Triangulation Scheme Research Articles

Parallel Delaunay triangulation in three dimensions

A generic parallel Delaunay triangulation scheme by means of zonal partition of points is proposed. For efficient Delaunay triangulation, points are first sorted into cells, each of which is allocated roughly equal number of points. The cells are naturally grouped into zones, in which Delaunay triangulation is constructed by simultaneous point insertion cell by cell within each zone. Tetrahedra at the boundary between zones are created in parallel by adding layers of cells at the boundary of each zone to ensure that circumspheres of boundary tetrahedra contain no points in their interior. Redundant tetrahedra at the boundary between zones can be easily eliminated by individual processors in a completely independent manner by means of the elegant minimum vertex allocation scheme, such that a simplex with k vertices from zones (z1,z2,…,zk) is allocated to zone z=min(z1,z2,…,zk).The parallel 3D Delaunay triangulation algorithm has been coded in Intel FORTRAN VS2010. The parallel zonal insertion on a PC can boost the speed of the single-processor insertion by 4.5 times for the insertion of 50 million randomly generated spatial points in 133s. The scalability of the parallel zonal insertion algorithm has also been tested on a proper multi-core machine with 12 processors running on OpenMP parallel directives with shared memory. Provided the number of zones is an integral multiple of the number of processors used, almost 100% scalability at 90% efficiency was observed for parallel insertion using 2, 4, 6, 8 and 12 processors, and a 10.8 time speed up was recorded in a parallel insertion of 20 million points in 2×2×3=12 zones by 12 processors.

NLOS환경에서의 최소자승법을 적용한 위치인식 보정 알고리즘

The compensation algorithm for localization using the least-squires method in NLOS(Non Line of Sight) environment is suggested and the performance of the algorithm is analyzed in this paper. In order to improve the localization correction rate of the moving node, 1) the distance value of the moving node that is moving as an constant speed is measured by SDS-TWR(Symmetric Double-Sided Two-Way Ranging); 2) the location of the moving node is measured using the triangulation scheme; 3) the location of the moving node measured in 2) is compensated using the least-squares method. By the experiments in NLOS environment, it is confirmed that the average localization error rates are measured to , and by the triangulation scheme, the Kalman filter and the least-squires method respectively. As a result, we can see that the localization error rate of the suggested algorithm is higher than that of the triangulation as average 86.0% and the Kalman filter as average 16.0% respectively.

Triangulation schemes of three-component systems

According to Gibbs' phase rule, a section of the phase diagram of a threecomponent system at P,T = const is a partition of the concentration triangle into the regions of the existence of phases, two�, and three� phase complexes. To describe the topology of such a section, it is convenient to denote one�, two�, and threephase regions by points, lines, and triangles, respectively. If the system at given Р and Т contains no phases with unlimited solubility of two or three com� ponents, the topology of the section can be repre� sented as a partition of the concentration triangle into elementary triangles with the vertices corresponding to components or compounds. The scheme of triangu� lation of the concentration triangle uniquely repre� sents the structure of the network of lines of monova� riant equilibria in the melting diagram. Such schemes also describe the structure of the piecewise continuous solidus surface of the phase diagrams of ternary sys� tems. The triangulation schemes of the solidus surface should be constructed for analyzing possible variants of the structure of the liquidus surface of ternary sys� tems (1, 2). Let us denote the solid phases by α, β, and γ and the liquid by L. Each threephase region αβγ of the solidus surface corresponds to the invariant point of the liquidus surface that characterizes the equilib� rium Lαβγ between the liquid phase and the solid phases. The monovariant equilibrium lines Lαβ, Lαγ, and Lβγ issuing from this point correspond to the sides of the abc triangle. Therefore, the figure formed by monovariant equilibrium lines and the invariant points in the liquidus surface is dual to the triangulation scheme of the solidus surface. This fact was used for classifying the melting diagrams of ternary systems with solid phases of constant compositions (3). Note also that the topology of the phase diagram of a ternary system can be regarded as the topology of the partition of the Р-Т space into regions each of which is represented by a certain triangulation scheme. The union of such schemes with the identified correspond� ing region of the

Liquidus surface projection for the Er-Sn-Se ternary system

The Er-Sn-Se system was studied by differential thermal analysis, X-ray powder diffraction, and microstructure examination and also by microhardness and density measurements. A congruent triangulation scheme and a liquidus surface projection were constructed. Fourteen primary crystallization fields, including those of the ternary compounds ErSnSe2, Er2SnSe4, Er2SnSe5, and Er2Sn3Se9, were found, and the types and coordinates of nonvariant and monovariant equilibria were determined.

Constructing truths in a culture of disbelief

While a multitude of immigration officers enforce the numerous laws and policies regulating the arrival of asylum seekers, their work is often hidden from the public eye and ignored by academic debate, leaving fundamental questions unanswered: Is the migration debate blinded by bureaucracy or oblivious to the complexity of the asylum screening process? This article originates from an ethnographic study, which included over 80 interviews, six months of participant observation and four years of familiarization with the main actors, framed by a triangulation scheme that allowed in-depth exploration of the field from within. The study’s conclusions expose how identifying immigration officers’ subculture is key to understanding asylum controls and to reach beyond the legal shield and the rhetorical concepts of political debate. Based on this empirical research, this article exposes how officers’ criteria for screening individuals are not derived from regulations or laws but their own categorizations, rules and values derived from ambiguous stereotypes nurtured by officers’ experiences and social prejudices.

A kinetic triangulation scheme for moving points in the plane

We present a simple randomized scheme for triangulating a set P of n points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of P move continuously along piecewise algebraic trajectories of constant description complexity. Our triangulation scheme experiences an expected number of O ( n 2 β s + 2 ( n ) log 2 n ) discrete changes, and handles them in a manner that satisfies all the standard requirements from a kinetic data structure: compactness, efficiency, locality and responsiveness. Here s is the maximum number of times at which any specific triple of points of P can become collinear, β s + 2 ( q ) = λ s + 2 ( q ) / q , and λ s + 2 ( q ) is the maximum length of Davenport–Schinzel sequences of order s + 2 on q symbols. Thus, compared to the previous solution of Agarwal, Wang and Yu (2006) [4], we achieve a (slightly) improved bound on the number of discrete changes in the triangulation. In addition, we believe that our scheme is conceptually simpler, and easier to implement and analyze.

Rapid localization of damage using a circular sensor array and Lamb wave based triangulation

A damage detection and imaging methodology based on symmetry of neighborhood sensor path and similarity of signal patterns with respect to radial paths in a circular array of sensors has been developed. It uses information regarding Lamb wave propagation along with a triangulation scheme to rapidly locate and quantify the severity of damage without using all of the sensor data. In a plate like structure, such a scheme can be effectively employed besides full field imaging of wave scattering pattern from the damage, if present in the plate. This new scheme is validated experimentally. Hole and corrosion type damages have been detected and quantified using the proposed scheme successfully. A wavelet based cumulative damage index has been studied which shows monotonic sensitivity against the severity of the damage, which is most desired in a Structural Health Monitoring system.

Existence of piecewise affine Lyapunov functions in two dimensions

In Marinosson (2002) [10], a method to compute Lyapunov functions for systems with asymptotically stable equilibria was presented. The method uses finite differences on finite elements to generate a linear programming problem for the system in question, of which every feasible solution parameterises a piecewise affine Lyapunov function. In Hafstein (2004) [2] it was proved that the method always succeeds in generating a Lyapunov function for systems with an exponentially stable equilibrium. However, the proof could not guarantee that the generated function has negative orbital derivative locally in a small neighbourhood of the equilibrium. In this article we give an example of a system, where no piecewise affine Lyapunov function with the proposed triangulation scheme exists. This failure is due to the triangulation of the method being too coarse at the equilibrium, and we suggest a fan-like triangulation around the equilibrium. We show that for any two-dimensional system with an exponentially stable equilibrium there is a local triangulation scheme such that the system possesses a piecewise affine Lyapunov function. Hence, the method might eventually be equipped with an improved triangulation scheme that does not have deficits locally at the equilibrium.

Swept Volume Approximation of Polygon Soups

We present a fast algorithm to approximate the swept volume (SV) boundary of arbitrary polygon soup models. Despite the extensive research on calculating the volume swept by an object along a trajectory, the efficient algorithms described have imposed constraints on both the trajectories and geometric models. By proposing a general algorithm that handles flat surfaces as well as volumes and disconnected objects, we allow SV calculation without resorting to preprocessing mesh repair nor deforming offsets. This is of particular interest in the domain of product lifecycle management (PLM), which deals with industrial computer aided design (CAD) models that are malformed more often than not. We incorporate the bounded distance operator used in path planning to efficiently sample the trajectory while controlling the total error. We develop a triangulation scheme that draws on the unique data set created by an advancing front level-set method to tessellate the SV boundary in linear time. We analyze its performance, and demonstrate its effectiveness both theoretically and on real cases taken from PLM.

Swinging and tumbling of elastic capsules in shear flow

The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules with both spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximate theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we can reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.

Investigation of phase equilibria and growth of BBO (β-BaB2O4) crystals in BaO–B2O3–Na2O ternary system

Abstract The BaO–B2O3–Na2O ternary system is of great importance for growing crystals of low-temperature modification of barium borate (β-BaB2O4). A new solid-state triangulation scheme was suggested based on the existence of NaBaBO3 compound. Primary crystallization areas of NaBaBO3 and two new compounds—NaBa4(BO3)3 and Ba5B4O11—were determined. It was shown that crystals grown from depleted sodium system BaB2O4–NaBaBO3 have great advantage concerning the quality.

Level set based topological shape optimization of geometrically nonlinear structures using unstructured mesh

Using hyperelastic materials and unstructured mesh, a level set based topological shape optimization method is developed for geometrically nonlinear structures in total Lagrangian framework. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in a level set function, which facilitates to handle complicated topological shape changes and eventually leads the initial implicit boundary to an optimal one according to the normal velocity field while both minimizing the objective function of instantaneous structural compliance and satisfying an allowable material volume constraint. In existing level set based methods, an initial reference domain or an ersatz material is employed for the penalization of whole domain to represent the current domain. However, these approaches end up with a convergence difficulty in nonlinear response analysis due to the inaccurate tangent stiffness. To overcome this difficulty, taking advantage of the obtained level set function, the current structural boundary is actually represented using a Delaunay triangulation scheme and a hyperelastic material law is employed to handle the large strain problem. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on a fast marching method. Since homogeneous material property and actual boundary are utilized, the convergence difficulty is significantly relieved.

Three-Dimensional Localization System for Impulsive Noise Sources Using Ultra-Wideband Digital Interferometer Technique

This paper presents an ultra-wideband (UWB) digital interferometer scheme for locating the impulsive noise radiation from partial discharge (PD) sources in three spatial dimensions. This UWB interferometer localization technique is based on the idea of extracting the phase differences at different frequencies between a pair of the received electromagnetic (EM) signals by the Fast Fourier Transform (FFT). These phase differences are directly related to the direction of arrival of the received signals and used to estimate the angular locations of the source in azimuth and elevation angles. The geometry of the problem is considered as two UWB digital interferometer sites for the experimental measurements. Then, the triangulation scheme was proposed to the 3-D source location. To show the validity and the accuracy of our proposed scheme, a comparison study is shown between time differences of arrival (TDOA) localization scheme which is estimated by conventional cross correlation method and this interferometer proposed localization technique.

Parallel divide-and-conquer scheme for 2D Delaunay triangulation

This work describes a parallel divide-and-conquer Delaunay triangulation scheme. This algorithm finds the affected zone, which covers the triangulation and may be modified when two sub-block triangulations are merged. Finding the affected zone can reduce the amount of data required to be transmitted between processors. The time complexity of the divide-and-conquer scheme remains O(n log n), and the affected region can be located in O(n) time steps, where n denotes the number of points. The code was implemented with C, FORTRAN and MPI, making it portable to many computer systems. Experimental results on an IBM SP2 show that a parallel efficiency of 44–95% for general distributions can be attained on a 16-node distributed memory system. Copyright © 2006 John Wiley & Sons, Ltd.

Optimal parametrization of tomographic models

SUMMARY The spacing of interpolation supports in the Earth can be optimized to fit local resolution by connecting natural neighbours with springs of length equal to the local resolving length and minimizing the potential energy of the system. A triangulation scheme for the starting configuration of the grid is implemented to avoid that the optimization converges to an unacceptable local minimum in the energy.

High-resolution optical angle sensors: approaching the diffraction limit to the sensitivity.

We carry out a detailed analysis of angle-sensitive devices based on the critical-angle effect. We consider their use in measuring small angular deflections of a laser beam. We establish the diffraction limit to the sensitivity for optical-angle sensors based on reflection and transmission of a laser beam. We find that this limit is identical to that of the triangulation scheme when using a position-sensitive detector or the autocollimation scheme. We analyze the main proposals to date of optical-angle sensors based on the critical-angle effect, focusing on their maximum sensitivity and their polarization dependence in practical conditions. We propose and analyze theoretically a novel and simple angle-sensitive device for sensing optical-beam deflections with very low polarization dependence and a maximum sensitivity close to the diffraction limit when used with typical laser beams. We discuss the basic principles for designing this type of device, provide numerical results, and point out a convenient fabrication procedure.

Instrumentation and localisation in quasi-structured environments for AGV positioning

This communication addresses the automated guided vehicles (AGVs) positioning issue. A summarised state-of-the-art section is included and the deadreckoning algorithm is analysed with a support on a triangulation scheme. This scheme is based on ultrasonic sensors or electromagnetic wave transmitter/receiver antennas sets. Simulation results for AGV movement to validate the control system efficiency and implementation issues of work in progress are presented.

On the reconstruction of height functions and terrain maps from dense range data

This paper describes a method for combining multiple, dense range images to create surface reconstructions of height functions. Height functions are a special class of three-dimensional (3-D) surfaces, where one 3-D coordinate is a function of the other two. They are relevant for application domains such as terrain modeling or two-and-half dimensional surface reconstruction. Dense range maps are produced by either a range measuring device combined with a scanning mechanism or a triangulation scheme, such as active or passive stereo. The proposed method follows from a statistical formulation that characterizes the optimal surface estimate as the one that maximizes the posterior probability conditional on the input data and prior information about the application domain. Because the domain of the reconstruction is a two-dimensional (2-D) scalar function, the optimal surface can be expressed as an image, and the variational form of that optimization produces a 2-D partial differential equation (PDE). The PDE consists of two parts: a first-order data term and a second-order smoothing term. Thus optimal surface reconstruction is formulated as the solution to a second-order, nonlinear, PDE on an image, which is related to the family of PDE-based image processing algorithms in the literature. This paper presents the theory for reconstruction and some particular aspects of the numerical implementation. It also analyzes results on both synthetic and real data sets, which show a 75%-95% reduction of the RMS sensor error.

Three-dimensional lightning observations of cloud-to-ground flashes using broadband interferometers

For the first time, the broadband radio interferometers have been developed to locate the sources of VHF/UHF radiation from lightning discharges in three spatial dimensions (3D) and time. The lightning observations have been conducted in Darwin, Australia during summer 1998 at two different sites. Each site consisted of a broadband interferometer and an electric field sensor as well as a GPS receiver. The triangulation scheme was proposed to estimate the 3D source locations. The system was able to observe different types of lightning discharges and estimate the initial and subsequent leader progression speeds from three negative cloud-to-ground lightning flashes. The initial leaders had progression speeds of about 10 5 m s −1 , typical for negatively charged initial leaders. The preliminary activity prior to the initial leader progression was also recognized. In cloud K-processes, a dart leader and an attempted leader were also found to be negative-polarity discharges and they propagated either upward or downward to ground with the estimated speeds of about 10 6 m s −1 , in agreement with previous studies. Two of the flashes contained subsequent leaders that took different channels and created new terminations on ground. These subsequent leaders required long duration to progress downward (about 35 and 65 ms) with the same speed as typical initial leaders before reaching the ground.

3D imaging of lightning channel and leader progression velocity

AbstractThree‐dimensional imaging of lightning channels by means of UHF interferometers is performed. To realize this, a field campaign was conducted with two observation sites in Darwin, Australia. The distance between the two sites is about 14 km, and the triangulation scheme is applied to estimate locations of UHF radiation sources. Since the UHF radiation is more likely during the leader progression than in the return stroke phase, imaging of lightning channels is obtained mainly for downward leaders. Velocities of downward leaders are estimated and statistics are presented for first and subsequent strokes. The result is consistent with those of former investigations obtained by optical observations. The statistics for the velocity of leader propagation inside thunderclouds are presented herein. Using optical measurement, velocity estimation of leader progressions inside thunderclouds is impossible, and the presented results are concluded to be the first results of their kind. © 2001 Scripta Technica, Electr Eng Jpn, 137(3): 22–28, 2001