基于非结构自适应网格的复合有限体积法

利用文献[1]中将Lax-Wendroff格式和Lax-Friedrichs格式整体复合作用构成二维无结构网格上的复合型有限体积法,同时利用Delaunay方法,根据流场流动特性变化的梯度值为指示器对网格进行加密和粗化,实现自适应,并将此方法应用到二维浅水波方程的求解上,进行了二维部分溃坝,倾斜水跃的数值实验.结果表明,该方法是一个计算稳定、能适应复杂的求解域、能很好地捕捉激波、且计算速度快的算法.     

基于指标形式张量的微分几何定理机器证明

提出了一个基于指标形式张量的微分几何定理的机器证明算法.该算法将微分几何定理转化成带指标的张量多项式的计算问题,然后通过利用重写规则,挖掘等价条件和分次选取条件等方法大大减少了这个多项式系统的方程个数.再利用这个多项式系统本身和关于哑元的方程三角化这个多项式系统,将所得到的首项代入结论, 从而得到了该定理的机器证明.该算法不仅能够证明基于指标形式张量的微分几何定理,也可以用于张量方程的求解.     

快速三维散乱数据点重建算法

提出了一种快速三维散乱数据点重建算法.我们对包围盒算法进行了改进,减少了建立散乱点近邻关系所需的计算量;同时针对位置相对平坦的数据点,结合最小二乘法给出了一种计算法矢的混合方法.实例表明,该算法是有效的.     

一种离散点插值算法用于重建光谱反射率

提出了一种用离散点插值算法来重建光谱反射率的方法。首先建立数字相机响应值与典型反射样品表面光谱反射率之间的查找表,然后进行Delaullay分区、提取和插值,最后通过数字相机的输出数据来准确地重建物体表面的光谱反射率。实验结果表明,该方法能够重建典型反射样品的光谱反射率,能够实时获取被摄场景的多光谱图像,易于硬件的实现。     

Improved keypoint descriptors based on Delaunay triangulation for image matching

In the current keypoint-based image matching methods, not all the keypoints can be reliably matched because of the influence of noise, illumination, and image distortion. In the paper, we propose a novel method based on the Delaunay triangulation to detect and remove possible mismatches. Given previously matched keypoints by a detector in two images, the proposed method utilizes four steps to remove the mismatched point pairs: first, triangulating keypoints in the reference image, and producing a graph consisting of edges that connects the keypoints; second, drawing a graph in the test image by connecting the corresponding points as same as in the reference image; third, detecting abnormal edges in the test image using special constraints; fourth, detecting and removing mismatched point pairs based on the abnormal edges. The experimental results show that the method can detect the mismatches accurately and improve the robustness of current matching algorithms.     

Simplicial algorithm to solve the nonlinear complementarity problem onS n×R + m

In this paper, a simplicial algorithm is developed to solve the nonlinear complementarity problem onS ⁿ×R ₊ ^m . Furthermore, a condition for convergence is formulated. The triangulation which underlies the algorithm is a combination of the V-triangulation ofS ⁿ and the K-triangulation ofR ₊ ^m . Therefore, we will call it the VK-triangulation.The author wishes to thank Professor G. van der Laan for his valuable comments.     

关于平面点集三角剖分的两类子集

给定欧氏平面上的一个点集合Ｓ，我们给出两类端点在Ｓ中的线段集合，第一类线段集合是Ｓ的任一三角剖分的子集，第二类线段集合是Ｓ的任一最小权三解剖分的子集，这两类子集是不相交的，这两类子集合的计算要用Ｏ(n³)时间和Ｏ（ｎ）空间．     

Calibration procedure for a laser triangulation scanner with uncertainty evaluation

Most of low cost 3D scanning devices that are nowadays available on the market are sold without a user calibration procedure to correct measurement errors related to changes in environmental conditions. In addition, there is no specific international standard defining a procedure to check the performance of a 3D scanner along time. This paper aims at detailing a thorough methodology to calibrate a 3D scanner and assess its measurement uncertainty. The proposed procedure is based on the use of a reference ball plate and applied to a triangulation laser scanner. Experimental results show that the metrological performance of the instrument can be greatly improved by the application of the calibration procedure that corrects systematic errors and reduces the device's measurement uncertainty.     

A research note on design of fair surfaces over irregular domains using data-dependent triangulation

Design of fair surfaces over irregular domain is a fundamental problem in computer aided geometric design (CAGD), and has applications in engineering sciences (i.e. aircraft science, automobile science and ship science etc.). In design of fair surfaces over irregular domain defined over scattered data it was widely accepted till recently that one should use Delaunay triangulation because of its global optimum property. However, in recent times it has been shown that for continuous piecewise polynomial parametric surfaces improvements in the quality of fit can be achieved if the triangulation pattern is made dependent upon some topological property of the data set or is simply data dependent. The smoothness and fairness of surface’s planar cuts is important because not only it ensures favorable hydrodynamic drag, but also helps in reducing manhours during the production of the surface. In this paper we discuss a method for construction of C¹ piecewise polynomial parametric fair surfaces which interpolate prescribed R³${\mathfrak{R}}^3$ scattered data using spaces of parametric splines defined on R³${\mathfrak{R}}^3$ triangulation. We show that our method is more specific to the cases when the projection on 2-D plane may consist of triangles of zero area. The proposed method is fast, numerically stable and robust, and computationally inexpensive. In the present work numerical examples dealing with surfaces approximated on standard curved plates, and ship hull surface have been presented.     

含运动物体流场计算的自适应非结构二维网格生成方法

采用自动插点的Delaunay方法和局部网格重新生成方法,对含运动边界自适应非结构二维网格生成方法进行了系统研究,实现了带有非定常运动物体流场的数值计算,并进行了数值实验.