二维静电场问题的面片拼接等几何分析方法研究

等几何分析方法在求解静电场问题时,实现了几何模型和计算模型的统一以及自适应网格划分过程,然而受制于单个NURBS曲面片拓扑的局限性,单片等几何分析方法难以处理含角点非凸几何域静电场及多媒质静电场问题.本文基于面片拼接技术,将单片等几何分析方法扩展到多片,并用来求解二维含角点非凸几何域静电场及多媒质静电场问题,NURBS曲面片拼接处的控制点和网格细分前后要求必须匹配.由于NURBS基函数不满足插值性,在非齐次Dirichlet边界条件的处理上本文采用Lagrange乘子法进行处理.数值算例表明：修正后的多面片等几何分析方法可以很好地处理二维含角点非凸几何域静电场及多媒质静电场问题,且相比传统的有限元法,该方法具有自由度消耗小、精度高、收敛速度快等优点.     

基于面片拼接的等几何分析方法求解波导本征值问题

基于NURBS的等几何分析方法集成了计算机辅助设计(CAD)和有限元方法的优点,CAD模型、网格划分和数值仿真均采用同样的几何描述.然而,由于单个NURBS曲面片拓扑的局限性,单片等几何分析方法难以处理介质分布不均匀以及截面形式复杂的多连通区域问题.本文基于面片拼接,将等几何分析方法用来求解此类问题的波导本征值.细分前后,NURBS曲面片拼接处的控制点和网格必须匹配.通过Galerkin法来离散波导本征值问题的Helmholtz控制方程,计算结果表明该方法具有自由度消耗小、精度高、收敛速度快等优点.     

人脑的NURBS曲面三维建模研究

作为医学信息多模态融合中的热门领域,人脑建模是EEG/f MRI脑功能研究中的前沿研究课题。寻找一种构建人脑几何模型的有效方法更是其中的焦点。为了寻求一种更为快速的新建模方法,提出了通过NURBS方法进行全局曲面差值,最终反求曲面这一方案。计算机仿真实验结果耗时十余秒,使用7 000余点构建实际包含7 0000点的脑模型,由此证明了NURBS方法在较少数据点下可以更快地对人脑进行建模。     

三维面部数据采集与NURBS曲面重构

为获取面部三维点云,并转换为高精度NURBS曲面,建立了面部图像采集与处理系统,并研究其中的点云自动拼接和曲面重构方法。首先,采用双光栅三维扫描仪将正弦光栅投射到人的面部,将被面部调制的变形光栅转换成两片分立点云。然后,通过标定块对测量系统进行标定,利用协方差求取旋转矩阵和平移向量实现点云自动拼接获取完整面部点云,并生成三角面片。最后,通过检测曲率、生成四边形网格、建立UV参数线等处理,进行曲面重构生成高精度NURBS四边域面部曲面,并对重构结果进行误差分析。结果表明:所重构面部曲面符合G1连续,标准偏差为0.009222 mm。本文所采用的高精度的面部曲面重构方法可用于复杂曲面的三维检测与重构中。     

基于NURBS建模计算形变目标RCS

采用非均匀有理B样条（NURBS）对目标进行建模,利用NURBS的局部特性模拟目标在复杂电磁环境中受到各种物理作用而产生的形变,再采用物理光学（PO）方法,在NURBS曲面上进行表面电流积分,计算出目标的RCS。NURBS建模方法可以更加精确地建立目标的几何模型;并在原模型的基础上,较方便地产生形变而不需要重新建模。文中分别计算了原模型和形变后模型的RCS,以研究形变对于目标散射特性的影响。原模型的RCS计算结果与参考文献一致,说明文中所研究方法的有效性。     

Maya 5面片建模

面片建模是Maya中的一种重要建模方法,涉及到创建一个由一些NURBS曲面构成并形成一个类似网格的连续曲面的模型。这种建模方法的优点在于可以得到甚至伴随纹理的参数化表达,而且这样得到的模型通常在几何方面更轻便一些(也就是说,具有更少的点线面数目)。然而,面片建模技术需要很多计划和实践才能取得象样的结果,通常,为了得到曲面所满足的正确的网格密度和区域,需要进行多次的模型重构。     

基于NURBS的三维人体曲面构建与拼接

通过特征点将人体划分为若干曲面，并采用NURBS的方法来构建曲面，最后通过遍历链表的方法进行曲面的拼接，降低了计算总量，并为后期曲面变形提供了良好的操作可能。     

一种基于NURBS的三维统计形状建模方法

针对当前主动形状模型构建中的实际问题,本文提出一种整合NURBS技术的三维统计形状建模方法。首先对目标样本进行多边形网格化处理,再对其进行NURBS建模和曲面空间变换,然后对NURBS曲面上的控制点进行主成分分析,以生成相应的统计形状模型。为了验证该方法的有效性,我们将该方法应用于部分人体器官的训练样本集进行建模测试。实验结果表明,该方法可较为合理和准确地描述目标形状的变化模式,并能提高建模效率,减少存储空间的占用。     

基于NURBS曲面的水稻叶形态建模

讨论了对水稻叶进行形态建模可采用的方法，介绍了一种基于NURBS曲面的水稻叶形态建模的方法，叙述了控制点的计算过程。利用NURBS在形状定义和设计方面的优点，可以根据实际情况灵活方便地对根据模型建立的叶片进行调整。本模型通过Open Inventor Java实现绘制渲染，效果良好。     

基于裁剪造型的等几何分析方法求解波导本征值问题

等几何分析方法使得几何模型和分析模型能够用NURBS统一表达,避免了模型转换过程,但由于其分析域是由张量积面片构成,很难处理截面形式复杂的多联通域问题。裁剪造型等几何分析方法通过背景曲面和裁剪曲线将复杂带孔结构作为一个被NURBS曲线裁剪后的参数区域直接映射而成,只需要一个参数空间就可以表示任意复杂的拓扑结构,该方法既保留了传统等几何分析方法的优点,又实现了对复杂多孔结构的处理。本文将裁剪造型的等几何分析方法扩展到TE波的波导本征值问题,对复杂多孔结构的截止波数进行有效求解,并通过相应的数值算例验证方法的有效性和高精度性。     

Application of physical optics to the RCS computation of bodiesmodeled with NURBS surfaces

The paper presents a method for the computation of the monostatic radar cross section (RCS) of electrically large conducting objects modeled by nonuniform rational B-spline (NURBS) surfaces using the physical optic (PO) technique. The NURBS surfaces are expanded in terms of rational Bezier patches by applying the Cox-De Boor transform algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. The PO integral is evaluated over the parametric space of the Bezier surfaces using asymptotic integration. The scattering field contribution of each Bezier patch is expressed in terms of its geometric parameters. Excellent agreement with PO predictions is obtained. The method is quite efficient because it makes use of a small number of patches to model complex bodies, so it requires very little memory and computing time     

Combining the moment method with geometrical modelling by NURBSsurfaces and Bezier patches

Induced current distributions on conducting bodies of arbitrary shape modelled by NURBS (non uniform rational B-splines) surfaces are obtained by using a moment method approach to solve an electric field integral equation (EFIE). The NURBS surfaces are expanded in terms of Bezier patches by applying the Cox-de Boor transformation algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. New basis functions have been developed which extend over pairs of Bezier patches. These basis functions can be considered as a generalization of “rooftop” functions. The method is applied to obtain RCS values of several objects modelled with NURBS surfaces. Good agreement with results from other methods is observed. The method is efficient and versatile because it uses geometrical modelling tools that are quite powerful     

Analysis of antennas on board arbitrary structures modeled by NURBSsurfaces

An accurate and efficient numerical scheme has been developed for predicting high-frequency radiation patterns of antennas mounted on arbitrary structures modeled by parametric surfaces. The method is based on geometric optics (GO) and the uniform theory of diffraction (UTD). Nonuniform rational B-splines (NURBS) surfaces have been used to describe the geometry of the structure. As most of the computer-aided geometric design (CAGD) tools available in the industry are biased on NURBS, the scheme can perform the electromagnetic analysis without any new or additional remeshing of the geometrical model. A special ray-tracing technique that combines GO and UTD with NURBS has been developed. This technique uses some selective criteria in order to identify rapidly the NURBS where a ray impact may occur. Impact point coordinates are obtained by means of an optimization procedure based on the conjugate gradient method (CGM). The accuracy and efficiency of the approach are shown comparing it with other methods     

Parametric shape representation by a deformable NURBS model for cardiac functional measurements

This paper proposes a method of parametric representation and functional measurement of 3-D cardiac shapes in a deformable nonuniform rational B-splines (NURBS) model. This representation makes it very easy to automatically evaluate the functional parameters and myocardial kinetics of the heart, since quantitative analysis can be followed in a simple way. In the model, local deformation and motion on the cardiac shape are expressed in adjustable parameters. Especially, an effective integral algorithm is used for volumetric measurement of a NURBS shape since the volume is the most basic parameter in cardiac functional analysis. This method promises the numerical computation to be very convenient, efficient, and accurate, in comparison with traditional methods. Practical experiments are carried out, and results show that the algorithm can get satisfactory measurement accuracy and efficiency. The parametric NURBS model in cylindrical coordinates is not only very suitable to fit the anatomical surfaces of a cardiac shape, but also easy for geometric transformation and nonrigid registration, and able to represent local dynamics and kinetics, and thus, can easily be applied for quantitative and functional analysis of the heart.     

NURBS自由曲面在光机设计和分析中的应用

针对光学曲面要求面形描述能力和拟合精度高以及光线追迹速度快的要求,研究了NURBS作为自由曲面的拟合、坐标空间转换和光线追迹算法。首先使用多分辨率B样条拟合方法浅度非球面,深度非球面和Peaks自由曲面进行NURBS拟合,RMS误差均小于10 nm,表现出很好的适应性。其次研究了NURBS曲面的参数空间到坐标空间的转化算法,与传统曲面求导方法相比,速度提高了3倍以上。在提出合理迭代初值计算方法的基础上,将计算每个曲面点的时间缩短至0.3 ms。最后通过NURBS曲面在自由曲面头盔系统的光机分析中和CODEV用户自定义曲面中的成功运用,证明了NURBS曲面能很好地满足光机设计、分析和加工的要求。     

Shape Reconstruction of Three-Dimensional Conducting Curved Plates Using Physical Optics, NURBS Modeling, and Genetic Algorithm

A microwave inverse scattering problem including a method for shape reconstruction of three-dimensional electrically large conducting patches with simple geometries using genetic algorithm is presented. Unknown shape reconstruction algorithm starts from the knowledge of the simulated radar cross-section (RCS) data through back-scattering far-field computation using physical optics approximation. The forward problem involves the computation of the multiple-frequency and multiple-direction RCS of three-dimensional large conducting patches modeled by nonuniform rational B-spline (NURBS) surfaces. The control points of NURBS are the geometrical parameters, which are optimized for the shape reconstruction procedure. The extended stationary phase method and critical cases, which occur in physical optics computations in the forward problem, are also discussed. Noise effect and the influence of increment in the number of control points of a NURBS over the inversion algorithm are investigated as well. Numerical results are presented to verify the operation of the proposed algorithm.