of song and zheng )上的单位外法向; u _ 0 ( x )是正的函数且满足一定的相容性条件:讨论m 1的情况时,在何种条件下使得问题的正解整体存在或是在有限时刻爆破。主要采用上下解的方法来得到结论。随后考虑相关问题:其中m , 0 ,为r ~ n ( n 1 )中的有界域,具有适当光滑的边界(
The main task of this paper concentrates on such parts as calibration of measurement sensor , high speed and accuracy image collection and processing , data fusion of different angle of view , visualization of measuring results . to accomplish sensor calibration , a pinhole model of the camera is employed and an equation of a light plane is setup . parameters such as the m array of the pinhole model and the normal vector of the light plane arc acquired through experiment . in image processing , we adopt the template - changing parallel thinning method to improve processing speed and accuracy 主要研究了摄像机针孔模型的建立及测量传感器的标定;图像的快速高精度的采集和处理,在图像处理中采用多帧平均算法,很好地解决了速度和精度之间的矛盾制约;根据旋动理论建立空间坐标变换数学模型,进而建立其不同视角下的测量数据融合算法,生成完整的物体三维数据集合;在vc平台下编写三维显示软件模块,完成三维测量结果的可视化,实现了三维物体的任意角度的观察、任意倍数的放大和缩小、任意方向平移及动画效果。
At the same time , holes which may appear in walkthrough will be analyzed and filled in the preprocessing stage ; this thesis proposes a local reconstruction and resampling algorithm to generate a set of new samples which distribute more uniformly on surfaces and then they are organized by obb - tree and normal vector clusters 为弥补参考图象对场景表达不完备问题,本文给出了重建平面的空洞分析和预填补算法,在预处理阶段即对漫游时可能出现的空洞进行分析和高质量的填补;本文提出了一个针对基于点表达的物体的局部重建和重采样算法。
The solutions include : the unit normal vector of the elastic - plastic boundary near the crack line , the elastic - plastic stress fields near crack line , law that the length of the plastic zone along the crack line is varied with an external loads , the maximum lengths of the plastic zone , the bearing capacity of a finite plate with an eccentric crack loaded by shear forces 这个解包括:裂纹线附近弹塑性边界上的单位法向矢量,裂纹线附近的弹塑性解析解、最大塑性区长度、裂纹线上的塑性区长度随荷载的变化规律及其承载力。