Irregular Triangle Meshes Research Articles

Laplacian2Mesh: Laplacian-Based Mesh Understanding.

Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.

Numerical study of viscosity and heat flux role in heavy species dynamics in Hall thruster discharge

A two- and three-dimensional velocity space axisymmetric hybrid-PIC model of Hall thruster discharge called Hybrid2D has been developed. The particle-in-cell (PIC) method was used for neutrals and ions (heavy species), and fluid dynamics on a magnetic field-aligned (MFA) mesh was used for electrons. A time-saving method for heavy species moment interpolation on a MFA mesh was developed. The method comprises using regular rectangle and irregular triangle meshes, connected to each other on a pre-processing stage. The electron fluid model takes into account neither inertia terms nor viscous terms and includes an electron temperature equation with a heat flux term. The developed model was used to calculate all heavy species moments up to the third one in a stationary case. The analysis of the viscosity and the heat flux impact on the force and energy balance has shown that for the calculated geometry of the Hall thruster, the viscosity and the heat flux terms have the same magnitude as the other terms and could not be omitted. Also, it was shown that the heat flux is not proportional to the temperature gradient and, consequently, the highest moments should be calculated to close the neutral fluid equation system. At the same time, ions can only be modeled as a cold non-viscous fluid when the sole aim of modeling is the calculation of the operating parameters or distribution of the local parameters along the centerline of the discharge channel. This is because the magnitude of the viscosity and the temperature gradient terms are negligible at the centerline. However, when a simulation’s focus is either on the radial divergence of the plume or on magnetic pole erosion, three components of the ion temperature should be taken into consideration. The non-diagonal terms of ion pressure tensor have a lower impact than the diagonal terms. According to the study, a zero heat flux condition could be used to close the ion equation system in calculated geometry.

DALM, Deformable Attenuation-Labeled Mesh for Tomographic Reconstruction and Segmentation

Most X-ray tomographic reconstruction methods represent a solution as an image on a regular grid. Such representation may be inefficient for reconstructing homogeneous objects from noisy or incomplete projections. Here, we propose a mesh-based method for reconstruction and segmentation of homogeneous objects directly from sinogram data. The outcome of our proposed method consists of curves outlining the regions of constant attenuation, and this output is represented using a labeled irregular triangle mesh. We find the solution by deforming the mesh to minimize the residual given by the sinogram data. Our method supports multiple materials, and allows for topological changes during deformation. An integral part of our algorithm is an efficient forward projection of the labeled mesh onto the sinogram domain. We initialize our algorithm based on graph total variation, also here taking advantage of the mesh representation. Experimental results on simulated datasets show that our method gives a compact representation of the reconstruction and also accurate segmentation results for challenging data with e.g. large noise, a small number of angles or problems with limited angle. We also demonstrate the result on real fan-beam data. The proposed geometric solution shows a further step towards using alternative representations for tomographic reconstruction.

Crack simulation and probability analysis using irregular truss structure modeling equivalent to a continuum structure

The problems related to agricultural structure engineering for crack simulation and reliability analysis are complicated because its variables contain wide ranges of mean and standard deviation. This paper describes an integrated model to perform crack simulation and reliability analysis of a continuum structure. The structure is assumed to be under a two-dimensional plane stress and the deformation is infinitesimal. A truss structure model that has the same behaviour as a continuum structure was developed using irregular triangle truss components where each element consists of two hinges with an axial degree of freedom at both of their ends. A Monte-Carlo simulation (MCS) was adopted for the reliability analysis. If the length of one side of the irregular triangle mesh is shorter than the thickness of the structure, the slenderness associated with compressive failure needs to be examined only for the short column. For that reason, the failure criterion suitable for the equivalent truss structure model was established by checking only axial stresses acting on truss members. Since nodes of the equivalent truss structure model for the structural analysis in this study consist of hinges, development of plastic hinges that occurred during crack propagation were not considered in this model. To simulate the development of crack, truss members over allowable stresses of tension or compression among truss members with the largest amount of stress at each completed structural analysis time step were sequentially removed. Since irregular triangle meshes have an uncertainty in themselves to compare with regular meshes, the equivalent truss structure model could describe crack propagation more realistically. The failure probabilities of structures under various loads and boundary conditions had good agreement with the analytical solutions directly solved from the limit state equations expressed in the form of moments. Keywords: crack simulation, probability analysis, irregular truss structure model, failure criteria, Monte Carlo simulation DOI: 10.3965/j.ijabe.20171001.2024 Citation: Choi W, Yoon S, Lee J. Crack simulation and probability analysis using irregular truss structure modeling equivalent to a continuum structure. Int J Agric & Biol Eng, 2017; 10(1): 234–247.

An irregular triangle mesh buffer analysis method for boundary representation geological object in three-dimension

Three-dimensional (3D) buffer analysis is a basic function of spatial analysis used widely in 3D Geographic Information Systems (3DGIS). Current buffer analysis methods for spatial points and curves generally function well. One exception is buffer zone of surface. Previous researchers in this field have used voxel models to overcome this limitation; however, defects with voxel model buffer analysis include redundancies, approximations, and poor visualization characteristics. In this contribution, a surface buffer analysis method is presented for the boundary representation of geological objects. Exact geometric representation is achieved via the construction of irregular triangle meshes in 3D. The results can be used for 3D structural modeling and then form the basis for spatial analysis or model-based quantitative assessment in mineral potential mapping and resource evaluation. Three comparisons between existing voxel methods and our new method, evaluating visualization, precision and redundancy, are conducted. The comparisons show that our proposed method is robust and provides a higher quality output than voxel modeling. Finally, uncertainty analysis of buffer distance in different geological objects was discussed.

An improved buffer analysis technique for model-based 3D mineral potential mapping and its application

Buffer zones in bo\ h two-dimensional (2D) and three-dimensional (3D) spaces are commonly used in prospectivity mapping. The method completes a modelling that starts with a real example and progresses to the development of a virtual model. This includes the consideration of lithological or structural contacts at depth, which is a theoretical concept based on extrapolation of data collected in the field, rather than an empirical observation of the feature based on physical samples. This contribution documents an improved buffer analysis method for the study of 3D-space that is implicit (rapid), precise (smooth) and based on triangulated characteristics, which can be used to construct influence domains of geological models. As traditional 2D GIS-based mineral potential mapping is gradually becoming limited with time, mineral potential mapping in three dimensions (3D) is increasingly becoming an important tool in finding concealed economic mineralization. This contribution documents an improved methodology of buffer analysis for prospectivity mapping processing mineralized favourable models rather than describing an advance in the geometry of surface rendering of “geological complexity”. Measures used in this buffer analysis include the: (1) voxelization of geological objects (i.e. assigning numerical values of features on a regular cube in 3D-space); (2) revision of the 3D Euclidean distance transform and the calculation of signed distance field; (3) extracting surfaces from the field; and (4) construction of a buffer-surface based on a “discrete smooth interpolation” (DSI) algorithm. Furthermore, this contribution constructs 3D models using a buffer analysis algorithm and prospectivity mapping introduced here, which is based on real data from the Jiama Cu-polymetallic deposit in Tibet and Daye Fe deposit in the Hubei Province, China. This contribution also presents a comparison between voxel and irregular triangle models, which illustrate that irregular triangle mesh buffer analysis (ITB) can improve modelling techniques for GIS-based 3D mineral potential mapping. The outcome is an increase in the accuracy of prospectivity mapping.

From stereoscopic images to semi-regular meshes

The pipeline to get the semi-regular mesh of a specific physical object is long and fastidious: physical acquisition (creating a dense point cloud), cleaning/meshing (creating an irregular triangle mesh), and semi-regular remeshing. Moreover, these three stages are generally independent, and processed successively by different tools. To overcome this issue, we propose in this paper a new framework to design semi-regular meshes directly from stereoscopic images. Our semi-regular reconstruction technique first creates a base mesh by using a feature-preserving sampling on the stereoscopic images. Afterwards, this base mesh is passed to a coarse-to-fine meshing process to get the semi-regular mesh of the original surface. Experimental results prove the reliability and the accuracy of our approach in terms of shape fidelity, compactness, but also runtime, since many steps have been parallelized on the GPU.

Geodesic-based manifold learning for parameterization of triangular meshes

Reverse Engineering (RE) requires representing with free forms (NURBS, Spline, Bezier) a real surface $$S_0$$ which has been point-sampled. To serve this purpose, we have implemented an algorithm that minimizes the accumulated distance between the free form and the (noisy) point sample. We use a dual-distance calculation point to / from surfaces, which discourages the forming of outliers and artifacts. This algorithm seeks a minimum in a function $$f$$ that represents the fitting error, by using as tuning variable the control polyhedron for the free form. The topology (rows, columns) and geometry of the control polyhedron are determined by alternative geodesic-based dimensionality reduction methods: (a) graph-approximated geodesics (Isomap), or (b) PL orthogonal geodesic grids. We assume the existence of a triangular mesh of the point sample (a reasonable expectation in current RE). A bijective composition mapping $$S_0 \subset \mathbb {R}^3 \longleftrightarrow \mathbb {R}^2$$ allows to estimate a size of the control polyhedrons favorable to uniform-speed parameterizations. Our results show that orthogonal geodesic grids is a direct and intuitive parameterization method, which requires more exploration for irregular triangle meshes. Isomap gives a usable initial parameterization whenever the graph approximation of geodesics on $$S_0$$ be faithful. These initial guesses, in turn, produce efficient free form optimization processes with minimal errors. Future work is required in further exploiting the usual triangular mesh underlying the point sample for (a) enhancing the segmentation of the point set into faces, and (b) using a more accurate approximation of the geodesic distances within $$S_0$$ , which would benefit its dimensionality reduction.

Domain Preparation for RANSE Simulations about Hull and Appendage Assemblies

Viscous flow simulations are increasingly employed for simulation-driven design of functional surfaces. While parametric modeling of complex shapes has reached a certain maturity, the transfer of data from the Computer Aided Design (CAD) model to the Computational Fluid Dynamics (CFD) code is non-trivial unless the shapes are topologically simple. Assemblies of hull and appendages, however, usually require manual preparation. A method will be presented that allows setting up watertight compositions of arbitrary shapes. The method was implemented within the CAD-CFD integration platform FRIENDSHIP-Framework. Closed surfaces are subdivided into irregular triangle meshes (trimeshes) of predefined tolerance, i.e. deviation allowed between the original shape and its finite approximation. Solids can then be made from the trimeshes. Assemblies of hull and appendages can thus be realised supporting Boolean operations. An STL-file export is offered to connect to grid generators such as HEXPRESS and SnappyHexMesh. The method automatically copes with changes in shape by means of parametric modeling. The paper elaborates on the algorithms and presents examples.

Motion estimation and compensation in the redundant-wavelet domain using triangle meshes

In this paper, a technique is presented that incorporates an irregular triangle mesh into wavelet-domain motion estimation and compensation using a shift-invariant redundant-wavelet transform. The main contribution of this work resides in a demonstration that triangle-mesh motion estimation and compensation can be deployed more effectively in the redundant-wavelet domain thanks to a simple correlation operator that is robust to the prediction residual, a noise-like signal that hinders spatial-domain gradient-based efforts to locate image edges which persist from frame to frame. In the proposed technique, motion compensation takes place through an affine transform mapping triangles from one frame to the next, while the motion-compensated residual is downsampled to a non-redundant form which is then coded using any wavelet-based still-image coder. Experimental results indicate that the proposed technique significantly outperforms not only the usual spatial-domain approach to mesh-based motion estimation and compensation, but also the emerging wavelet-based coders that employ traditional block-based structures, particularly for sequences with fast or complex motion.

Dynamically refining animated triangle meshes for rendering

We present a method to dynamically apply local refinements to an irregular triangle mesh as it deforms in real time. The method increases surface smoothness in regions of high deformation by splitting triangles in a fashion similar to one or two steps of Loop subdivision. The refinement is computed for an arbitrary triangle mesh, and the subdivided triangles are simply passed to the rendering engine, leaving the mesh itself unchanged. The algorithm can thus be easily plugged into existing systems to enhance the visual appearance of animated meshes. The refinement step has very low computational overhead and is easy to implement. We demonstrate the use of the algorithm in a physics-based facial animation system.

Geometry images

Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)-regular connectivity, which has advantages for many graphics applications. However, current techniques for remeshing arbitrary surfaces create only semi-regular meshes. The original mesh is typically decomposed into a set of disk-like charts, onto which the geometry is parametrized and sampled. In this paper, we propose to remesh an arbitrary surface onto a completely regular structure we call a geometry image. It captures geometry as a simple 2D array of quantized points. Surface signals like normals and colors are stored in similar 2D arrays using the same implicit surface parametrization --- texture coordinates are absent. To create a geometry image, we cut an arbitrary mesh along a network of edge paths, and parametrize the resulting single chart onto a square. Geometry images can be encoded using traditional image compression algorithms, such as wavelet-based coders.