Symmetric Mesh Research Articles

Symmetry‐Aware Mesh Segmentation into Uniform Overlapping Patches

AbstractWe present intrinsic methods to address the fundamental problem of segmenting a mesh into a specified number of patches with a uniform size and a controllable overlap. Although never addressed in the literature, such a segmentation is useful for a wide range of processing operations where patches represent local regions and overlaps regularize solutions in neighbour patches. Further, we propose a symmetry‐aware distance measure and symmetric modification to furthest‐point sampling, so that our methods can operate on semantically symmetric meshes. We introduce quantitative measures of patch size uniformity and symmetry, and show that our segmentation outperforms state‐of‐the‐art alternatives in experiments on a well‐known dataset. We also use our segmentation in illustrative applications to texture stitching and synthesis where we improve results over state‐of‐the‐art approaches.

3D shape analysis of the brain's third ventricle using a midplane encoded symmetric template model

BackgroundStructural changes of the brain's third ventricle have been acknowledged as an indicative measure of the brain atrophy progression in neurodegenerative and endocrinal diseases. To investigate the ventricular enlargement in relation to the atrophy of the surrounding structures, shape analysis is a promising approach. However, there are hurdles in modeling the third ventricle shape. First, it has topological variations across individuals due to the inter-thalamic adhesion. In addition, as an interhemispheric structure, it needs to be aligned to the midsagittal plane to assess its asymmetric and regional deformation. MethodTo address these issues, we propose a model-based shape assessment. Our template model of the third ventricle consists of a midplane and a symmetric mesh of generic shape. By mapping the template's midplane to the individuals’ brain midsagittal plane, we align the symmetric mesh on the midline of the brain before quantifying the third ventricle shape. To build the vertex-wise correspondence between the individual third ventricle and the template mesh, we employ a minimal-distortion surface deformation framework. In addition, to account for topological variations, we implement geometric constraints guiding the template mesh to have zero width where the inter-thalamic adhesion passes through, preventing vertices crossing between left and right walls of the third ventricle. The individual shapes are compared using a vertex-wise deformity from the symmetric template. ResultsExperiments on imaging and demographic data from a study of aging showed that our model was sensitive in assessing morphological differences between individuals in relation to brain volume (i.e. proxy for general brain atrophy), gender and the fluid intelligence at age 72. It also revealed that the proposed method can detect the regional and asymmetrical deformation unlike the conventional measures: volume (median 1.95ml, IQR 0.96ml) and width of the third ventricle. Similarity measures between binary masks and the shape model showed that the latter reconstructed shape details with high accuracy (Dice coefficient ≥0.9, mean distance 0.5mm and Hausdorff distance 2.7mm). ConclusionsWe have demonstrated that our approach is suitable to morphometrical analyses of the third ventricle, providing high accuracy and inter-subject consistency in the shape quantification. This shape modeling method with geometric constraints based on anatomical landmarks could be extended to other brain structures which require a consistent measurement basis in the morphometry.

Simulation of mixed lubrication of rigid plain journal bearing by finite difference method with a skewed discretisation mesh

Numerical simulation of lubrication of journal bearing often uses a rectangular discretisation mesh. Steady-state mixed hydro-dynamic lubrication of rigid plain journal bearing is investigated by using finite difference form of Patir-Cheng average Reynolds equation under Reynolds boundary condition. Two kinds of non-orthogonal discretisation meshes, i.e., helix mesh and symmetric herringbone mesh are considered respectively. Three difference schemes, i.e.: 1) central finite difference; 2) second order upwinding; 3) a new central finite difference considering the film thickness at the projected positions from the nodes of neighbouring rows; are used to difference the shear induced flow term (i.e., Couette term). The effectiveness of the three schemes is discussed using the skewed discretisation mesh by comparing theoretical predictions of load with that found in the literature for smooth lubrication using the rectangular discretisation mesh. The effect of the skewed angle of mesh on the predicted parameters such as load, friction coefficient, attitude angle and maximum pressure is investigated for both smooth and rough surfaces. It is found that generally these schemes may provide a reasonable satisfactory solution. However, when symmetric herringbone mesh is used, a larger relative deviation is found as the skewed angle is larger and the eccentricity ratio is smaller.

On Uniform Traffic Pattern of Symmetric Midimew Connected Mesh Network

A Symmetric Midimew Mesh connected network (SMMN) is a hierarchical interconnection networks (HIN) that capable to interconnect vast number of nodes that could reach up to millions of nodes in the network. SMMN has multiple basic modules of 2D-mesh networks that are recursively interconnected by Midimew network to create higher-level networks. In this paper, we explain the architectural details of SMMN,we also present the a deadlock-free routing algorithm for SMMN using four virtual channels and evaluate the performance of dynamic communication of SMMN network using proposed routing algorithm under uniform traffic pattern .We also evaluate the performance of dynamic communication of TESH network using topaz simulator. It is shown that the SMMN network has high throughput and low latency, which yield higher performance of dynamic communication compare to other Hierarchical networks.

Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients

Abstract In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x 0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h p+1 |ln h|2) and O(h p+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients.

Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

We consider the initial boundary value problem for the inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and a nonsmooth right hand side data in a bounded convex polyhedral domain. We analyze two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right hand side data $f(x,t)\in L^\infty(0,T;\dot H^q(\Omega))$, $-1< q \le 1$, for both semidiscrete schemes. For lumped mass method, the optimal $L^2(\Omega)$-norm error estimate requires symmetric meshes. Finally, numerical experiments for one- and two-dimensional examples are presented to verify our theoretical results.

Symmetry preserving in Topological Mapping for tension structures

When using Topological Mapping (TM) together with the Force Density Method (FDM) in order to find a first form of equilibrium for a tension structure whose fixed nodes coincide in plan view with the vertices of a regular polygon, it has been observed that the symmetry may be lost. The problem is related to the mapping procedure that is introduced in the process. However, if some rules are followed in constructing the topology for the mesh, the symmetry can be preserved. With a symmetric mesh, the later cutting pattern generation process becomes simpler, easier, and cheaper. This paper will provide one simple algorithm that has been proved to work effectively in preserving the symmetry in the cited type of tension structures. Several examples are presented in order to better illustrate the applicability of these easy prescriptions.

Computationally Tractable Stochastic Image Modeling Based on Symmetric Markov Mesh Random Fields

In this paper, the properties of a new class of causal Markov random fields, named symmetric Markov mesh random field, are initially discussed. It is shown that the symmetric Markov mesh random fields from the upper corners are equivalent to the symmetric Markov mesh random fields from the lower corners. Based on this new random field, a symmetric, corner-independent, and isotropic image model is then derived which incorporates the dependency of a pixel on all its neighbors. The introduced image model comprises the product of several local 1D density and 2D joint density functions of pixels in an image thus making it computationally tractable and practically feasible by allowing the use of histogram and joint histogram approximations to estimate the model parameters. An image restoration application is also presented to confirm the effectiveness of the model developed. The experimental results demonstrate that this new model provides an improved tool for image modeling purposes compared to the conventional Markov random field models.

Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations

We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition $v(x)$ and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain $\Omega$. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., $v \in H^2(\Omega)\cap H^1_0(\Omega)$ and $v \in L_2(\Omega)$. For the lumped mass method, the optimal $L_2$-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study.

An adaptive splitting approach for the quenching solution of reaction–diffusion equations over nonuniform grids

The numerical solution of a nonlinear degenerate reaction–diffusion equation of the quenching type is investigated. While spatial derivatives are discretized over symmetric nonuniform meshes, a Peaceman–Rachford splitting method is employed to advance solutions of the semidiscretized system. The temporal step is determined adaptively through a suitable arc-length monitor function. A criterion is derived to ensure that the numerical solution acquired preserves correctly the positivity and monotonicity of the analytical solution. Weak stability is proven in a von Neumann sense via the ∞-norm. Computational examples are presented to illustrate our results.

Exploring a Low-Cost and Power-Efficient Hybridization Technique for 3D NoC-Bus Hybrid Architecture Using LastZ-Based Routing Algorithms

Three-dimensional (3D) integration in which m ultiple active silicon layers are stacked above each other and vertically interconnected offers shorter interconnection wire for Networks-on-Chip (NoC). The simple 3D NoC architectures such as Symmetric 3D Mesh NoC could not exploit the beneficial feature of a negligible inter-layer dista nce in 3D chips. In order to exploit the intrinsic capability of reducing the wire length in 3D ICs, 3D NoC-Bus Hybrid architecture was proposed. This architecture suffers from naive and straightforward hybridization between NoC and bus media. In this paper, an efficient hybridization scheme is presented to enhance system performance, power consumption, and area of 3D NoC-Bus Hybrid architectures. The hybridization mechanism benefiting from a rule called LastZ enables low-cost inter-layer communication architecture. In the proposed architecture, instead of using the conventional 6×6 routers, 5×6 routers were utilized which offers many advantages. To estimate the efficiency of the proposed architecture, the system has been simulated using synthetic (uniform, hotspot 10%, and Negative Exponential Distribution) traffic patterns as well as real benchmarks, including the one with an integrated videoconference application. Compared to a conventional 3D NoC-Bus Hybrid Mesh architecture, our extensive simulations reveal significant area, power, and performance improvements for the proposed LastZ-based hybridization scheme.

A Probabilistic Approach to Analysis of Reliability in n-D Meshes with Interconnect Router Failures

The routing algorithms for parallel computers, on-chip networks, multi-core processors, and multiprocessors system-on-chip (MP-SoCs) exhibit router failures must be able to handle interconnect router failures that render a symmetrical mesh non-symmetrically. When developing a routing methodology, the time complexity of calculation should be minimal, and thus complicated routing strategies to introduce profitable paths may not be appropriate. Several reports have been released in the literature on using the concept of fault rings to provide detour paths to messages blocked by faults and to route messages around the fault regions. In order to analyze the performance of such algorithms, it is required to investigate the characteristics of fault rings. In this paper, we introduce a novel performance index of network reliability presenting the probability of message facing fault rings, and evaluating the performance-related reliability of adaptive routing schemes in n-D mesh-based interconnection networks with a variety of common cause fault patterns. Sufficient simulation results of Monte-Carlo method are conducted to demonstrate the correctness of the proposed analytical model.

Comparison of first‐ and second‐order 2D finite element models for calculating AC loss in high temperature superconductor coated conductors

PurposeThe purpose of the paper is to provide a comparison of first‐ and second‐order two dimensional finite element models for evaluating the electromagnetic properties and calculating AC loss in high‐temperature superconductor (HTS) coated conductors.Design/methodology/approachThe models are based on the two‐dimensional (2D) H formulation, which is based on directly solving the magnetic field components in 2D. Two models – one with a minimum symmetric triangular mesh and one with a single‐layer square mesh – are compared based on different types of mesh elements: first‐order (Lagrange – linear) and second‐order (Lagrange – quadratic) mesh elements, and edge elements.FindingsThe number and type of mesh elements are critically important to obtain the minimum level of discretization to achieve accurate results. Artificially increasing the superconductor layer and choosing a minimum symmetric mesh with triangular edge elements can provide a sufficiently accurate estimation of the hysteretic superconductor loss for a transport current.Originality/valueThis paper describes how the selection of mesh type and number of elements affects the computation speed and convergence properties of the finite element model using two different types of meshing. It offers an insight into the different factors modelers must consider when modeling HTS coated conductors and the methods that may be applied when extending the model to complex device geometries, such as wound coils.

Condition number bounds and mesh quality

AbstractWe analyze the effect of mesh distortion on the condition number of the representative mass matrix M and stiffness matrix K arising in a typical finite element scheme. Bounds are stated for the respective condition numbers in terms of the Jacobian of the map from a reference element. These results are then used to construct the related bounds in terms of representative metrics for mesh distortion. These bounds are easily pre‐computable and provide a new explicit mathematical relation between matrix conditioning and mesh quality metrics. Numerical studies for a 2D test problem using a representative cell quality metric demonstrate the upper bound property and the dependence on cell quality for a quadrilateral cell. Analogous results for a 3D test problem under progressive symmetric mesh distortion of an interior hexahedral cell are also provided, as well as a study on a complex 3D geometry. We conclude by presenting practical adaptive mesh grading applications employing aforementioned mesh quality metrics. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Numerical Modeling of the Gas Migration Test at the Grimsel Test Site (Switzerland)

The Gas Migration Test (GMT) at the Grimsel Test Site underground laboratory in central Switzerland was designed to investigate gas migration through an engineered barrier system (EBS). The EBS consists of a concrete silo embedded in a sand/bentonite buffer emplaced in a silo cavern that intersects a shear zone in the surrounding granite host rock. The experiment was performed in a series of stages: (a) excavation of the access drift and silo cavern, (b) construction and instrumentation, (c) saturation of the EBS, (d) water tests, (e) long-term gas injection at different rates, (f) postgas water testing, (g) gas injection with a “cocktail” of gas tracers, and (h) depressurization and dismantling. A numerical model was developed for the design and analysis of the different stages and to describe the relevant phenomena associated with gas migration from a potential repository for transuranic waste.A numerical model of the GMT was implemented with the two-phase-flow code TOUGH2, representing the GMT silo with a multilayered radially symmetric mesh and the surrounding water-conducting granite shear zone with a two-dimensional vertical feature. The different stages of the experiment were simulated in sequence using the results of the previous stage as initial conditions for the subsequent stage. Two-phase-flow parameters for the EBS were derived from laboratory experiments on core samples of the different materials that comprise the EBS, while hydraulic properties of the sand/bentonite and of relevant interface zones were calibrated to the pressure responses in the silo and selected piezometers in the sand/bentonite. The results of the numerical modeling of the GMT experiment show that the main features and processes of the different stages of the experiment could be reasonably well reproduced. Following the initial calibration of effective properties from the water test response during stage 4, property changes during the subsequent test phase were calibrated as stress-or pressure-dependent permeability changes. During the gas injection phases, the pressure-dependent permeability change could be related to the minimum effective stresses along interfaces. The inferred coupled hydromechanical phenomena were implemented using pressure-dependent permeability relationships on interfaces at the top of the silo and between the sand/bentonite and the granite host rock. During the recovery sequence following the first injection gas phase, the calibrated decrease in permeability of the sand/bentonite above the silo was related to the pressure decline in the upper cavern, but there was no apparent stress change. However, the calibrated permeability reduction in the sand/bentonite was in the range of values measured during the EBS excavation. In addition, time-dependent permeability relationships were calibrated for the tunnel seal to account for the gradual decrease in water inflow from the upper cavern into the access tunnel and the drift.

Performances comparison between multilevel hierarchical and mesh FPGA interconnects

This paper evaluates a new multilevel hierarchical FPGA (MFPGA). The specific architecture includes two unidirectional programmable networks: a downward network based on the Butterfly-Fat-Tree topology; and a special upward network. New tools are developed to place and route several benchmark circuits on this architecture. Comparison with the traditional symmetric Manhattan mesh architecture shows that MFPGA can implement circuits with a smaller area and better speed.

Superconvergence in high-order Galerkin finite element methods

In this paper, we shall use local estimates to give the superconvergence of high-order Galerkin finite element method for the elliptic equation of second order with constant coefficients by using the symmetric technique and integral identity. We get improved superconvergence on the inner locally symmetric mesh with respect to a point x 0 for rectangular and triangular meshes.

Parameterization and parametric design of mannequins

This paper presents a novel feature based parameterization approach of human bodies from the unorganized cloud points and the parametric design method for generating new models based on the parameterization. The parameterization consists of two phases. First, the semantic feature extraction technique is applied to construct the feature wireframe of a human body from laser scanned 3D unorganized points. Secondly, the symmetric detail mesh surface of the human body is modeled. Gregory patches are utilized to generate G1 continuous mesh surface interpolating the curves on feature wireframe. After that, a voxel-based algorithm adds details on the smooth G1 continuous surface by the cloud points. Finally, the mesh surface is adjusted to become symmetric. Compared to other template fitting based approaches, the parameterization approach introduced in this paper is more efficient. The parametric design approach synthesizes parameterized sample models to a new human body according to user input sizing dimensions. It is based on a numerical optimization process. The strategy of choosing samples for synthesis is also introduced. Human bodies according to a wide range of dimensions can be generated by our approach. Different from the mathematical interpolation function based human body synthesis methods, the models generated in our method have the approximation errors minimized. All mannequins constructed by our approach have consistent feature patches, which benefits the design automation of customized clothes around human bodies a lot.

Estimation of Asymmetry in Facial Actions for the Analysis of Motion Dysfunction Due to Paralysis

A mesh-based approach to estimate asymmetries in facial actions for the analysis of facial motion dysfunction due to paralysis is presented. Pre-designed facial actions are captured using a laser rangefinder system and then analyzed in three-dimension for patients with Bell's palsy. The asymmetry computations are based on analyzing the deformations in a symmetric generic face mesh that was adapted to the range maps of measured facial actions. In the mesh adaptation, 42 nodes are pre-determined as mapping points and extracted from the corresponding color image, which was taken at the same time as shape measurement. These mapping points are used to calculate the coefficients of a polynomial function, which is approximated by the least squares estimation during rest of the node mapping. A 3D mesh model of each action is thus generated by iterative adaptation to the range data. The asymmetry is computed by analyzing the amount of deformation in identical patches of left and right sides of the 3D mesh of each action against those of relaxed condition. Asymmetry distributions are obtained by plotting right patch deformations against the left. Standard error and standard deviation of distributions of each patient are obtained and analyzed to determine the degree of motion dysfunction.

Curve interpolation based on Catmull-Clark subdivision scheme*

Abstract An efficient algorithm for curve interpolation is proposed. The algorithm can produce a subdivision surface that can interpolate the predefined cubic B-spline curves by applying the Catmull-Clark scheme to a polygonal mesh containing symmetric zonal meshes which possesses some special properties. Many kinds of curve interpolation problems can be dealt with by this algorithm such as interpolating single open curve or closed curve a mesh of nonintersecting or intersecting curve. The interpolating surface is C 2 everywhere excepting at a finite number of points. At the same time, sharp creases can also be modeled on the limit subdivision surface by duplicating the vertices of the tagged edges of initial mesh.i. e. the surface is only C 0 along the cubic B-spline curve that is defined by the tagged edges. Because of being simple and easy to implement, this method can be used for product shape design and graphic software development.