Interpolating minimal energy C1‐Surfaces on Powell–Sabin Triangulations: Application to the resolution of elliptic problems

In this article, we present a method to obtain a C¹‐surface, defined on a bounded polygonal domain Ω, which interpolates a specific dataset and minimizes a certain “energy functional.” The minimization space chosen is the one associated to the Powell–Sabin finite element, whose elements are C¹‐quadratic splines. We develop a general theoretical framework for that, and we consider two main applications of the theory. For both of them, we give convergence results, and we present some numerical and graphical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 798–821, 2015     

基于智能相机的高速三维表面信息获取

为了大幅度提高三维信息获取速度,提出了一种基于智能相机和激光三角法的高速三维信息获取与表面重建的系统,介绍了该系统的硬件架构和信号处理。实验结果表明,采用数字信号处理器和并行处理方式,该系统获取三维表面信息速度可达5600点/s以上。     

无衍射光束在激光三角测量系统中的应用研究

无衍射贝塞耳光束是近年来国内外极为重视的一个新兴研究领域.这种光束同时具有焦深长,中心光斑小的特点.利用这一特点,作者首次提出将其作为入射光束应用于激光三角测量系统,以解决传统激光三角测量系统无法满足大量程与高分辨率测量要求的问题.文中给出了无衍射光束的理论及实现方法.在三角测量物 象位置关系的基础上,设计了无衍射激光三角测量系统及其参数并给出了实验结果.理论分析与实验结果表明,这种新型系统明显优于传统的三角测量系统.     

基于紧密中心性的无线mesh骨干网网关部署

将定向天线和Delaunay图应用于无线mesh骨干网络的网关部署,提出了基于紧密中心性的无线mesh骨干网络网关部署算法。根据已知的mesh路由器和网关的最大流通量对网络进行划分,形成Delaunay子图,在划分的子图中根据欧几里德距离找出距离中心点最近的3个节点,形成候选网关集,在候选网关集中选择到其他节点总路径最短的节点作为网关的部署位置,将每个子图的网关位置输出。仿真结果表明,根据网关最大流通量进行合理网络划分后,算法能最小化网络的网关数量,由mesh路由器到网关的总路径长度优于随机算法。     

A study of gridless method with dynamic clouds of points for solving unsteady CFD problems in aerodynamics

When solving unsteady computational fluid dynamics problems in aerodynamics with a gridless method, a cloud of points is usually required to be regenerated due to its accommodation to moving boundaries. In order to handle this problem conveniently, a fast dynamic cloud method based on Delaunay graph mapping strategy is proposed in this paper. A dynamic cloud method makes use of algebraic mapping principles and therefore points can be accurately redistributed in the flow field without any iteration. In this way, the structure of the gridless clouds is not necessarily changed so that the clouds regeneration can be avoided successfully. The spatial derivatives of the mathematical modeling of the flow are directly determined by using weighted least‐squares method in each cloud of points, and then numerical fluxes can be obtained. A dual time‐stepping method is further implemented to advance the two‐dimensional Euler equations in arbitrary Lagarangian–Eulerian formulation in time. Finally, unsteady transonic flows over two different oscillating airfoils are simulated with the above method and results obtained are in good agreement with the experimental data. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical simulations of the steady Navier–Stokes equations using adaptive meshing schemes

In this paper, we consider an adaptive meshing scheme for solution of the steady incompressible Navier–Stokes equations by finite element discretization. The mesh refinement and optimization are performed based on an algorithm that combines the so‐called conforming centroidal Voronoi Delaunay triangulations (CfCVDTs) and residual‐type local a posteriori error estimators. Numerical experiments in the two‐dimensional space for various examples are presented with quadratic finite elements used for the velocity field and linear finite elements for the pressure. The results show that our meshing scheme can equally distribute the errors over all elements in some optimal way and keep the triangles very well shaped as well at all levels of refinement. In addition, the convergence rates achieved are close to the best obtainable. Extension of this approach to three‐dimensional cases is also discussed and the main challenge is the efficient implementation of three‐dimensional CfCVDT generation that is still under development. Copyright © 2007 John Wiley & Sons, Ltd.     

Design of optical triangulation devices

This paper presents the derivation of the precise relation between the displacement of a light spot on an object's surface and the displacement of its image on the detector in an optical triangulation device, along with applications of the design of triangulation devices. Based on this relation, improved designs of optical triangulation devices, including devices of adjustable configurations, are proposed and discussed.     

A new simplicial variable dimension algorithm to find equilibria on the product space of unit simplices

A new simplicial variable dimension restart algorithm is introduced to solve the nonlinear complementarity problem on the product spaceS of unit simplices. The triangulation which underlies the algorithm differs from the triangulations ofS used thus far. Moreover, the number of rays along which the algorithm can leave the arbitrarily chosen starting point is much larger. More precisely, there is a ray leading from the starting point to each vertex ofS. In caseS is the product ofn one-dimensional unit simplices the alogrithm is similar to the octahedral algorithm onR ⁿ having 2 ⁿ rays. Also, the accuracy of an approximate solution in the terminal simplex of the algorithm is in general better than for the other algorithms onS. Computational results will show that the number of iterations for the new algorithm is much less. The examples concern the computation of equilibria in noncooperative games, exchange economies and trade models. This author is financially supported by the Netherlands Organisation for the Advancement of Pure Research (ZWO), Grant 46-98. This research is part of the VF-program “Equilibrium and Disequilibrium in Demand and Supply” which has been approved by the Netherlands ministry of education and sciences.     

Fundamental Uncertainty Rotationally Symmetric and Anamorphic Laser Triangulation

Rotationally symmetric triangulation （RST） sensor is one of the newest developments in laser distance measurement. Speckle is also the fundamental uncertainty factor in this kind of sensors. A detailed analysis of centroid uncertainty in RST is presented in this paper. The analytic expression of centroid uncertainty limit when measuring an optical rough surface is derived. It is shown that the uncertainty limit in RST, and also in anamorphic triangulation, is dependent on the solid angle subtended by entrance pupil as seen from the illuminated laser spot, as well as the laser wavelength. Results of simulation and experiments verify the deriving. The uncertainty limit in RST is about 1/5 of the one in traditional triangulation with same numerical aperture and triangulation angel. It＇s also analysed how the aberration of the optical system influence the uncertainty limit.     

Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.