Source Mesh Research Articles

The Effect of Manufacturing Variations on Unsteady Interaction in a Transonic Turbine

This effort focuses on the comparison of unsteadiness due to as-measured turbine blades in a transonic turbine to that obtained with blueprint geometries via computational fluid dynamics (CFD). A Reynolds-averaged Navier–Stokes flow solver with the two-equation Wilcox turbulence model is used as the numerical analysis tool for comparison between the blueprint geometries and as-manufactured geometries obtained from a structured light optical measurement system. The nominal turbine CFD grid data defined for analysis of the blueprint blade were geometrically modified to reflect as-manufactured turbine blades using an established mesh metamorphosis algorithm. The approach uses a modified neural network to iteratively update the source mesh to the target mesh. In this case, the source is the interior CFD surface grid while the target is the surface blade geometry obtained from the optical scanner. Nodes interior to the CFD surface were updated using a modified iterative spring analogy to avoid grid corruption when matching as-manufactured part geometry. This approach avoids the tedious manual approach of regenerating the CFD grid and does not rely on geometry obtained from coordinate measurement machine (CMM) sections, but rather a point cloud representing the entirety of the turbine blade. Surface pressure traces and the discrete Fourier transforms (DFT) thereof from numerical predictions of as-measured geometries are then compared both to blueprint predictions and to experimental measurements. The importance of incorporating as-measured geometries in analyses to explain deviations between numerical predictions of blueprint geometries and experimental results is readily apparent. Further analysis of every casting produced in the creation of the test turbine yields variations that one can expect in both aero-performance and unsteady loading as a consequence of manufacturing tolerances. Finally, the use of measured airfoil geometries to reduce the unsteady load on a target blade in a region of interest is successfully demonstrated.

Learning Detail Transfer based on Geometric Features

The visual richness of computer graphics applications is frequently limited by the difficulty of obtaining high-quality, detailed 3D models. This paper proposes a method for realistically transferring details specifically, displacement maps from existing high-quality 3D models to simple shapes that may be created with easy-to-learn modeling tools. Our key insight is to use metric learning to find a combination of geometric features that successfully predicts detail-map similarities on the source mesh; we use the learned feature combination to drive the detail transfer. The latter uses a variant of multi-resolution non-parametric texture synthesis, augmented by a high-frequency detail transfer step in texture space. We demonstrate that our technique can successfully transfer details among a variety of shapes including furniture and clothing.

Conservative interpolation between general spherical meshes

Abstract. An efficient, local, explicit, second-order, conservative interpolation algorithm between spherical meshes is presented. The cells composing the source and target meshes may be either spherical polygons or latitude–longitude quadrilaterals. Second-order accuracy is obtained by piece-wise linear finite-volume reconstruction over the source mesh. Global conservation is achieved through the introduction of a supermesh, whose cells are all possible intersections of source and target cells. Areas and intersections are computed exactly to yield a geometrically exact method. The main efficiency bottleneck caused by the construction of the supermesh is overcome by adopting tree-based data structures and algorithms, from which the mesh connectivity can also be deduced efficiently.The theoretical second-order accuracy is verified using a smooth test function and pairs of meshes commonly used for atmospheric modelling. Experiments confirm that the most expensive operations, especially the supermesh construction, have O(NlogN) computational cost. The method presented is meant to be incorporated in pre- or post-processing atmospheric modelling pipelines, or directly into models for flexible input/output. It could also serve as a basis for conservative coupling between model components, e.g., atmosphere and ocean.

Spatial Matching of Animated Meshes

AbstractThis paper presents a new technique which makes use of deformation and motion properties between animated meshes for finding their spatial correspondences. Given a pair of animated meshes exhibiting a semantically similar motion, we compute a sparse set of feature points on each mesh and compute spatial correspondences among them so that points with similar motion behavior are put in correspondence. At the core of our technique is our new, dynamic feature descriptor named AnimHOG, which encodes local deformation characteristics. AnimHOG is ob‐tained by computing the gradient of a scalar field inside the spatiotemporal neighborhood of a point of interest, where the scalar values are obtained from the deformation characteristic associated with each vertex and at each frame. The final matching has been formulated as a discreet optimization problem that finds the matching of each feature point on the source mesh so that the descriptor similarity between the corresponding feature pairs as well as compatibility and consistency as measured across the pairs of correspondences are maximized. Consequently, reliable correspondences can be found even among the meshes of very different shape, as long as their motions are similar. We demonstrate the performance of our technique by showing the good quality of matching results we obtained on a number of animated mesh pairs.

On mesh restrictions to satisfy comparison principles, maximum principles, and the non-negative constraint: Recent developments and new results

ABSTRACTThis article concerns mesh restrictions that are needed to satisfy several important mathematical properties—maximum principles, comparison principles, and the nonnegative constraint—for a general linear second-order elliptic partial differential equation. We critically review some recent developments in the field of discrete maximum principles, derive new results, and discuss some possible future research directions in this area. In particular, we derive restrictions for a three-node triangular (T3) element and a four-node quadrilateral (Q4) element to satisfy comparison principles, maximum principles, and the nonnegative constraint under the standard single-field Galerkin formulation. Analysis is restricted to uniformly elliptic linear differential operators in divergence form with Dirichlet boundary conditions specified on the entire boundary of the domain. Various versions of maximum principles and comparison principles are discussed in both continuous and discrete settings. In the literature, it is well-known that an acute-angled triangle is sufficient to satisfy the discrete weak maximum principle for pure isotropic diffusion. Herein, we show that this condition can be either too restrictive or not sufficient to satisfy various discrete principles when one considers anisotropic diffusivity, advection velocity field, or linear reaction coefficient. Subsequently, we derive appropriate restrictions on the mesh for simplicial (e.g., T3 element) and nonsimplicial (e.g., Q4 element) elements. Based on these conditions, an iterative algorithm is developed to construct simplicial meshes that preserve discrete maximum principles using existing open source mesh generators. Various numerical examples based on different types of triangulations are presented to show the pros and cons of placing restrictions on a computational mesh. We also quantify local and global mass conservation errors using representative numerical examples and illustrate the performance of metric.

Automatic deformable surface registration for medical applications by radial basis function-based robust point-matching

Deformable surface mesh registration is a useful technique for various medical applications, such as intra-operative treatment guidance and intra- or inter-patient study. In this paper, we propose an automatic deformable mesh registration technique. The proposed method iteratively deforms a source mesh to a target mesh without manual feature extraction. Each iteration of the registration consists of two steps, automatic correspondence finding using robust point-matching (RPM) and local deformation using a radial basis function (RBF). The proposed RBF-based RPM algorithm solves the interlocking problems of correspondence and deformation using a deterministic annealing framework with fuzzy correspondence and RBF interpolation. Simulation tests showed promising results, with the average deviations decreasing by factors of 21.2 and 11.9, respectively. In the human model test, the average deviation decreased from 1.72±1.88mm to 0.57±0.66mm. We demonstrate the effectiveness of the proposed method by presenting some medical applications.

Optimization-based mesh correction with volume and convexity constraints

We consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.

Finding complete 3D vertex correspondence for statistical shape modeling.

A statistical shape model that accurately generalizes a family of 3D shapes requires establishing correspondences across the set of shapes. However in 3D anatomical meshes, finding a sufficient number of landmarks to accurately describe the shape can be a challenge, and often only a few points are easily identifiable due to the smooth nature of the object surface. Using a sparse set of landmarks, this paper finds a dense set of vertex correspondences across a set of 3D aortic root meshes. This is achieved by non-rigidly transforming a source mesh to a target mesh. Then, for every vertex on the target, a corresponding vertex on the deformed source is found, resulting in complete correspondence. A more accurate transformation results in better correspondence establishment, and our mesh registration experiments show an average Hausdorff distance of 3.65mm, and an average point-to-mesh distance of 0.41mm, i. e. within one voxel.

An in-core grid index for transferring finite element data across dissimilar meshes

The simulation of a manufacturing process chain with the finite element method requires the selection of an appropriate finite element solver, element type and mesh density for each process of the chain. When the simulation results of one step are needed in a subsequent one, they have to be interpolated and transferred to another model. This paper presents an in-core grid index that can be created on a mesh represented by a list of nodes/elements. Finite element data can thus be transferred across different models in a process chain by mapping nodes or elements in indexed meshes. For each nodal or integration point of the target mesh, the index on the source mesh is searched for a specific node or element satisfying certain conditions, based on the mapping method. The underlying space of an indexed mesh is decomposed into a grid of variable-sized cells. The index allows local searches to be performed in a small subset of the cells, instead of linear searches in the entire mesh which are computationally expensive. This work focuses on the implementation and computational efficiency of indexing, searching and mapping. An experimental evaluation on medium-sized meshes suggests that the combination of index creation and mapping using the index is much faster than mapping through sequential searches.

A Script-Based, Parameterized Finite Element Mesh for Design and NDE on a GPU

ABSTRACTFinite element mesh generators exist in the public domain, a few even based on a parametric device description. The typical mesh generator requires some man–machine interaction to define the points and boundary conditions, and does not work for non-stop optimization iterations for which we need a mesh dynamically evolving through the iterations with optimization variables as changing parameters. Such mesh generators as do exist are rare, commercial, and not easily available to researchers except at great cost and never with the code to modify them to suit individual needs. We take a regular open source mesh generator and write a script-based interface as open source to run non-stop for optimization. We then use it to create a non-destructive evaluation system for army ground vehicles’ defect characterization and use it equally for machine design. A simple scheme of averaging neighbour heights gives us a smooth geometry without having to use Bezier curves. The mesh runs on the central processing unit but finite element optimization is on the graphics processing unit for speed and practicable testing times.

Impact of mesh partitioning methods in CFD for large scale parallel computing

It was well known that high performance computing depends on load balance and mesh cell distributions. A well balanced load can improve efficiency of parallel computing and minimizing the number of cells with remote neighbors can reduce the time spent on the data communication among processors. Mesh partitioning methods were able to optimize the mesh cell distributions for large scale parallel computing. In this paper, the open source mesh partitioning software packages, such as Metis, ParMetis, Scotch, PT-Scotch and Zoltan, were ported into Code_Saturne, which is an open source CFD software package, for realizing the optimization on large scale CFD applications. Through the studies, it was found that the mesh partitioning methods strongly affect the CFD code on high performance computing especially for large scale parallel computing.

A Skeleton-Based Approach for Consistent Segmentation Transfer

We present a skeleton-based approach for mapping consistently a segmentation of a source mesh to a target mesh. The source and target meshes are semantically similar but their geometries may be different. We assume that the segmentation of the source mesh and the skeleton correspondence between the meshes are provided. Our method first establishes the skeleton-boundary correspondence and then performs the boundary transfer procedure. The skeleton-boundary correspondence is useful for computing approximately the target boundaries. The boundary transfer procedure aims to produce the segment boundaries of the target mesh such that their geometric details are consistent to the ones of the corresponding source segment boundaries. We have applied our method for various models and compared with the state-of-the-art techniques. Our method computes segment boundaries of the target mesh which are similar to the ones of the source mesh.

Mesh Infrastructure for Coupled Multiprocess Geophysical Simulations

We have developed a sophisticated mesh infrastructure capability to support large scale multiphysics simulations such as subsurface flow and reactive contaminant transport at storage sites as well as the analysis of the effects of a warming climate on the terrestrial arctic. These simulations involve a wide range of coupled processes including overland flow, subsurface flow, freezing and thawing of ice rich soil, accumulation, redistribution and melting of snow, biogeochemical processes involving plant matter and finally, microtopography evolution due to melting and degradation of ice wedges below the surface. In addition to supporting the usual topological and geometric queries about the mesh, the mesh infrastructure adds capabilities such as identifying columnar structures in the mesh, enabling deforming of the mesh subject to constraints and enabling the simultaneous use of meshes of different dimensionality for subsurface and surface processes. The generic mesh interface is capable of using three different open source mesh frameworks (MSTK, MOAB and STKmesh) under the hood allowing the developers to directly compare them and choose one that is best suited for the application's needs. We demonstrate the results of some simulations using these capabilities as well as present a comparison of the performance of the different mesh frameworks.

Model Merging Through Mean Value Coordinates

Merging a model to another model, including the mesh and its texture, is a useful technology for generating new models. This paper introduces a novel method to merge models through Mean Value Coordinates (MVC). The method firstly computes the MVC of the vertices of a source mesh with respect to its merging boundary. As the target mesh is specified, the differences between the two meshes’ boundaries are computed. The source mesh is transformed fluently according to the differences through MVC, and then construct a new mesh with the target. With the same framework, smoothing the seaming line can be achieved by interpolating tangent vector variations. And a new texture is similarly constituted by interpolating the color differences on the boundaries to make a consistent model. This method avoids the mesh parameterizations or the solving a large linear system, but merges through computing closeform expressions. Experiments show that model merging with this method is less artifacts and faster than some other methods.

Landmark transfer with minimal graph

We present an efficient and robust algorithm for the landmark transfer on 3D meshes that are approximately isometric. Given one or more custom landmarks placed by the user on a source mesh, our method efficiently computes corresponding landmarks on a family of target meshes. The technique is useful when a user is interested in characterization and reuse of application-specific landmarks on meshes of similar shape (for example, meshes coming from the same class of objects). Consequently, across a set of multiple meshes consistency is assured among landmarks, regardless of landmark geometric distinctiveness. The main advantage of our method over existing approaches is its low computation time. Differently from existing non-rigid registration techniques, our method detects and uses a minimum number of geometric features that are necessary to accurately locate the user-defined landmarks and avoids performing unnecessary full registration. In addition, unlike previous techniques that assume strict consistency with respect to geodesic distances, we adopt histograms of geodesic distance to define feature point coordinates, in order to handle the deviation of isometric deformation. This allows us to accurately locate the landmarks with only a small number of feature points in proximity, from which we build what we call a minimal graph. We demonstrate and evaluate the quality of transfer by our algorithm on a number of Tosca data sets.

A 3D Facial Expression Tracking Method Using Piecewise Deformations

We present a new fast method for 3D facial expression tracking based on piecewise non-rigid deformations. Our method takes as input a video-rate sequence of face meshes that record the shape and time- varying expressions of a human face, and deforms a source mesh to match each input mesh to output a new mesh sequence with the same connectivity that reflects the facial shape and expressional variations. In mesh matching, we automatically segment the source mesh and estimate a non-rigid transformation for each segment to approximate the input mesh closely. Piecewise non-rigid transformation significantly reduces computational complexity and improves tracking speed because it greatly decreases the unknowns to be estimated. Our method can also achieve desired tracking accuracy because segmentation can be adjusted automatically and flexibly to approximate arbitrary deformations on the input mesh. Experiments demonstrate the efficiency of our method.

Large-Scale CFD Parallel Computing Dealing with Massive Mesh

In order to run CFD codes more efficiently on large scales, the parallel computing has to be employed. For example, in industrial scales, it usually uses tens of thousands of mesh cells to capture the details of complex geometries. How to distribute these mesh cells among the multiprocessors for obtaining a good parallel computing performance (HPC) is really a challenge. Due to dealing with the massive mesh cells, it is difficult for the CFD codes without parallel optimizations to handle this kind of large-scale computing. Some of the open source mesh partitioning software packages, such as Metis, ParMetis, Scotch, PT-Scotch, and Zoltan, are able to deal with the distribution of large number of mesh cells. Therefore they were employed as the parallel optimization tools ported into Code_Saturne, an open source CFD code, for testing if they can solve the issue of dealing with massive mesh cells for CFD codes. Through the studies, it was found that the mesh partitioning optimization software packages can help CFD codes not only deal with massive mesh cells but also have a good HPC.

PROCESSING A COMPLEX ARCHITECTURAL SAMPLING WITH MESHLAB: THE CASE OF PIAZZA DELLA SIGNORIA

Abstract. The paper presents a recent 3D scanning project performed with long range scanning technology showing how a complex sampled dataset can be processed with the features available in MeshLab, an open source tool. MeshLab is an open source mesh processing system. It is a portable and extensible system aimed to help the processing of the typical not-so-small unstructured models that arise in 3D scanning, providing a set of tools for editing, cleaning, processing, inspecting, rendering and converting meshes. The MeshLab system started in late 2005 as a part of a university course, and considerably evolved since then thanks to the effort of the Visual Computing Lab and of the support of several funded EC projects. MeshLab gained so far an excellent visibility and distribution, with several thousands downloads every month, and a continuous evolution. The aim of this scanning campaign was to sample the façades of the buildings located in Piazza della Signoria (Florence, Italy). This digital 3D model was required, in the framework of a Regional Project, as a basic background model to present a complex set of images using a virtual navigation metaphor (following the PhotoSynth approach). Processing of complex dataset, such as the ones produced by long range scanners, often requires specialized, difficult to use and costly software packages. We show in the paper how it is possible to process this kind of data inside an open source tool, thanks to the many new features recently introduced in MeshLab for the management of large sets of sampled point.

Archeological excavation monitoring using dense stereo matching techniques

Abstract Several new tools to obtain three-dimensional information from unorganized image sets are now available for the public use. The main advantage of this software, which is based on dense stereo matching, is the possibility to generate 3D content without the need of high-cost hardware (e.g. 3D scanning devices). Nevertheless, their use in real-world application domains (like cultural heritage) is still not very diffused, due to the non-straightforward usability of the raw data produced. In this paper, we investigate the use of automatic dense stereo reconstruction tools for the monitoring of an excavation site. A methodology for the effective acquisition and processing of data is presented. In addition, the results of the data assessment demonstrate the repeatability of the data acquisition process, which is a key factor when qualitative analysis is performed. The use of three-dimensional data is integrated in an open source mesh processing tool, thus showing that a spatio-temporal analysis can be performed in a very intuitive way using off-the-shelf or free/open digital tools. Moreover, the use of peculiar rendering and the creation of snapshots from arbitrary points of view increase the amount of documentation data, and suggest a perfect integration of data produced with dense stereo matching in the future standard documentation for excavation monitoring.

Evaluation of mesh morphing and mapping techniques in patient specific modeling of the human pelvis

Robust generation of pelvic finite element models is necessary to understand the variation in mechanical behaviour resulting from differences in gender, aging, disease and injury. The objective of this study was to apply and evaluate mesh morphing and mapping techniques to facilitate the creation and structural analysis of specimen-specific finite element (FE) models of the pelvis. A specimen-specific pelvic FE model (source mesh) was generated following a traditional user-intensive meshing scheme. The source mesh was morphed onto a computed tomography scan generated target surface of a second pelvis using a landmarked-based approach, in which exterior source nodes were shifted to target surface vertices, while constrained along a normal. A second copy of the morphed model was further refined through mesh mapping, in which surface nodes of the initial morphed model were selected in patches and remapped onto the surfaces of the target model. Computed tomography intensity based material properties were assigned to each model. The source, target, morphed and mapped models were analyzed under axial compression using linear static FE analysis and their strain distributions evaluated. Morphing and mapping techniques were effectively applied to generate good quality geometrically complex specimen-specific pelvic FE models. Mapping significantly improved strain concurrence with the target pelvis FE model.