3D Triangular Mesh Research Articles

Visual simulation of weathering coated metallic objects

Weathering, referring to techniques for depicting outdoor objects as having suffered rain and wind damage, has a long history of research, and many methods can be found in the literature. Metal is a representative target of weathering, as metallic surface corrosion is a widespread deterioration phenomenon in our daily life. However, few weathering methods consider the effects of rust-preventive paint, while real metal is usually treated with a preservative. This paper presents a novel procedural method for weathering coated metal objects. In our method, a coated surface is imposed on a 3D triangular mesh. We enable the mechanical deterioration of coating film, and we deform the mesh model to express cracking and peeling. As further defacing elements on the coating film, runoff rust and darkening are reproduced by changing the color and reflectance of the surface. Besides, by locally adjusting the control parameters of the designated areas on the surface, the process of deterioration can be arbitrarily directed. Several visual simulation results are shown to prove empirically the faithfulness of the proposed methods.

Automatic triangular and triangular-prism mesh generation for overland and subsurface water flow simulations

In this paper, an automatic mesh generator is developed to simulate density-dependent water flow and transport problems in watershed systems. The two-dimensional (2D) triangular mesh is generated by global Delaunay triangulation, and the three-dimensional (3D) triangular-prism mesh is generated by vertical stretch. The implementation procedures of mesh generation are adjusted according to the interaction options of one-dimensional (1D) river, 2D overland, and 3D subsurface flows. An improved boundary point generation algorithm is proposed to maintain appropriate correspondence of points and edges according to the discrete patterns of river reaches and dead ends. Overlapped nodes are generated on zero-width river reaches and zero-width junctions without storage to construct the numerical models for 2D overland simulations. An additional triangular mesh generation method is proposed to create additional triangles for filling the empty water zones of finite-width river reaches, junctions with storage, finite-width ponds, lakes, and dead ends. The boundary loops bounding each water area are identified correctly, and the additional grids are created compatibly, aiming at the finite-depth and zero-depth patterns of storage zones. The computation equations of relevant parameters used for 3D stretch from triangles to triangular-prisms are built, and the 1D/2D/3D correspondence on river reaches, junctions, ponds, lakes, dead ends, and control structures is established. Finally, practical examples for discretizing real-world water areas are provided to demonstrate the robustness and effectiveness of our developed mesh generator by using the skewness as the mesh quality metric.

Pixel2Mesh: 3D Mesh Model Generation via Image Guided Deformation.

In this paper, we propose an end-to-end deep learning architecture that generates 3D triangular meshes from single color images. Restricted by the nature of prevalent deep learning techniques, the majority of previous works represent 3D shapes in volumes or point clouds. However, it is non-trivial to convert these representations to compact and ready-to-use mesh models. Unlike the existing methods, our network represents 3D shapes in meshes, which are essentially graphs and well suited for graph-based convolutional neural networks. Leveraging perceptual features extracted from an input image, our network produces the correct geometry by progressively deforming an ellipsoid. To make the whole deformation procedure stable, we adopt a coarse-to-fine strategy, and define various mesh/surface related losses to capture properties of various aspects, which benefits producing the visually appealing and physically accurate 3D geometry. In addition, our model by nature can be adapted to objects in specific domains, e.g., human faces, and be easily extended to learn per-vertex properties, e.g., color. Extensive experiments show that our method not only qualitatively produces the mesh model with better details, but also achieves the higher 3D shape estimation accuracy compared against the state-of-the-arts.

Watershed segmentation of topographical features on freeform surfaces and its application to additively manufactured surfaces

With the advancement of modern enabling technologies, surfaces of high value-added products are changing from traditional simple geometries to complex geometries that feature freeform shapes. The analysis of topographical features on freeform surfaces is challenging because surface shapes are no longer planar and measurement data often require surface description in the form of triangular meshes. An approach is proposed to extend the watershed segmentation from planar surfaces to freeform surfaces. Surface topography is first extracted from measured surfaces (mesh surfaces) using proper mathematical operations, e.g. fitting and filtration. The watershed segmentation based on Maxwell's theory is extended to 3D triangular meshes and applied to the extracted surface topography defined as a scalar function associated with the vertices of the mesh surface. Critical surface points such as peaks, pits and saddles are identified to construct a Pfaltz graph. Ridge lines and course lines are then traced starting from saddles and following the steepest uphill and downhill paths to peaks and pits, respectively. Wolf pruning of the change tree is employed to merge over-segmented regions. The extended watershed segmentation method is applied to segment surface topography of the additively processed scaffold and lattice surfaces.

Panoramic Image Generation Using Centerline- Constrained Mesh Parameterization for Arbitrarily Shaped Tunnel Lining

Three-dimensional (3D) triangular meshes has been widely used in tunnel engineering. This paper proposes an algorithm for unwrapping 3D tunnel lining meshes into straight two-dimensional (2D) meshes to generate a 2D seamless panoramic image of the tunnel lining. The proposed algorithm is divided into three steps. In the first step, the centerline is extracted and the L1-median is used to represent the centerline of the tunnel; in the second step, a centerline constraint, which is linear to ensure that the equations to be solved are also linear, is added to least squares conformal mapping (LSCM) to unwrap the tunnel mesh; and in the third step, a panoramic image of the tunnel lining is obtained through texture projection or image correction. Adding a centerline constraint allows the panoramic image to retain mileage information and global shape. The strict geometric relationship between the 3D mesh and panorama guarantees the panorama's accuracy and realizes the two-way mapping of 2D and 3D data analyses. Moreover, a projection strategy is proposed to efficiently process the multiple tiles and non-manifold tunnel meshes which cannot be unwrapped directly using mesh parameterization algorithms. The experimental results show that centerline-constrained LSCM (CLSCM), which is suitable for any arbitrarily shaped tunnel lining, can preserve the global shape and local details better than the conventional method and can be extended to unwrap any strip-shaped structured meshes.

Simulated Annealing to Unfold 3D Meshes and Assign Glue Tabs

3D mesh unfolding transforms a 3D mesh model into one or multiple 2D planar patches. The technique is widely used to fabricate papercrafts, where 3D objects can be reconstructed from printed paper or paper-like materials. The applicability, visual quality, and stability of such papercraft productions is still challenging since it requires a reasonable formulation of these factors. In this paper, we unfold a 3D mesh into a single connected 2D patch. We also introduce glue tabs as additional indicators in order to provide users with extra space to apply glue for better reconstruction quality. To improve space efficiency, we do not apply glue tabs on every edge, while still guaranteeing the stability of the constructed paper model. A minimum spanning tree (MST) describes possible unfoldings, whereas simulated annealing optimisation is used to find an optimal unfolding. Our approach allows us to unfold 3D triangular meshes into single 2D patches without shape distortions, and employing only a small number of glue tabs. A visual indicator scheme is also incorporated as a post-process to guide users during the model reconstruction process. Finally, we qualitatively evaluate the applicability of the presented approach in comparison to the conventional technique and the achieved results.

Mesh Simplification With Appearance-Driven Optimizations

In this work, we propose a novel solution for simplifying texture-mapped three-dimensional (3D) meshes. It simplifies a 3D triangular mesh to optimally preserve the visual appearance of the original texture-mapped model at reduced vertex budgets. While taking the prevalent strategy of iterative edge contraction, the proposed scheme is novel in that it takes into account the local texture image characteristics when prioritizing local mesh simplification operators, and conducts closed-form optimization when computing the texture coordinates of each replacement vertex. Outstanding performance of the proposed scheme is demonstrated both qualitatively and quantitatively by experimental results. Further, validity of the proposed algorithmic components is well proved through ablation study.

A Novel Subdomain 2D/Q-2D Finite Element Method for Power/Ground Plate-Pair Analysis

Upon excitation by a surface magnetic current, a power/ground plate-pair supports only $\mathrm{TM}^{z}$ modes. This means that the magnetic field has only azimuthal components permitting a simple but effective domain decomposition method (DDM) to be used. In the proximity of an antipad, field interactions are rigorously modeled by a quasi-two-dimensional (Q-2D) finite element method (FEM) making use of three-dimensional (3D) triangular prism mesh elements. Since high-order $\mathrm{TM}^{z}$ modes are confined in the close proximity of the antipad, field interactions in the region away from the antipad only involve the fundamental mode and are rigorously modeled by a 2D FEM. This approach reduces 3D computation domain into a hybrid 2D/Q-2D domain. The discretization of this hybrid domain results in a global matrix system consisting of two globally coupled matrix equations pertinent to 2D and Q-2D domains. In this article, these two matrix equations are “decoupled” using a Riemann solver and the information exchange between the two domains is facilitated using numerical flux. The resulting decoupled two matrix equations are iteratively solved using the Gauss–Seidel algorithm. The accuracy, efficiency, and robustness of the proposed DDM are verified by four representative examples.

Improved Simultaneous Mesh Untangling and Quality Improvement Methods of 2D Triangular Meshes

Few inverted or poor quality elements can ruin both the accuracy and efficiency of numerical solutions. This paper proposes improved mesh untangling and quality improvement methods using the modified mesh quality metric for 2D triangular meshes. The new mesh quality metric ensures highly inverted elements assign higher penalty when the signed area of the element is negative, and also produces more accurate signed areas for valid elements. Therefore, the proposed methods can quickly remove inverted elements and also improve worst element qualities compared with the existing methods. We also combine Delaunay-based edge flip with optimization-based mesh untangling and quality improvement methods to further improve worst element qualities. Numerical results show that the proposed methods yield better quality meshes for improvement of the worst quality and are faster than existing methods.

A New Mesh Moving Technique for a Fluid–Structure Interaction Problem Using Mesh Deformation Energy Minimization

When mesh boundaries move in a simulation because of the motion of a target object such as translation, rotation, and oscillation, the mesh should be regenerated to the points it will obey the locations of its new boundaries. Because recreating new mesh from the beginning is a time-consuming task, new mesh is usually created by deforming an initial mesh, which is called the mesh moving method (or mesh deformation method). In this paper, we present a new mesh moving method that produces a higher quality deformed mesh than the current mesh moving methods. In the proposed method, the deformation of mesh is evaluated by two energy quantities that are related to (i) the distortion of mesh that is invariant to translation, rotation, and size changes of the elements of the mesh and (ii) the deformation of mesh calculated using elements’ size based on stiffened-linear elasticity equations. The total deformation energy of mesh is defined as a weighted sum of these two quantities. Because there is no need to pre-fix the locations of the outer boundary points for most mesh moving problems, we use new constraints, allowing the outer boundary points to move along tangential directions in the proposed method. The deformed mesh is computed by calculating the positions of the mesh points where the total deformation energy of the mesh is minimized. For test purposes, the proposed method is applied to 2D triangular meshes and a 3D tetrahedral mesh, where the meshes are deformed by the motions of the target objects such as translation, rotation, and deformation. When the quality of the deformed meshes computed with the proposed method are compared with the ones computed with current mesh moving methods, the meshes from the proposed method are shown to be better than the other meshes.

Surface texture evaluation of additively manufactured metallic cellular scaffolds for acetabular implants using X-ray computed tomography

The surface topography of acetabular implants plays a key role in providing cell attachment and proliferation. The measurement and characterisation of the surface texture of the cellular scaffold layer on the acetabular cup are very difficult due to the 3D nature of scaffold geometry. It is proposed to use X-ray computed tomography (XCT) to measure the surface texture of an electron beam melting-produced titanium acetabular cup. The surface texture of its cellular scaffold is evaluated using the newly developed 3D surface texture parameters, which allows surface characterisation on 3D triangular mesh surfaces. Four commonly used height parameters, i.e. the arithmetical mean height Sa, the root mean square height Sq, the skewness Ssk and the kurtosis Sku, are calculated from surface patches extracted from the XCT scanned triangular mesh surface. In addition, the surface peak density and pit density, which are more related to cell communication and proliferation, are estimated based on the 3D watershed segmentation. The Wolf pruning with an empirical threshold 12 µm is used to control the over-segmentation.

Progressive sketching with instant previewing

Sketch-based modeling uses freeform strokes as basic modeling metaphor and the modeling process typically involves two phases: sketching and sculpting. This paper presents a method to enhance the sketching phase to have the features of both sketching and sculpting. The key idea of the method is progressive sketching with instant previewing, which has the capacity of intuitively creating complex initial shapes that interpolate all the sketched strokes. The process lets the user iteratively sketch and meanwhile updates the reconstructed 3D shape instantly, which enables the user to be aware of the up-to-date shape. The underlying technique supporting this process is a novel surface construction algorithm that produces 3D triangular mesh models typically with only a single connected component and gradual shape changes during iterative sketching as well. To demonstrate the capability of the method, a sketching-based modeling prototype is also developed, which includes both sketching and sculpting functions. Experiments show that the proposed method can allow users to intuitively and flexibly create and edit 3D models even with complex topology, which is usually difficult for conventional sketch-based modeling systems.

Generalized prism grid: a pillar-based unstructured grid for simulation of reservoirs with complicated geological geometries

Grid generation is critical to numerical reservoir simulations. High-quality grids guarantee the fidelity of a reservoir model and keep the flow calculations simple. In this study, we propose a 3D unstructured grid, the generalized prism grid (GPG), to model reservoirs with complicated geological geometries, including horizons, pinch-outs, faults, fractures, and bore holes. GPG is a layered, pillar-based grid. The location of a face node is specified by its elevation, and the pillar to which it is attached. Compared with the hexahedral corner point grid (CPG), GPG is a polygon prism and therefore more flexible; whereas, compared with the 2.5D perpendicular bisection (PEBI) grid, GPG allows polygons morphing through the stratum. We built a gridding algorithm to fulfil the features of GPG. The algorithm first constructs a 2D triangular mesh for one layer by setting up control points and grid densities for geological objects, such as fractures, faults, and wells, distributing triangular grid points with the “advancing front method,” and performing Delaunay optimization to the points. The polygon mesh is the dual grid of the triangular mesh. Taking the polygon mesh as a reference, the mesh for each layer of the strata is a morphing of it, with edges being stretched and points being assigned with heights. We also designed a compact file format to store GPG data and implemented the flux calculation method for GPG in a reservoir simulator. The attractive features of GPG are demonstrated through four examples. The conciseness and flexibility of GPG make it a potential new standard grid format replacing CPG.

A new mesh visual quality metric using saliency weighting-based pooling strategy

Several metrics have been proposed to assess the visual quality of 3D triangular meshes during the last decade. In this paper, we propose a mesh visual quality metric by integrating mesh saliency into mesh visual quality assessment. We use the Tensor-based Perceptual Distance Measure metric to estimate the local distortions for the mesh, and pool local distortions into a quality score using a saliency weighting-based pooling strategy. Three well-known mesh saliency detection methods are used to demonstrate the superiority and effectiveness of our metric. Experimental results show that our metric with any of three saliency maps performs better than state-of-the-art metrics on the LIRIS/EPFL general-purpose database. We generate a synthetic saliency map by assembling salient regions from individual saliency maps. Experimental results reveal that the synthetic saliency map achieves better performance than individual saliency maps, and the performance gain is closely correlated with the similarity between the individual saliency maps.

A dynamic neural network model for accelerating preliminary parameterization of 3D triangular mesh surfaces

This study proposes an effective and fast preliminary mapping algorithm for 3D triangular mesh surfaces. The proposed method exploits barycentric mapping theory and dynamic neural network for computing parametric coordinates corresponding to vertices of 3D triangular mesh. The dynamic network model iteratively moves internal nodes in 2D parametric space until they convergently reach an equilibrium state. The method effectively computes parametric space coordinates of large meshes (having more than 1.5 K vertices) in less time compared to the traditional method using inverse matrix calculation. The proposed method is tested on many surfaces of varying size, and experimental results prove its efficiency and efficacy.

Technical Note: Solving the "Chinese postman problem" for effective contour deformation.

To develop a practical approach for accurate contour deformation when deformable image registration (DIR) is used for atlas-based segmentation or contour propagation in image-guided radiotherapy. We developed a contour deformation approach based on 3D mesh operations. The 2D contours represented by a series of points in each slice were first converted to a 3D triangular mesh, which was deformed by the deformation vectors resulting from DIR. A set of parallel 2D planes then cut through the deformed 3D mesh, generating unordered points and line segments, to be reorganized into a set of 2D contour points. The reorganization problem was equivalent to solving the "Chinese postman problem" (CPP) by traversing a graph built from the unordered points with the least cost. Alternatively, deformation could be applied to a binary image converted from the original contours. The deformed binary image was then converted back into contours at the CT slice locations. We validated the mesh-based contour deformation approach using lung and heart contours from 10 patients with thoracic cancer. DIR could change the 3D mesh considerably, complicating 2D contour representations after deformation. CPP could effectively reorganize the points in 2D planes regardless of how complicated the 2D contours were. Among the 10 patients, the Dice similarity coefficient between the mesh-based contour and binary image-based contour was 97.6% ± 0.3% for lung and 97.5% ± 0.7% for heart, and the Hausdoroff distance between them was 19.8 ± 5.1 mm for lung and 6.1 ± 2.2 mm for heart. Subjective evaluation showed that the mesh-based approach could keep fine details, especially for the lung. The image-based approach seemed to overprocess contours and suffered from image resolution limits. We developed a practical approach for accurate contour deformation and demonstrated its effectiveness for both clinical and research applications.

Study on digital teeth selection and virtual teeth arrangement for complete denture

Background and objectiveIn dentistry, the complete denture is a conventional treatment for edentulous patients. The computer-aided design and computer-aided manufacturing (CAD/CAM) has been applied on the digital complete denture which is developed rapidly. Tooth selection and arrangement is one of the most important parts in digital complete denture. In this paper, we propose a new method of personalized teeth arrangement. MethodsThis paper presents a method of arranging teeth virtually for a complete denture. First, scan and extract the feature points of the 3D triangular mesh data of artificial teeth (PLY format), then establish a tooth selection system. Second, scan and mark the anatomic characteristics of the maxillary and mandibular cast surfaces, such as facial midline, the curve of the arches. With the enter information, the study calculates the common arrangement lines of artificial teeth. Third, select the preferred artificial teeth and automatically arrange them virtually in the correct position by using our own software. After that, design the gingival part of the dentures on the basic of the arranged teeth on the screen and then fabricated it by using Computerized Numerical Control (CNC) technology, Rapid Prototyping (RP) technology or 3D printer technology. Finally, select artificial teeth were embedded in wax rims. ResultsThis system can choose artificial teeth reasonably and the teeth placement can meet the dentist's request to a certain extent, whereas all the operations are based on the medical principles. ConclusionsThe study performed here involves computer sciences, medicine, and dentistry, a teeth selection system was proposed and virtual teeth arrangement was described. This study has the capacity of helping operators to select teeth, which improved the accuracy of tooth arrangement, and customized complete denture.

Scalable intraband wavelet‐based coding scheme for irregular meshes

SummaryThis paper describes a novel scalable 3D triangular mesh coding method based on wavelet transform and successive approximation quantization. The algorithm efficiently exploits the intracorrelations between wavelet coefficients independently in each subband. Non‐significant wavelet coefficients are clustered, in a per bit‐plane manner, by using an octree‐based approach. An hierarchical bitstream is then generated allowing to gradually decode the 3D mesh at the desired quality or resolution representation. Our proposal can be executed on arbitrary topology meshes by using irregular wavelet decomposition. Objective and subjective quality evaluation on representative 3D meshes shows that the proposed codec provides competitive compression results when compared to the state‐of‐the‐art. Furthermore, it fits well to applications that require fast interactive handling of highly detailed 3D meshes, over networks with limited and/or variable bandwidth.

DRACO-STEM: An Automatic Tool to Generate High-Quality 3D Meshes of Shoot Apical Meristem Tissue at Cell Resolution.

Context: The shoot apical meristem (SAM), origin of all aerial organs of the plant, is a restricted niche of stem cells whose growth is regulated by a complex network of genetic, hormonal and mechanical interactions. Studying the development of this area at cell level using 3D microscopy time-lapse imaging is a newly emerging key to understand the processes controlling plant morphogenesis. Computational models have been proposed to simulate those mechanisms, however their validation on real-life data is an essential step that requires an adequate representation of the growing tissue to be carried out.Achievements: The tool we introduce is a two-stage computational pipeline that generates a complete 3D triangular mesh of the tissue volume based on a segmented tissue image stack. DRACO (Dual Reconstruction by Adjacency Complex Optimization) is designed to retrieve the underlying 3D topological structure of the tissue and compute its dual geometry, while STEM (SAM Tissue Enhanced Mesh) returns a faithful triangular mesh optimized along several quality criteria (intrinsic quality, tissue reconstruction, visual adequacy). Quantitative evaluation tools measuring the performance of the method along those different dimensions are also provided. The resulting meshes can be used as input and validation for biomechanical simulations.Availability: DRACO-STEM is supplied as a package of the open-source multi-platform plant modeling library OpenAlea (http://openalea.github.io/) implemented in Python, and is freely distributed on GitHub (https://github.com/VirtualPlants/draco-stem) along with guidelines for installation and use.

Colour Hue and Texture Evaluation for 3D Symbolization of Indoor Environments Using RGB-D Data

In this work an evaluation procedure of the use of colour hue and texture for 3D symbolization of indoor environments using RGB-D data is presented. The main characteristics of the proposed method involve RGB-D cameras to collect colour and depth data and the evaluation of the visual variables colour hue and texture combined with visual aspects such as lighting and camera configuration for the symbolization of 3D indoor environments. High quality coloured point clouds of indoor environments are obtained with the Kinect sensor and then registered and processed in order to create 3D models. These sets of point clouds can be detected, recognized and classified under one of the three following main categories: ceiling, wall or floor. After classification is done, the resulting point clouds are properly treated as 3D triangular meshes in the MeshLab software. These meshes are then filtered to form complete surfaces which are then refined before being considered for visual variable application. We evaluated the proposed method on several indoor environments to show that it efficiently combines the colour and depth data obtained from RGB-D cameras with different parameters defined for the visual variables colour hue and texture for 3D symbolization of indoor environments.