Mesh Projection Research Articles

ImplicitPCA: Implicitly-proxied parametric encoding for collision-aware garment reconstruction

The emerging remote collaboration in a virtual environment calls for quickly generating high-fidelity 3D humans with cloth from a single image. To estimate clothing geometry and topology, parametric models are widely used but often lack details. Alternative approaches based on implicit functions can generate accurate details but are limited to closed surfaces and may not produce physically correct reconstructions, such as collision-free human avatars. To solve these problems, we present ImplicitPCA, a framework for high-fidelity single-view garment reconstruction that bridges the good ends of explicit and implicit representations. The key is a parametric SDF network that closely couples parametric encoding with implicit functions and thus enjoys the fine details brought by implicit reconstruction while maintaining correct topology with open surfaces. We further introduce a collision-aware regression network to ensure the physical correctness of cloth and human. During inference, an iterative routine is applied to an input image with 2D garment landmarks to obtain optimal parameters by aligning the cloth mesh projection with the 2D landmarks and fitting the parametric implicit fields with the reconstructed cloth SDF. The experiments on the public dataset and in-the-wild images demonstrate that our result outperforms the prior works, reconstructing detailed, topology-correct 3D garments while avoiding garment-body collisions.

Adaptive Mesh Generation Technique for Efficient Electromagnetic Computation in RFIC Designs

A novel adaptive mesh generation technique for efficient electromagnetic simulation of radio-frequency integrated circuits (RFICs) is herein presented. By exploring the geometrical and physical characteristics of RFICs, some adaptive mesh treatments, such as mesh projection, edge refinement, via polymerization, etc., are utilized to improve the accuracy and efficiency of electromagnetic computations. For strong coupling structures, such as two conductors in close proximity for a relatively large area, a projection-based mesh scheme is introduced to improve the accuracy of numerical integration. Moreover, the current most likely concentrates near the edges of conductors due to the edge effect. To better model the edge effect, an edge refinement scheme is applied. For via arrays that appear common in RFICs, an automatic via aggregation approach is adopted to improve computational efficiency yet still keep good computational accuracy. Finally, some numerical examples are given to validate the computational accuracy and efficiency of the novel adaptive mesh generation technique.

Rigorous Modal Characterization of First- and Second-Order Symmetric Waveguides Using Specular Periodic Boundary Conditions in 2D-FEM

Symmetries are widely exploited in the electromagnetic characterization of millimeter-wave devices and antennas, as they usually bring an improvement in resource usage and accuracy in full-wave simulations. Given the rising relevance of higher order symmetric devices, a challenge of integrating many different symmetries into compact formulations appears, with the objective of finding synergies and combining the strengths each one separately brings. In this work, we present a 2-D finite element method (FEM) formulation that fulfills this task for arbitrary waveguide cross sections presenting at the same time specular first-order and rotational second-order symmetries. It is based on newly introduced specular periodic boundary conditions (SPBCs), which effectively exploit the best case simulation domain for this problem. Furthermore, they avoid the need of using a mesh matching or projection procedure for periodic boundaries, while also bringing an improvement to mode classification.

UAV-based bridge geometric shape measurement using automatic bridge component detection and distributed multi-view reconstruction

UAV cameras combined with image-based reconstruction are promising non-contact tools for bridge shape inspection while computational efficiency is low, particularly on large-scale image sets. This paper describes an efficient image-based reconstruction pipeline for bridge geometry measurements. A full bridge three-dimensional reconstruction task is decomposed into multiple distributed tasks of reconstructing bridge sub-models using sub-image sets. A deep learning-based object detection method combined with Euclidean clustering is proposed to automatically generate cropped sub-image sets. An image mask generation technique based on 3D-to-2D mesh projection is used to keep valid pixels for camera pose estimation. The proposed method was validated in a laboratory test for arch shape measurement and in a field test for suspension cable shape measurement. The results show significant improvement about computational efficiency without accuracy reduction, compared with conventional image reconstruction methods.

LEoPart: A particle library for FEniCS

This paper introduces LEoPart, an add-on for the open-source finite element software library FEniCS to seamlessly integrate Lagrangian particle functionality with (Eulerian) mesh-based finite element (FE) approaches. LEoPart- which is so much as to say: ‘Lagrangian–Eulerian on Particles’ - contains tools for efficient, accurate and scalable advection of Lagrangian particles on simplicial meshes. In addition, LEoPart comes with several projection operators for exchanging information between the scattered particles and the mesh and vice versa. These projection operators are based on a variational framework, which allows extension to high-order accuracy. In particular, by implementing a dedicated PDE-constrained particle–mesh projection operator, LEoPart provides all the tools for diffusion-free advection, while simultaneously achieving optimal convergence and ensuring conservation of the projected particle quantities on the underlying mesh. A range of numerical examples that are prototypical to passive and active tracer methods highlight the properties and the parallel performance of the different tools in LEoPart. Lastly, future developments are identified. The source code for LEoPart is actively maintained and available under an open-source license at https://bitbucket.org/jakob_maljaars/leopart.

HIGH QUALITY TEXTURE MAPPING PROCESS AIMED AT THE OPTIMIZATION OF 3D STRUCTURED LIGHT MODELS

Abstract. This article presents the evaluation of a pipeline to develop a high-quality texture mapping implementation which makes it possible to carry out a semantic high-quality 3D textured model. Due to geometric errors such as camera parameters or limited image resolution or varying environmental parameters, the calculation of a surface texture from 2D images could present several color errors. And, sometimes, it needs adjustments to the RGB or lightness information on a defined part of the texture. The texture mapping procedure is composed of mesh parameterization, mesh partitioning, mesh segmentation unwraps, UV map and projection of island, UV layout optimization, mesh packing and mesh baking. The study focuses attention to the mesh partitioning that essentially assigns a weight to each mesh, which reveals a mesh’s weight calculated by considering the flatness and distance of the mesh with respect to a chart. The 3D texture mapping has been developed in Blender and implemented in Python. In this paper we present a flowchart that resumes the procedure which aims to achieve a high-quality mesh and texture 3D model starting from the 3D Spider acquire, integrated with the SfM texture and using the texture mapping to reduce the color errors according to a semantic interpretation.

Conservative, high-order particle–mesh scheme with applications to advection-dominated flows

By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle–mesh scheme for flow and transport problems which allows for diffusion-free advection while satisfying mass and momentum conservation – locally and globally – and extending to high-order spatial accuracy. This is achieved via the introduction of a novel particle–mesh projection operator which casts the particle–mesh data transfer as a PDE-constrained optimization problem, permitting advective flux functionals at cell boundaries to be inferred from particle trajectories. This optimization problem seamlessly fits in a HDG framework, whereby the control variables in the optimization problem serve as advective fluxes in the HDG scheme. The resulting algebraic problem can be solved efficiently using static condensation. The performance of the scheme is demonstrated by means of numerical examples for the linear advection–diffusion equation and the incompressible Navier–Stokes equations. The results demonstrate optimal spatial accuracy, and when combined with a θ time integration scheme, second-order temporal accuracy is shown.

Weighted Average Continuity Approach and Moment Correction: New Strategies for Non-consistent Mesh Projection in Structural Mechanics

Tying non-matching meshes is needed in many instances of finite element modeling. Multiple techniques have been proposed in the literature to accomplish the correct communication between different discretizations. They all seek to achieve some trade-off in terms of accuracy, complexity and computational cost. In this work we review several of the existing techniques and benchmark them on several simple test problems in terms of accuracy and computational cost. We also discuss some of the drawbacks and limitations of the existing methods. We then propose two novel contributions. First, a new approach that imposes the continuity of the displacement field at the interface in a point-wise manner only after an integral weighted averaging procedure over each interface. Second, a procedure for the correction of the interpolation operator based on the balance of internal forces and moments at the interface is proposed, which is applicable to all the reviewed methods, both existing and the new proposed one. All the considered approaches are benchmarked on several test problems in terms of various error measures for displacements, stresses, interface forces and moments, total work at the interface and computational cost.

Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection

We present a novel approach to 3D structural shape optimization that leans on an Immersed Boundary Method. A boundary tracking strategy based on evaluating the intersections between a fixed Cartesian grid and the evolving geometry sorts elements as internal, external and intersected. The integration procedure used by the NURBS-Enhanced Finite Element Method accurately accounts for the nonconformity between the fixed embedding discretization and the evolving structural shape, avoiding the creation of a boundary-fitted mesh for each design iteration, yielding in very efficient mesh generation process. A Cartesian hierarchical data structure improves the efficiency of the analyzes, allowing for trivial data sharing between similar entities or for an optimal reordering of the matrices for the solution of the system of equations, among other benefits. Shape optimization requires the sufficiently accurate structural analysis of a large number of different designs, presenting the computational cost for each design as a critical issue. The information required to create 3D Cartesian h-adapted mesh for new geometries is projected from previously analyzed geometries using shape sensitivity results. Then, the refinement criterion permits one to directly build h-adapted mesh on the new designs with a specified and controlled error level. Several examples are presented to show how the techniques here proposed considerably improve the computational efficiency of the optimization process.

Extension of the noise propagation matrix method for higher mode solutions

The noise propagation matrix method (NPMM) has been extended to get higher mode solutions. Previous studies show that the NPMM can be used to compute the dominance ratio of a system. It is essentially the same as the Coarse Mesh Projection Method (CMPM), both of which use the noise propagation matrix (NPM) to determine the dominance ratio, either after finishing the Monte Carlo simulation or on-the-fly during the simulation. Since only the fundamental fission source information is explicitly utilized while the higher mode information is implicitly contained in the statistical noises, the NPMM can usually only give an approximate estimation of the dominance ratio after thousands of cycles. In this study, the NPMM is extended by simulating the higher modes explicitly, so that the dominance ratio estimation can be more accurate and efficient. Besides, the higher mode solutions can be obtained at the same time with good accuracy and efficiency.

Theoretical Convergence Rate Lower Bounds for Variants of Coarse Mesh Finite Difference to Accelerate Neutron Transport Calculations

The lower bounds for the theoretical convergence rate of variants of the Coarse Mesh Finite Difference (CMFD) method for neutron transport acceleration are studied in this paper by generalization of the method into three categories: artificially diffusive CMFD, flux relaxation, and higher-order spatial prolongation operators. A Fourier analysis of the methods demonstrates that artificial diffusion and flux relaxation are mathematically equivalent and arbitrarily scale the coarse mesh to fine mesh projection (CMP) vector. The high-order spatial prolongation method is shown to affect the shape of the CMP vector. As a result, any of the CMFD variants based on these three sets of modifications correspond to a specific CMP vector. The optimization process is performed for the multidimensional vector, and the minimum spectral radius among all possible CMP vectors is shown to be the theoretical lower bound for the CMFD convergence rate. The spectral radius associated with the CMFD convergence rate lower bound is found to be slightly smaller (less than 0.04) than optimally diffusive CMFD (odCMFD), and the difference between odCMFD to the CMFD lower bound is much smaller than the difference between both standard CMFD and partial current–based CMFD to the CMFD lower bound. In addition, the odCMFD method has a distinct advantage in ease of implementation and minimal overhead. Conversely, the implementation necessary to achieve the CMFD lower bound would be very complicated, especially for two- and three-dimensional problems.

Detail‐Preserving Explicit Mesh Projection and Topology Matching for Particle‐Based Fluids

AbstractWe propose a new explicit surface tracking approach for particle‐based fluid simulations. Our goal is to advect and update a highly detailed surface, while only computing a coarse simulation. Current explicit surface methods lose surface details when projecting on the isosurface of an implicit function built from particles. Our approach uses a detail‐preserving projection, based on a signed distance field, to prevent the divergence of the explicit surface without losing its initial details. Furthermore, we introduce a novel topology matching stage that corrects the topology of the explicit surface based on the topology of an implicit function. To that end, we introduce an optimization approach to update our explicit mesh signed distance field before remeshing. Our approach is successfully used to preserve the surface details of melting and highly viscous objects, and shown to be stable by handling complex cases involving multiple topological changes. Compared to the computation of a high‐resolution simulation, using our approach with a coarse fluid simulation significantly reduces the computation time and improves the quality of the resulting surface.

An h-Adaptive RKDG Method for the Vlasov–Poisson System

In this paper, we propose a new h-adaptive indicator for the Runge---Kutta discontinuous Galerkin (RKDG) scheme in simulations of the Vlasov---Poisson (VP) system. This adaptive indicator, tailored for the VP system, is based on the principle that each cell assumes solution variations as equally as possible. Under the framework of the RKDG method, such adaptive indicator is particularly simple and cheap for the computation. Its effectiveness is demonstrated by extensive numerical tests. The detailed adaptive algorithm as well as some important implementation issues, including the grid and data structure, adaptive criteria, data prolongation/projection and mesh projection, is presented.

Freeform texture representation and characterisation based on triangular mesh projection techniques

Abstract Texture characterisation for freeform non-Euclidean surfaces is becoming increasingly important due to the widespread of the use of such surfaces in different applications, e.g. the additive manufacturing. Four main steps are required to analyse and characterise those surfaces which include new surface representation, surface filtration and decomposition, texture representation methods and finally the calculation of the surface parameters. Recently, the representation, as well as the filtration and decomposition, of freeform surfaces have been investigated and some algorithms have been proposed. This paper, however, shed the light on how to represent the texture of freeform non-Euclidean surfaces before calculating the parameters. A novel model for freeform surface parameterisation is introduced; this new model proposes the use of a projection algorithm before the actual calculation of the parameters. Different projection algorithms have been adopted from the mesh projection techniques found in the field of computer graphics. The results of applying those algorithms to represent the texture of both simulated and bio-engineering surfaces are shown, also a comparison between those algorithms has been carried out. Furthermore, examples of calculating some of the surface parameters for freeform surfaces are given.

Applications of mesh parameterization and deformation for unwrapping 3D images of rock tunnels

This paper presents analysis on two 3D mesh to 2D map strategies applied to unwrap images of rock tunnels and facilitate visualization of large datasets. First, we examined mesh parameterization algorithms which are used in computer graphics to convert a 3D mesh model to a 2D representation.We found that while these methods were automatic and could provide 2D maps with minimal metric distortion (ie: conservation of lengths in 3D when mapped to 2D), they exhibited twisted shapes and were not intuitive to interpret. Second, we proposed two novel approaches, combining mesh deformation algorithms, which are used in computer animation to reshape a 3D mesh to resemble a 3D plane, and projection onto a 2D plane. We found that while these methods required user interaction and introduced a greater amount of metric distortion, their outputs were fairly intuitive to interpret. To compare the relative merits of mesh parameterization and mesh deformation and projection, the different strategies are applied to a 8.2m wide by 41m long by 6.7m high subsection of a mining tunnel. The metric distortion produced was calculated and their respective output 2D maps are presented and discussed.

A superconvergence result of the natural convection equations

This paper presents a superconvergence result of the stationary natural convection equations. The superconvergence result is obtained by applying a coarse mesh projection for finite element approximation. This projection method is actually a postprocessing procedure that constructs a new approximation based on a high order polynomial on coarse mesh, under some regularity assumption. Finally, numerical experiment is presented for testing, which confirms the theoretic analysis. Copyright © 2015 John Wiley & Sons, Ltd.

Deformed Core Reactivity Evaluation with Mesh Projection–Based Method

Fast reactor designs are currently being revisited aiming at having a consolidated safety dossier. In that frame, studying any perturbation of nominal operating condition is mandatory.Among different initiators, particular attention is being paid to reactivity insertion due to core assembly bowing and deformation and induced lattice readjustments as a consequence of events such as earthquakes.In this study, a deterministic calculation scheme based on the mesh projection method has been used in order to evaluate the reactivity changes occurring in a deformed sodium fast reactor core.With the microscopic cross sections calculated by ECCO, full three-dimensional core calculations are being conducted with ERANOS (DIF3D), VARIANT, and SNATCH to solve neutron transport equations in either diffusion, nodal variational, or Sn transport approximations.A simple analytical model based on perturbation theory has been developed to identify the main phenomena leading to changes in the core reactivity. Reactivity changes induced by small deformations can be estimated as a summation of reactivity perturbations of individual subassemblies.The results obtained with this method have been checked by comparing them to those obtained with Monte Carlo simulations. A good agreement is being found allowing the use of this method in realistic problems with significant computer resource reduction.The different contributions to the reactivity changes confirm the results of the analytical model.

Breast volume measurement by mesh projection method based on 3D point cloud data

Purpose – The purpose of this paper is to explore a novel breast volume measuring method by mesh projection based on three-dimensional (3D) point cloud data. Design/methodology/approach – Mesh projection method, a rapid and accurate method to calculate the volume of models described by triangular meshes, was transplanted to calculate breast volume based on 3D point cloud data derived from a [TC]2 3D scanner. A simple landmarking procedure was developed to decide breast boundary. Breast volumes derived from mesh projection method were compared to the results of water displacement by statistical analysis to validate its accuracy. Findings – A novel breast volume measurement method is developed based on mesh projection method. By comparison of water displacement, mesh projection method is proved to be accurate to calculate breast volume. Furthermore, a simple and standard breast boundary landmarking procedure is established, which avoids the arbitrariness of the definition of breast boundary and improves the repetition of landmarking. Practical implications – A simple and convenient tool is provided for bra industries to rapidly and accurately measure breast volume. Originality/value – Mesh projection method is primarily applied to determine breast volume based on 3D point cloud data. Meanwhile, a simple and standard breast boundary landmarking procedure is put forward.

Surface Mesh Generation based on Imprinting of S-T Edge Patches

One of the most robust and widely used algorithms for all-hexahedral meshes is the sweeping algorithm. However, for multi- sweeping, the most difficult problems are the surface matching and interval assignment for edges on the source and target surfaces. In this paper, a new method to generate surface meshes by imprinting edge patches between the source and target surfaces is proposed. The edge patch imprinting is based on a cage-based morphing of edge patches on the different sweeping layers where deformed and undeformed cages are extracted by propagating edge patches on the linking surfaces. The imprinting results in that the source or target surfaces will be partitioned with the imprinted edge patches. After partitioning, every new source surface should be matched to a new specific target surface where surface mesh projection from one-to-one sweeping based on harmonic mapping[19] can be applied. In addition, 3D edge patches are projected onto 2D computational domains where every sweeping level is planar in order to increase the robustness of imprinting. Finally, the algorithm time complexity is discussed and examples are provided to verify the robustness of our proposed algorithm.

As-rigid-as-possible mesh deformation and its application in hexahedral mesh generation

This paper presents an efficient and stable as-rigid-as-possible mesh deformation algorithm for planar shape deformation and hexahedral mesh generation. The deformation algorithm aims to preserve two local geometric properties: scale-invariant intrinsic variables and elastic deformation energy, which are together represented in a quadric energy function. To preserve these properties, the position of each vertex is further adjusted by iteratively minimizing this quadric energy function to meet the position constraint of the controlling points. Experimental results show that the deformation algorithm is efficient, and can obtain physically plausible results, which have the same topology structure with the original mesh. Such a mesh deformation method is useful to project the source surface mesh onto the target surfaces in hexahedral mesh generation based on sweep method, and application results show that the proposed method is feasible to mesh projection not only between similar surface contours but also dissimilar surface contours.