客车车身数值模型的建立

客车车身由大量的相互约束自由曲面组成.利用B样条和NURBS曲线曲面,以测量得到的数据为原始数据,运用逆向工程原理,建立了客车车身曲面片的数值模型.并利用重顶点技术,对有公共交接的曲面进行光顺拼接及对三角域进行缝合,最终建立客车车身数值模型.     

三角域上B-B曲面和矩形域上B E、ZIER曲面之间的几何连续条件

利用KAHMAN R关于曲面片之间的GC2连续条件得到了 当三角域上B-B曲面已知时,三角域上B-B曲面和矩形域上B　E、ZIER曲面之间的GC2连续条件。     

三角域Bezier曲面若干算法研究

从待拟合曲面的曲率变化大小出发 ,有针对性地提出新的三角域 Bezier曲面拟合算法和曲面曲率变化小的曲面拟合方法 ,进一步推导了曲面曲率变化大的曲面拟合方法 ;另外还研究了三角域 Bezier曲面对矩形域 Bezier曲面的逼近算法 ,给出了三角 Bezier曲面片表示矩形 Bezier曲面片的显式公式 ,通过图示形象化描绘了特征顶点递推过程 ,并指出了特征顶点递推公式。该算法在彩色 CRT校正透镜CAD系统中得到成功应用     

三角域Bezier曲面片G1样条曲面造型

将三角域Bezier曲面片与B样条方法结合起来,构造出插值于任意拓扑结构多面体的分片G1连续的样条拼接曲面.     

三角域和四角域上Bernstein-Bezier曲面片的拼接

给出了具有公共边的三角域和四角域上Bernstein-Bezier曲面片光滑拼接的条件,该过程不需提高曲面的次数,有效地解决了构型复杂、形状和边界不规则的几何造型问题.     

三角域上B-B曲面片的保凸对接

本由曲面凸性的定义，得到了三角域上Bernstein-Bezier曲面片在光滑连接条件下，整个曲面保凸对接时曲面 Bezler点所满足的条件．     

三角矩阵的等价标准型

给出域上上三角矩阵的等价标准型.作为应用,证明了一个秩r上三角矩阵可分解为有限个秩s上三角矩阵的和,并证明了域上上三角矩阵环的每个理想都是主理想,且由唯一的约化标准上三角矩阵生成.     

三角域Bezier曲面片G^1样条曲面造型

将三角域Bezier曲面片与B样条方法结合起来,构造出插值于任意拓扑结构多面体的分片G^1连续的样条拼接曲面．     

三角域和矩形域上Bezier曲面之间的几何连续条件

Kahman给出了相邻的矩形域上的 Bezier曲面及相邻的三角域上 Bezier曲面之间 GC2连续条件 .利用相邻矩形域上的 Bezier曲面之间的 GC2 连续条件及 Bezier曲面的高阶编导数 ,得到了相邻的三角域和矩形域上 Bezier曲面 GC2 连续的一个充分条件 ,该条件计算方法简便 ,几何意义明确 ,便于在计算机辅助几何设计中应用     

三角域上的Wang-Ball曲面带形状参数的扩展

为了扩大自由型曲面的选择范围,本文引入一个形状参数,给出了三角域上Wang-Ball曲面的扩展。通过改变形状参数的值,可以调控曲面的形状。形状参数几何意义是明确的,随着参数的增大,曲面向控制网格靠近。     

两相邻3次B样条曲面G~1连续充分条件

根据参数曲面几何连续性定义,利用3次B样条曲面的矩阵表达式,给出了两邻接3次B样条曲面间的G1光滑拼接的充分条件.该拼接算法易于实现,数值算例表明了算法的有效性.     

两邻接二次B样条曲面G1光滑拼接的充分条件

利用二次B样条曲面的矩阵表达式,将B样条曲面进行分片表示,给出了两邻接二次B样条曲面间的G1光滑拼接的充分条件.该拼接算法易于实现,在CAGD的复杂曲面造型中,具有一定的实用价值.     

Developable Bézier function surface

Developable surface plays an important role in engineering domains are common representation forms in a computer aided geometric function surface up to now. General characterizations of developable function surface of degree 2 on the triangular domain must be a parabolic of degree 3 on the triangular domain and of degree (2,2) on the rectangular domain are presented. The conclusions can be easily extended to bivariate polynomial function surface.     

4阶三角多项式空间中的T-Bézier基在三角域上的推广

由于T-Bézier曲线曲面是张量积形式的,为了进一步研究非多项式空间中的T-Bézier基,完善其关于三角域部分的理论,将4阶T-Bézier基推广到三角域上,构造了满足非负性、规范性、对称性、边界性质和线性无关性的基函数,并证明了三角域上相应曲面的一些性质,最后给出了一些应用。     

Constructing parametric triangular patches with boundary conditions

The problem of constructing a parametric triangular patch to smoothly connect three surface patches is studied. Usually, these surface patches are defined on different parameter spaces. Therefore, it is necessary to define interpolation conditions, with values from the given surface patches, on the boundary of the triangular patch that can ensure smooth transition between different parameter spaces. In this paper we present a new method to define boundary conditions. Boundary conditions defined by the new method have the same parameter space if the three given surface patches can be converted into the same form through affine transformation. Consequently, any of the classic methods for constructing functional triangular patches can be used directly to construct a parametric triangular patch to connect given surface patches with G^1 continuity. The resulting parametric triangular patch preserves precision of the applied classic method.     

Constructing parametric triangular patches with boundary conditions

The problem of constructing a parametric triangular patch to smoothly connect three surface patches is studied. Usually, these surface patches are de?ned on di?erent parameter spaces. Therefore, it is necessary to de?ne interpolation conditions, with values from the given surface patches, on the boundary of the triangular patch that can ensure smooth transition between di?erent parameter spaces. In this paper we present a new method to de?ne boundary conditions. Boundary conditions de?ned by the new method have the same parameter space if the three given surface patches can be converted into the same form through a?ne transformation. Consequently, any of the classic methods for constructing functional triangular patches can be used directly to construct a parametric triangular patch to connect given surface patches with G1 continuity. The resulting parametric triangular patch preserves precision of the applied classic method.     

应用耦合法计算大型铝电解槽的电流场

本文建立了大型铝电解槽电流场的数学模型,应用有限元和边界元耦合法进行计算,方便地处理了阴极炭块的非均匀正交各向异性问题;在计算中使用了具有场域自动剖分,矩阵分块,矩阵行优化排序和非零存贮等稀疏矩阵技术的计算程序,在对多种结壳情况下铝电解槽电流场的数值计算结果进行分析的基础上,得出了一种使铝液中水平电流较小的结壳形状。     

基于低秩矩阵近似的鲁棒DOA估计方法

针对非均匀噪声背景下传统非离散化方法在少快拍条件下波达方向（DOA）估计性能恶化的问题, 提出基于原子范数最小化和零化滤波器的非离散化参数估计方法. 该方法利用参数空间连续性构建基于原子集合的阵列信号稀疏表示模型, 将信号协方差矩阵的恢复问题转化为原子${\ell _0}$范数最小化问题. 基于信号协方差矩阵的厄米特托普利兹结构和低秩特性, 将原子${\ell _0}$范数最小化问题转化为实际可解的基于低秩矩阵近似的半定规划问题, 从而恢复信号协方差矩阵. 根据零化滤波理论通过求解零化滤波器系数获取DOA参数估计. 仿真结果表明, 在非均匀噪声和少快拍同时存在条件下, 该方法比现有同类方法具有更高的估计精度和鲁棒性. 在不同最大噪声功率比条件下,本文方法的均方根误差比现有方法平均减小59.4%.      

Parameterization for fitting triangular mesh

In recent years, with the development of 3D data acquisition equipments, the study on reverse engineering has become more and more important. However, the existing methods for parameterization can hardly ensure that the parametric domain is rectangular, and the parametric curve grid is regular. In order to overcome these limitations, we present a novel method for parameterization of triangular meshes in this paper. The basic idea is twofold: first, because the isotherms in the steady temperature do not intersect with each other, and are distributed uniformly, no singularity (fold-over) exists in the parameterization; second, a 3D harmonic equation is solved by the finite element method to obtain the steady temperature field on a 2D triangular mesh surface with four boundaries. Therefore, our proposed method avoids the embarrassment that it is impossible to solve the 2D quasi-harmonic equation on the 2D triangular mesh without the parametric values at mesh vertices. Furthermore, the isotherms on the temperature field are taken as a set of iso-parametric curves on the triangular mesh surface. The other set of iso-parametric curves can be obtained by connecting the points with the same chord-length on the isotherms sequentially. The obtained parametric curve grid is regular, and distributed uniformly, and can map the triangular mesh surface to the unit square domain with boundaries of mesh surface to boundaries of parametric domain, which ensures that the triangular mesh surface or point cloud can be fitted with the NURBS surface.