Planar Mesh Research Articles

Summary on several key techniques in 3D geological modeling.

Several key techniques in 3D geological modeling including planar mesh generation, spatial interpolation, and surface intersection are summarized in this paper. Note that these techniques are generic and widely used in various applications but play a key role in 3D geological modeling. There are two essential procedures in 3D geological modeling: the first is the simulation of geological interfaces using geometric surfaces and the second is the building of geological objects by means of various geometric computations such as the intersection of surfaces. Discrete geometric surfaces that represent geological interfaces can be generated by creating planar meshes first and then spatially interpolating; those surfaces intersect and then form volumes that represent three-dimensional geological objects such as rock bodies. In this paper, the most commonly used algorithms of the key techniques in 3D geological modeling are summarized.

Electric Dipole Antenna in Presence of a Double Wire-Mesh Planar Interference Filter

In this letter, we derive a new full-wave analytical field solution for the problem of two separated planar thin-wire meshes excited by a short horizontal electric dipole (HED). Both meshes are constructed from identical perfectly conducting parallel wires with small period (interwire spacing) compared to wavelength. A fast-converging solution is obtained employing averaged boundary conditions and image theory approach. A set of computed near- and far-field patterns is presented.

Numerical investigation of the air–oil two-phase flow inside an oil-jet lubricated ball bearing

The air–oil two-phase flow inside an oil-jet lubricated ball bearing was investigated by the CFD method. The VOF method for multiphase flow was used to track the air–oil two-phase flow. The sliding mesh plane was applied between the flow field inside the bearing and the flow field on both outsides of the bearing. The results suggest that the air–oil distribution inside the oil-jet lubricated ball bearing is not uniform. The lowest oil volume fraction appears in the upstream side near the nozzle. The flow velocity and the pressure of the air–oil phase increase inside a faster bearing. The average oil volume fraction becomes lower as the speed increases. With the increase of the oil flow rate, the oil volume fraction in the bearing and the drag against the rotation of the rolling elements and cage increase. The nonuniformity of the air–oil distribution is also enhanced. The nonuniform air–oil distribution should be considered for the heat transfer analysis of the oil-jet lubricated ball bearing. Optimizing the oil-jet lubrication according to the air–oil distribution inside the oil-jet lubricated ball bearing is significant for the high-speed rotation to achieve lower drag loss and greater cooling effect.

Low voltage, low energy, and repetitive (4 Hz) operation of a conventional vircator for microwave emission in the range of 4–8 GHz

AbstractIn this paper, we are presenting the microwave emission results of a vircator that emits its radiation lying well-within the microwave range of electromagnetic spectrum viz 4–8 GHz and the energy needed per shot is as low as 25 Joules only. In this reported experiment, the pulse forming line is charged to a voltage of 160 kV and the measured diode voltage is 50 kV in the experiment. The primary energy is nearly 50 Joules only and hence the energy efficiency of the high voltage pulse transformer and pulse forming line combination for the given experiment is nearly 50%. The experiment is the first of its kind in establishing (experimentally) the low voltage operation of a conventional vircator, which has a planar cylindrical cathode and stainless steel mesh anode, for the microwave emission purpose. Moreover, because of the low voltage and low energy operation we could operate the whole system in repetitive mode and we could achieve as high as 4 Hz operation with this device. Interestingly, the current density of the velvet cathode used in the present experiment is nearly 300 A/cm2 in the present reported set of experiments. One interesting observation emerging out from the present experiment is that in the low voltage operation of the vircator the beam acceleration potential is relatively low and hence the axial velocities of reflexing electrons (trapped between cathode and virtual cathode) is also limited and far less than 1.8 × 108 m/s and hence with small anode cathode gaps like that of 3 mm, which is the case of present experiments, it becomes feasible to achieve radiation frequency of 4–8 GHz from the vircator.

ACQUIRE HIGH QUALITY MESHES OF SCALE MODELS FOR AN AUTOMATIC MODELLING PROCESS

Abstract. Urban scale models depicting whole towns such as the hundred-scale model collection known as plans-reliefs are a valuable source of information of cities and their surroundings. These physical representations of French strongholds from the 17th through the 19th century suffer from many problems that are, among other things, wear and tear or the lack of visibility and accessibility. A virtual collection would allow remote accessibility for visitors as well as history researchers. Moreover, it may also be linked to other digital collections and therefore, promote the collection to make people come to the museums to see the physical scale models. We also work on other physical town scale models like Epinal for which the scale is a bit higher. In a first part, we define a protocol for acquiring 3D meshes of town scale models from both photogrammetric and scanning methods. Then we compare the results of both methods The photogrammetric protocol has been elaborated by choosing the most accurate software, 123DCatch, which asks for about 60 pictures, and defining the settings needed to obtain exploitable photographs. In the same way, we defined the devices and settings needed for the laser scan acquisition method. In a second part, we segment the 3D meshes in planes by using Geomagic, which has been chosen between several programs, for its accurate resulting geometry.

Efficient computation of constrained parameterizations on parallel platforms

Constrained isometric planar parameterizations are central to a broad spectrum of applications. In this work, we present a non linear solver developed on OpenCL that is efficiently parallelizable on modern massively parallel architectures. We establish how parameterization relates to mesh smoothing and show how to efficiently and robustly solve the planar mesh parameterization problem with constraints. Furthermore, we demonstrate the applicability of our approach to real-time cut-and-paste editing and interactive mesh deformation.

Planar Numerical Signature Theory Applied to Object Recognition

Geometric invariants play a crucial role in the field of object recognition where the objects of interest are affected by a group of transformations. However, designing robust algorithms that are tolerant to noise and image occlusion remains an open problem. In particular, numerical signature-invariants in terms of joint invariants, as an approximation to the differential signature-invariants, suffer instability, bias, noise and indeterminacy in the resulting signatures. This paper addresses some of these issues in respect of planar signatures. To improve the stability in the Euclidean case, we replace Heron's formula by the "accurate area" and then we demonstrate that the proposed algorithm is, not only numerically stable but is also, in terms of mean square error, a closer approximation (by at least a factor of three) compared with the original formulation of Calabi. To reduce noise in the resulting curves "the n-difference technique" and "the m-mean signature method" are introduced and we show that these methods are capable of minimizing noise by more than 90 %. The n-difference technique can also be applied to eliminate indeterminacy in the outputs. For the equiaffine case, we improve and extend the required formulation for the implementation of Signature theory for any planar meshes with a general position property. Moreover, we introduce a general formulation for the full conic sections to determine an equiaffine-invariant numerical approximation to the equiaffine arc length, measured along the given curve between any two points of the mesh. Finally, we demonstrate the discriminative power of the concept of discrete signature analysis for distinguishing normal and abnormal regions in the medical imaging domain.

The Modified Direct Method: An Iterative Approach for Smoothing Planar Meshes

The Modified Direct Method (MDM) is an iterative method for smoothing planar triangular, quadrilateral and tri-quad meshes, which has been developed from the non-iterative smoothing method for planar meshes that was originated by Balendran [1]. Its simple aim is to make triangular elements as close to equilateral as possible and quadrilateral elements as close to square as possible. The MDM is the computationally simpler of the two methods. The performance of the MDM for both triangular and quadrilateral meshes is effectively identical to that of Laplacian smoothing; however, it outperforms Laplacian smoothing for tri-quad meshes. Test examples show that the MDM is always convergent for triangular, quadrilateral and tri-quad meshes.

Preliminary experimental investigation of boundary layer in decelerating flow

Investigations of characteristics of turbulence inside boundary layer under decelerating flow were studied by means of constant temperature anemometer. The decelerating flow was simulated in the closed circuit wind tunnel 0.9 m × 0.5 m at IT AS CR. The free stream turbulence was either natural or risen up by square mesh plane grid. The details of experimental settings and measurement procedures of the instantaneous longitudinal velocity component are described and the distributions of intensity, skewness and kurtosis of turbulent fluctuations are discussed in the contribution.

Local meshing plane analysis as a source of information about the gear quality

In the paper the application of the local meshing plane concept is discussed and applied for detecting of tooth degradation due to fatigue, and for overall gear quality assessment. Knowing the kinematic properties of the machine (i.e. gear tooth numbers) it is possible to modify the diagnostic signal in such a manner that its fragments will be linked to different rotating parts. This allows for presentation of either raw or processed gearbox signal in a form of three dimensional map on the plane “pinion teeth×gear teeth”, called local meshing plane. The meshing plane in Cartesian coordinates z1×z2 allows for precise location and assessment of gear faults in terms of meshing quality of consecutive tooth pairs. Although the method was applied to simulated signals generated by the gearbox model, similar results were obtained for the measurement signals recorded during the back-to-back test stand experiment.The described method could be used for assessing the manufacturing quality of gears, the assembly quality as well as for the gear failure evaluation during normal exploitation.

A Triangulation-Invariant Method for Anisotropic Geodesic Map Computation on Surface Meshes

This paper addresses the problem of computing the geodesic distance map from a given set of source vertices to all other vertices on a surface mesh using an anisotropic distance metric. Formulating this problem as an equivalent control theoretic problem with Hamilton-Jacobi-Bellman partial differential equations, we present a framework for computing an anisotropic geodesic map using a curvature-based speed function. An ordered upwind method (OUM)-based solver for these equations is available for unstructured planar meshes. We adopt this OUM-based solver for surface meshes and present a triangulation-invariant method for the solver. Our basic idea is to explore proximity among the vertices on a surface while locally following the characteristic direction at each vertex. We also propose two speed functions based on classical curvature tensors and show that the resulting anisotropic geodesic maps reflect surface geometry well through several experiments, including isocontour generation, offset curve computation, medial axis extraction, and ridge/valley curve extraction. Our approach facilitates surface analysis and processing by defining speed functions in an application-dependent manner.

Shape‐Up: Shaping Discrete Geometry with Projections

AbstractWe introduce a unified optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one‐ring cells, volume elements, or feature curves. Our method is based on two key concepts: a shape proximity function and shape projection operators. The proximity function encodes the distance of a desired least‐squares fitted elementary target shape to the corresponding vertices of the 3D model. Projection operators are employed to minimize the proximity function by relocating vertices in a minimal way to match the imposed shape constraints. We demonstrate that this approach leads to a simple, robust, and efficient algorithm that allows implementing a variety of geometry processing applications, simply by combining suitable projection operators. We show examples for computing planar and circular meshes, shape space exploration, mesh quality improvement, shape‐preserving deformation, and conformal parametrization. Our optimization framework provides a systematic way of building new solvers for geometry processing and produces similar or better results than state‐of‐the‐art methods.

Modeling Polyhedral Meshes with Affine Maps

AbstractWe offer a framework for editing and modeling of planar meshes, focusing on planar quad, and hexagonal‐dominant meshes, which are held in high demand in the field of architectural design. Our framework manipulates these meshes by affine maps that are assigned per‐face, and which naturally ensure the planarity of these faces throughout the process, resulting in a linear subspace of compatible planar deformations for any given mesh. Our modeling metaphors include classical handle‐based editing, mesh interpolation, and shape‐space exploration, all of which allow for an intuitive way to produce new polyhedral and near‐polyhedral meshes by editing.

Evaluation of the Buckling Load of an Elliptic Paraboloid Cable-Braced Grid Shell Using the Continuum Analogy

A cable-braced grid shell is a new type of single-layer latticed shell suitable for glass roofs. Compared with traditional single-layer latticed shells, this new type of shell has a unique mesh shape (planar quadrilateral mesh), mesh form (steel and crossing cables), and surface shape (from the translation surface method). The grid shell is a single-layer latticed structure, and therefore stability is one of the key factors in the structural design. Therefore, in this paper, an elliptic paraboloid cable-braced grid shell with imperfections is used as an example with which to determine the formulas for the buckling load based on the continuum analogy. The main contents of this paper include the formula for the linear buckling load of an elliptic paraboloid cable-braced grid shell with imperfections, which is determined based on the continuum analogy. The equivalent rigidity for the cable-braced grid shell is then determined, and the effect of the cables on the shear rigidity is discussed. Finally, the formula for the linear buckling load is verified with numerical examples, and the errors are analyzed and a corresponding correction factor is given.

A combined experimental–numerical investigation of ductile fracture in bending of a class of ferritic–martensitic steel

We present a combined experimental–numerical study on fracture initiation at the convex surface and its propagation during bending of a class of ferritic–martensitic steel. On the experimental side, so-called free bending experiments are conducted on DP1000 steel sheets until fracture, realizing optical and scanning electron microscopy analyses on the post mortem specimens for fracture characterization. A blended Mode I – Mode II fracture pattern, which is driven by cavitation at non-metallic inclusions as well as martensitic islands and resultant softening-based intense strain localization, is observed. Phenomena like crack zig-zagging and crack alternation at the bend apex along the bending axis are introduced and discussed. On the numerical side, based on this physical motivation, the process is simulated in 2D plane strain and 3D, using Gurson’s dilatant plasticity model with a recent shear modification, strain-based void nucleation, and coalescence effects. The effect of certain material parameters (initial porosity, damage at coalescence and failure, shear modification term, etc.), plane strain constraint and mesh size on the localization and the fracture behavior are investigated in detail.

Multi-tooth contact behavior of helical gear applying modified meshing equation

In tooth contact analysis, the numerical process of searching for true contact lines or points is always a daunting task. The true contact lines for ideal helical gear transmission can be easily obtained through the helical gear meshing theory; however, in practice, this approach does not work well due to effect of tooth elasticity that shifts the contact lines from their ideal position. To address this problem, an approximate method to seek the true contact positions is proposed applying a modified meshing equation for a pair of helical gear with error free and no shaft deformation. First, the helical gear tooth deformation is calculated with the combination of contact mechanics and finite element method. Second, the deformed tooth flanks are fitted with Chebyshev polynomials. Third, the modified meshing equation is formulated by accounting for the influence of not only gear rigid body movement but also the gear deformation on the meshing process. Finally, the true contact points are determined by solving the correlated tooth flank equations, meshing equations, and force balance equations. The deformations of the gear and pinion teeth within the meshing plane are analyzed, and the contact load distributions along with the Von Mises stresses over a mesh cycle are examined. The study indicates that the proposed numerical method can yield true contact lines quickly while avoiding costly computational time in the traditional true contact line searching process that searches iteratively in the whole meshed tooth flank.

Entire Chromatic Number and Entire Coloring Algorithms of Regular Planar Meshes

In this paper, we propose three entire coloring schemes for regular planar meshes — square meshes, hexagonal meshes and honeycomb meshes, respectively. Based on these schemes, we propose three efficient entire coloring algorithms for these three planar meshes and prove that the entire chromatic number of square meshes is 7 (maximum degree plus 3), the entire chromatic number of hexagonal meshes is 9 (maximum degree plus 2), and the entire chromatic number of honeycomb meshes is 7 (maximum degree plus 4).

COMPARING ANALYTICAL AND NUMERICAL CALCULATIONS OF SHIELDING EFFECTIVENESS OF PLANAR METALLIC MESHES WITH MEASUREMENTS IN CASCADED REVERBERATION CHAMBERS

Large electrical systems or facilities can be satisfactorily shielded by using low-cost meshed metallic nets. Here the shielding efiectiveness for two such planar meshes is calculated analytically and verifled both experimentally by using cascaded reverberation chambers as well as numerically with results computed using a full wave electromagnetic solver. It is shown that all three methods agree and, in addition, that non-square shaped aperture meshes can be handled with an equivalent square area shaped aperture.

Modeling of an On-Chip Power/Ground Meshed Plane Using Frequency Dependent Parameters

This paper proposes a new modeling method for estimating the impedance of an on-chip power/ground meshed plane. Frequency dependent R, L, and C parameters are extracted based on the proposed method so that the model can be applied from DC to high frequencies. The meshed plane model is composed of two parts: coplanar multi strip (CMS) and conductor-backed CMS. The conformal mapping technique and the scaled conductivity concept are used for accurate modeling of the CMS. The developed microstrip approach is applied to model the conductor-backed CMS. The proposed modeling method has been successfully verified by comparing the impedance of RLC circuit based on extracted parameters and the simulated impedance using a 3D-field solver.

Modeling Fraunhofer diffractive characteristics for modulation transfer function analysis of tilted ring metallic mesh

In order to analyze the Fraunhofer diffractive characteristics and modulation transfer function (MTF) of a tilted ring metallic mesh, an optical intensity distribution model of Fraunhofer diffraction is built using Huygens–Fresnel diffraction theory and the diffraction integral is carried out directly in the tilted mesh plane. The diffraction characteristics of the tilted ring metallic mesh are in good agreement with experimental results, which proves the correctness of the model established. MTF of an optical system with metallic mesh is calculated based on the model established and Fourier transform. Analysis shows that the degradation of MTF caused by diffraction of a ring mesh is much less than that of a square mesh whether they are vertical or tilted to the optical axis. Therefore, ring mesh can provide higher imaging quality than square mesh when they are used as high-pass filters in optical windows. A tilted array diffraction modulating factor is abstracted and believed useful in the analysis of diffractive characteristics of tilted square mesh and ring mesh, and it can be extended to Fraunhofer diffractive characteristics analysis of other tilted diffraction arrays.