Triangle Meshes Research Articles

Fast Shape-Preserving Method for Integrating Polygon into Two-and-Half Dimensional Triangulation

This paper presents an approach in integrating polygons into a triangulation. The motivation behind this work is to find a way to overcome the lack of appropriate shape-preserving methods for modifying 2.5D triangle meshes. Widely used approaches for constructing Constrained Delone Triangulation (CDT) work in two steps: first constructing pure Delone triangulation, and next inserting the line segments one-by-one into it [1], [2], [3]. The presented method implements an effective mesh data structure and a walking-on-mesh approach allowing for fast polygon traversal looking for the intersected edges of the 2.5D mesh. Instead of reconnecting vertices or re-triangulating the affected mesh area, we introduce new mesh vertices and subdivide the mesh in order to integrate the polygon. The technique also examines and enhances the aspect ratios of the 2.5D triangles that are present in (and near) the partitioned area while maintaining the shape.

Trench visualisation from a semiautonomous excavator with a base grid map using a TOF 2D profilometer

Real-time, three-dimensional (3D) visualisation technology can be used at construction sites to improve the quality of work. A 3D view of the landscape under work can be compared to a target 3D model of the landscape to conveniently show needed excavation tasks to a human excavator operator or to show the progress of an autonomous excavator. The purpose of this study was to demonstrate surface visualisation from measurements taken with a pulsed time-of-flight (TOF) 2D profilometer on-board a semiautonomous excavator. The semiautomatic excavator was implemented by recording the feedback script parameters from the work performed on the excavator by a human driver. 3D visualisation maps based on the triangle mesh technique were generated from the 3D point cloud using measurements of the trenches dug by a human and an autonomous excavator. The accuracy of the 3D maps was evaluated by comparing them to a high-resolution commercial 3D scanner. An analysis of the results shows that the 2D profilometer attached to the excavator can achieve almost the same 3D results as a high-quality on-site static commercial 3D scanner, whilst more easily providing an unobstructed view of the trench during operation (a 3D scanner placed next to a deep trench might not have a full view of the trench). The main technical advantages of our 2D profilometer are its compact size, measurement speed, lack of moving parts, robustness, low-cost technology that enables visualisations from a unique viewpoint on the boom of the excavator, and readiness for real-time control of the excavator’s system. This research is expected to encourage the efficiency of the digging process in the future, as well as to provide a remarkable view of trench work using an excavator as a moving platform to facilitate data visualisation.Graphical abstract

TopoCluster: A Localized Data Structure for Topology-Based Visualization.

Unstructured data are collections of points with irregular topology, often represented through simplicial meshes, such as triangle and tetrahedral meshes. Whenever possible such representations are avoided in visualization since they are computationally demanding if compared with regular grids. In this work, we aim at simplifying the encoding and processing of simplicial meshes. The article proposes TopoCluster, a new localized data structure for tetrahedral meshes. TopoCluster provides efficient computation of the connectivity of the mesh elements with a low memory footprint. The key idea of TopoCluster is to subdivide the simplicial mesh into clusters. Then, the connectivity information is computed locally for each cluster and discarded when it is no longer needed. We define two instances of TopoCluster. The first instance prioritizes time efficiency and provides only a modest savings in memory, while the second instance drastically reduces memory consumption up to an order of magnitude with respect to comparable data structures. Thanks to the simple interface provided by TopoCluster, we have been able to integrate both data structures into the existing Topological Toolkit (TTK) framework. As a result, users can run any plugin of TTK using TopoCluster without changing a single line of code.

ConTesse: Accurate Occluding Contours for Subdivision Surfaces

This article proposes a method for computing the visible occluding contours of subdivision surfaces. The article first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when a sampled occluding contour is valid, that is, when it may be assigned consistent visibility. Previous methods do not guarantee these conditions, which helps explain why smooth contour visibility has been such a challenging problem in the past. The article then proposes an algorithm that, given a subdivision surface, finds sampled contours satisfying these conditions, and then generates a new triangle mesh matching the given occluding contours. The contours of the output triangle mesh may then be rendered with standard non-photorealistic rendering algorithms, using the mesh for visibility computation. The method can be applied to any triangle mesh, by treating it as the base mesh of a subdivision surface.

The Convergence of Discrete Uniformizations for Genus Zero Surfaces

The notion of discrete conformality proposed by Luo (2004) and Bobenko et al. (2015) on triangle meshes has rich mathematical theories and wide applications. Gu et al. (2019) and Wu and Zhu (2020) proved that the discrete uniformizations approximate the continuous uniformization for closed surfaces of genus $$\ge 1$$ , given that the approximating triangle meshes are reasonably good. In this paper, we generalize this result to the remaining case of genus zero surfaces, by reducing it to planar cases via stereographic projections.

Progressive Compression of Triangle Meshes

This paper details the first publicly available implementation of the progressive mesh compression algorithm described in the paper entitled "Compressed Progressive Meshes" [R. Pajarola and J. Rossignac, IEEE Transactions on Visualization and Computer Graphics, 6 (2000), pp. 79-93]. Our implementation is generic, modular, and includes several improvements in the stopping criteria and final encoding. Given an input 2-manifold triangle mesh, an iterative simplification is performed, involving batches of edge collapse operations guided by an error metric. During this compression step, all the information necessary for the reconstruction (at the decompression step) is recorded and compressed using several key features: geometric quantization, prediction, and spanning tree encoding. Our implementation allowed us to carry out an experimental comparison of several settings for the key parameters of the algorithm: the local error metric, the position type of the resulting vertex (after collapse), and the geometric predictor.

A Texture Integrated Deep Neural Network for Semantic Segmentation of Urban Meshes

3-D geo-information is essential for many urban related applications. Point cloud and mesh are two common representations of the 3-D urban surface. Compared to point cloud data, mesh possesses indispensable advantages, such as high-resolution image texture and sharp geometry representation. Semantic segmentation, as an important way to obtain 3-D geo-information, however, is mainly performed on the point cloud data. Due to the complex geometry representation and lack of efficient utilizing of image texture information, the semantic segmentation of the mesh is still a challenging task for urban 3-D geo-information acquisition. In this article, we propose a texture and geometry integrated deep learning method for the mesh segmentation task. A novel texture convolution module is introduced to capture image texture features. The texture features are concatenate with nontexture features on a point cloud that represents by the center of gravity (COG) of the mesh triangles. A hierarchical deep network is employed to segment the COG point cloud. Our experimental results show that the proposed network significantly improves the accuracy with the introduced texture convolution module (1.9% for overall accuracy and 4.0% for average F1 score). It also compares with other state-of-the-art methods on the public SUM-Helsinki dataset and achieves considerable results.

Research on fairings with different aspect ratio under subsonic flow Based On FLUENT

When rocket flying at high speed, large air resistance will generate at the front and around the rocket fairing. Results in significant reduction of the rocket's range and speed. The research shows that the air resistance produced by the fairing accounts for more than half of the total resistance of the rocket. As the shape of fairing is axisymmetric, a 2D model with triangle mesh was used for simulation to analyze the pressure around fairing. Eight group of fairing with aspect ratio from 0.25 to 2 were studied under the compressible non viscous airflow with 200 m/s incoming speed. The air resistance decreases with the increase of the aspect ratio, and the high pressure area around the fairing also reduces from more than a half to one third of the total fairing length. In these eight groups of fairings, the fairing with aspect ratio 2 performs best, receives the minimum air resistance and with pressure mainly distributed at the front end of the fairing.

Evaluation of the auto surfacing methods to create a surface body of the mandible model

Designing an anatomical structure for a surgical procedure is not a simple task. It is especially true of the craniofacial area, which consists of bone tissues with very complex geometry. CAD modelers need appropriate knowledge and skills in medicine and technical sciences to fully use the currently available tools in related processes with the reconstruction of the craniofacial areas. The presented preliminary studies are based on four patients treated at the Department of Maxillofacial Surgery. The segmentation process of the mandible model was performed in the ITK SNAP software. The process of generating surface body models was performed in the Auto Surfacing module in Geomagic software using two different methods: organic and mechanical. Then compare both methods for the accuracy of generating a CAD model of the mandible based on a triangle mesh structure in the Focus Inspection and the GOM Inspect software.

Evaluation of the Auto Surfacing methods to create a surface body of the mandible model

Designing an anatomical structure for a surgical procedure is not a simple task. It is especially true of the craniofacial area, which consists of bone tissues with very complex geometry. CAD modelers need appropriate knowledge and skills in medicine and technical sciences to fully use the currently available tools in related processes with the reconstruction of the craniofacial areas. The presented preliminary studies are based on four patients treated at the Department of Maxillofacial Surgery. The segmentation process of the mandible model was performed in the ITK SNAP software. The process of generating surface body models was performed in the Auto Surfacing module in Geomagic software using two different methods: organic and mechanical. Then compare both methods for the accuracy of generating a CAD model of the mandible based on a triangle mesh structure in the Focus Inspection and the GOM Inspect software.

Geodesic Tracks: Computing Discrete Geodesics With Track-Based Steiner Point Propagation.

This article presents a simple yet effective method for computing geodesic distances on triangle meshes. Unlike the popular window propagation methods that partition mesh edges into intervals of varying lengths, our method places evenly-spaced, source-independent Steiner points on edges. Given a source vertex, our method constructs a Steiner-point graph that partitions the surface into mutually exclusive tracks, called geodesic tracks. Inside each triangle, the tracks form sub-regions in which the change of distance field is approximately linear. Our method does not require any pre-computation, and can effectively balance speed and accuracy. Experimental results show that with 5 Steiner points on each edge, the mean relative error is less than 0.3 % for common 3D models used in the graphics community. We propose a set of effective filtering rules to eliminate a large amount of useless broadcast events. For a 1000K-face model, our method runs 10 times faster than the conventional Steiner point method that examines a complete graph of Steiner points in each triangle. We also observe that using more Steiner points increases the accuracy at only a small extra computational cost. Our method works well for meshes with poor triangulation and non-manifold configuration, which often poses challenges to the existing PDE methods. We show that geodesic tracks, as a new data structure that encodes rich information of discrete geodesics, support accurate geodesic path and isoline tracing, and efficient distance query. Our method can be easily extended to meshes with non-constant density functions and/or anisotropic metrics.

SurfaceVoronoi

In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites P = { Pi } m i =1 on the surface. We propose two key techniques to solve this problem. First, as the partition is determined by minimizing the m distance fields, each of which rooted at a source site, we suggest keeping one or more distance triples, for each triangle, that may help determine the Voronoi bisectors when one uses a mark-and-sweep geodesic algorithm to predict the multi-source distance field. Second, rather than keep the distance itself at a mesh vertex, we use the squared distance to characterize the linear change of distance field restricted in a triangle, which is proved to induce an exact VD when the base surface reduces to a planar triangle mesh. Specially, our algorithm also supports the Euclidean distance, which can handle thin-sheet models (e.g. leaf) and runs faster than the traditional restricted Voronoi diagram (RVD) algorithm. It is very extensible to deal with various variants of surface-based Voronoi diagrams including (1) surface-based power diagram, (2) constrained Voronoi diagram with curve-type breaklines, and (3) curve-type generators. We conduct extensive experimental results to validate the ability to approximate the exact VD in different distance-driven scenarios.

MeshTaichi

Meshes are an indispensable representation in many graphics applications because they provide conformal spatial discretizations. However, mesh-based operations are often slow due to unstructured memory access patterns. We propose MeshTaichi, a novel mesh compiler that provides an intuitive programming model for efficient mesh-based operations. Our programming model hides the complex indexing system from users and allows users to write mesh-based operations using reference-style neighborhood queries. Our compiler achieves its high performance by exploiting data locality. We partition input meshes and prepare the wanted relations by inspecting users' code during compile time. During run time, we further utilize on-chip memory (shared memory on GPU and L1 cache on CPU) to access the wanted attributes of mesh elements efficiently. Our compiler decouples low-level optimization options with computations, so that users can explore different localized data attributes and different memory orderings without changing their computation code. As a result, users can write concise code using our programming model to generate efficient mesh-based computations on both CPU and GPU backends. We test MeshTaichi on a variety of physically-based simulation and geometry processing applications with both triangle and tetrahedron meshes. MeshTaichi achieves a consistent speedup ranging from 1.4× to 6×, compared to state-of-the-art mesh data structures and compilers.

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.

Globally Injective Flattening via a Reduced Harmonic Subspace

We present a highly efficient-and-robust method for free-boundary flattening of disk-like triangle meshes in a globally injective manner. We show that by restricting the solution to a low-dimensional subspace of harmonic maps, we can dramatically accelerate the process while obtaining a low-distortion result. The algorithm consists of two main steps. A linear subspace construction, and a nonlinear nonconvex optimization for finding a low-distortion globally injective map within that subspace. The complexity of the first step dominates the algorithm's runtime and is merely that of solving a linear system. We combine recent results for computing locally-and-globally injective maps with that of harmonic maps into a conceptually simple algorithm that guarantees global injectivity. We demonstrate the great efficiency of our method over a dataset of 100 large scale models with more than 2M triangles each. Our algorithm is 10 times faster on average compared to the state-of-the-art Efficient Bijective Parameterizations (EBP) method [Su et al. 2020], on these high-resolution meshes, and more than 20 times faster on challenging examples (Figures 1,11). The speedup over [Jiang et al. 2017; Smith and Schaefer 2015] is even more dramatic.

Process planning of cylindrical printing for a novel 2T2R-type rotary 3D printer and an initial feasibility investigation

Due to solid freeform fabrication (SFF)’s manufacturing capability, additive manufacturing (AM) or 3D printing, is developing rapidly and has received much attention, leading to various aerospace, military and robotics applications. Slicing and path planning are two critical steps of AM, determining the manufactured part’s geometric accuracy and mechanical performance to a large extent. Many research works focus on the detailed strategies and algorithms of slicing and path planning. However, instead of 3D printing, most available studies concentrate only on 2.5D printing, where slicing and printing along the Z direction and filling 2D contours in the XY plane are applied. Although multi-direction and curved layer slicing have been proposed, little attention has been paid to path planning on the curved layers, especially tool path generation for the revolving parts requiring supports, such as screw conveyors and the propeller or fan. Hence, the primary purpose of this paper is to propose a novel cylindrical slicing strategy (a type of curved layer slicing) based on the triangle mesh model for curved layer Material Extrusion (CLMEX). It could be learned that the support structure is necessary for cases with traditional bottom-up printing, while supportless printing may be feasible with cylindrical slicing. Besides, a preliminary experiment is conducted to illustrate the proposed method and validate its feasibility based on a novel 2T2R-type rotary Material Extrusion (MEX) 3D printer designed in the authors’ previous research. This early-stage work generally intends to investigate the process planning and show the initial feasibility of cylindrical printing using a novel 2T2R-type rotary 3D printer. This research provides process designers with a novel and feasible slicing method for multi-axis 3D printers having a rotary build platform.

Priority‐based encoding of triangle mesh connectivity for a known geometry

AbstractIn certain practical situations, the connectivity of a triangle mesh needs to be transmitted or stored given a fixed set of 3D vertices that is known at both ends of the transaction (encoder/decoder). This task is different from a typical mesh compression scenario, in which the connectivity and geometry (vertex positions) are encoded either simultaneously or in reversed order (connectivity first), usually exploiting the freedom in vertex/triangle re‐indexation. Previously proposed algorithms for encoding the connectivity for a known geometry were based on a canonical mesh traversal and predicting which vertex is to be connected to the part of the mesh that is already processed. In this paper, we take this scheme a step further by replacing the fixed traversal with a priority queue of open expansion gates, out of which in each step a gate is selected that has the most certain prediction, that is one in which there is a candidate vertex that exhibits the largest advantage in comparison with other possible candidates, according to a carefully designed quality metric. Numerical experiments demonstrate that this improvement leads to a substantial reduction in the required data rate in comparison with the state of the art.

Solid Modelling for Manufacturing: From Voelcker’s Boundary Evaluation to Discrete Paradigms

Herb Voelcker and his research team laid the foundations of Solid Modelling, on which Computer-Aided Design is based. He founded the ambitious Production Automation Project, that included Constructive Solid Geometry (CSG) as the basic 3D geometric representation. CSG trees were compact and robust, saving a memory space that was scarce in those times. But the main computational problem was Boundary Evaluation: the process of converting CSG trees to Boundary Representations (BReps) with explicit faces, edges and vertices for manufacturing and visualization purposes. This paper presents some glimpses of the history and evolution of some ideas that started with Herb Voelcker. We briefly describe the path from “localization and boundary evaluation” to “localization and printing”, with many intermediate steps driven by hardware, software and new mathematical tools: voxel and volume representations, triangle meshes, and many others, observing also that in some applications, voxel models no longer require Boundary Evaluation. In this last case, we consider the current research challenges and discuss several avenues for further research. • History and evolution from boundary evaluation to boundary printing. • From continuous surface reconstruction to discrete paradigms. • Boundary evaluation on discrete models. • Boundaries in manufacturing.

Efficient and Robust Shadowing Determination for Mesh-Based Physical Optics Analysis

Visibility status determination for every mesh element/edge with respect to an illuminating source is routinely required in mesh-based physical optics (PO) methods, where the scatterer is represented by subwavelength sized elements. This article presents an optimally efficient shadowing determination algorithm for both plane wave and point source (Hertzian dipole) illumination of large-scale triangle meshes. It is based on a recursive multilevel field-of-view (image space) subdivision buffer approach, whereby a point’s status is determined by only checking against a small subset of elements. It is error-free and formulated to maintain efficiency for inhomogeneous meshes and grazing incidence, which result in concentration of projected elements in small areas of the buffer plane. A key step is to separate the grazing and nongrazing parts of the mesh. Very challenging test cases affirm the algorithm’s expected optimal and robust linear computational cost scaling of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}(N)$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> denotes the number of mesh elements. For fixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> , almost constant runtimes under extreme illumination and mesh variations, further demonstrate robustness.

Human Action Recognition of Triangle Mesh Sequence Representation

Considering the existing research works of human motion recognition are based on skeleton and video representations, a human motion classification method for triangle mesh sequence representation is proposed. Firstly, selecting the first frame of the triangle mesh sequence as the template model, the difference between each subsequent frame of the sequence and the template model is calculated by using the shape difference operator, which is expressed as the shape difference information tensor; Then, the shape difference information tensor is input into the deep network composed of two-dimensional convolution network and long short-term memory network to extract sequential action features for human action classification. The experimental results show that the classification accuracy of this method on human motion dataset AMASS reaches 100.00%.