Mesh Simplification Algorithm Research Articles

A progressive mesh simplification algorithm based on neural implicit representation

AbstractProgressive mesh simplification (PM) algorithm aims to generate simplified mesh at any resolution for the input high‐precision mesh, and only needs to be optimized or fitted once. Most of the existing PM algorithms are obtained based on heuristic mesh simplification algorithms, which leads to redundant storage space and poor practice‐ability of the algorithm. In this article, a progressive mesh simplification algorithm based on neural implicit representation (NePM) is proposed, and NePM transforms algorithm process into an implicit continuous optimization problem through neural network and probabilistic model. NePM uses Gaussian mixture model to model high‐precision mesh and samples the probabilistic model to obtain simplified meshes at different resolutions. In addition, the simplified mesh is optimized through multi‐level neural network, preserving characteristics of the input high‐precision mesh. Thus, the algorithm in this work lowers the memory usage of the PM and improves the practicability of the algorithm while ensuring the accuracy.

Stochastic Geometric Iterative Method for Loop Subdivision Surface Fitting

In this paper, we propose a stochastic geometric iterative method (S-GIM) to approximate the high-resolution 3D models by finite loop subdivision surfaces. Given an input mesh as the fitting target, the initial control mesh is generated using the mesh simplification algorithm. Then, our method adjusts the control mesh iteratively to make its finite loop subdivision surface approximate the input mesh. In each geometric iteration, we randomly select part of points on the subdivision surface to calculate the difference vectors and distribute the vectors to the control points. Finally, the control points are updated by adding the weighted average of these difference vectors. We prove the convergence of S-GIM and verify it by demonstrating error curves in the experiment. In addition, compared with existing geometric iterative methods, S-GIM has a shorter running time under the same number of iteration steps.

A NOVEL QUADRATIC ERROR METRIC MESH SIMPLIFICATION ALGORITHM FOR 3D BUILDING MODELS BASED ON ‘LOCAL-VERTEX’ TEXTURE FEATURES

Abstract. 3D building model is an important part of 3D GIS. However, with the rapid development of data acquisition technology, the data volume of the 3D building model has increased dramatically. Levels of detail (LOD) technology determines the resource allocation for object rendering based on the position (Screen Size) and importance of the nodes of the model in the display environment, reducing the model’s volume and thus obtaining efficient rendering computations. To ensure the smooth rendering and efficient loading of 3D building models, it is essential to simplify the 3D building models to generate LOD. By taking the texture discontinuity and topological complexity into account, this paper proposes a quadratic error metric mesh simplification algorithm based on "local-vertex" texture features for 3D building models simplification. Using the texture features of the model texture map and the vertex curvature at local vertices, we increase the edge collapse cost of the model in the rich texture areas. After each simplification operation, we use centre of gravity coordinate method to optimize the texture coordinates to preserve the model’s detailed features and topological relationships. A series of experimental comparisons with other state-of-the-art methods verify the effectiveness of the proposed method for simplifying 3D building models. The method in this paper helps to maintain the detailed features and topological relationships of 3D building models while reducing the volume of model and better generating LOD for application in 3D GIS.

Retraction Note: Urban Landscape Ecological Design and Stereo Vision Based on 3D Mesh Simplification Algorithm and Artificial Intelligence

Retraction Note: Urban Landscape Ecological Design and Stereo Vision Based on 3D Mesh Simplification Algorithm and Artificial Intelligence

A Model Simplification Algorithm for 3D Reconstruction

Mesh simplification is an effective way to solve the contradiction between 3D models and limited transmission bandwidth and smooth model rendering. The existing mesh simplification algorithms usually have problems of texture distortion, deformation of different degrees, and no texture simplification. In this paper, a model simplification algorithm suitable for 3D reconstruction is proposed by taking full advantage of the recovered 3D scene structure and calibrated images. First, the reference 3D model scene is constructed on the basis of the original mesh; second, the images are collected on the basis of the reference 3D model scene; then, the mesh and texture are simplified by using the reference image set combined with the QEM algorithm. Lastly, the 3D model data of a town in Tengzhou are used for experimental verification. The results show that the algorithm proposed in this paper basically has no texture distortion and deformation problems in texture simplification and can effectively reduce the amount of texture data, with good feasibility.

Extraction of English Keyword Information Based on CAD Mesh Model

Traditional methods only consider topic information in English vocabulary information extraction, lose the statistical feature information of the keywords themselves, and easily ignore the semantic information of the words. In order to improve the extraction efficiency of English keyword information, based on the CAD mesh model, this paper adds constraint factors such as vertex neighborhood flatness, vertex degree, side length, and flatness on both sides of the side on the basis of the original QEM quadratic error simplification algorithm, and it incorporates a smoothing effect into the edge folding cost function. Moreover, based on the proposed normal vector-based QEM mesh simplification algorithm, the point selection after the edge folding operation is fixed as the vertices of the original edge, and it is applied to the mesh parameterization. In addition, the algorithm solves the local parameterization problem of partially deleted vertices after the simplification operation of each layer is completed. After the model is constructed, the performance of the model is verified through experiments. The research shows that the English keyword information extraction model constructed in this paper is effective.

A Digital Twin-Oriented Lightweight Approach for 3D Assemblies

In the design and operation scenarios driven by Digital Twins, large computer-aided design (CAD) models of production line equipment can limit the real-time performance and fidelity of the interaction between digital and physical entities. Digital CAD models often consist of combined parts with characteristics of discrete folded corner planes. CAD models simplified to a lower resolution by current mainstream mesh simplification algorithms might suffer from significant feature loss and mesh breakage, and the interfaces between the different parts cannot be well identified and simplified. A lightweight approach for common CAD assembly models of Digital Twins is proposed. Based on quadric error metrics, constraints of discrete folded corner plane characteristics of Digital Twin CAD models are added. The triangular regularity in the neighborhood of the contraction target vertices is used as the penalty function, and edge contraction is performed based on the cost. Finally, a segmentation algorithm is employed to identify and remove the interfaces between the two CAD assembly models. The proposed approach is verified through common stereoscopic warehouse, robot base, and shelf models. In addition, a scenario of a smart phone production line is applied. The experimental results indicate that the geometric error of the simplified mesh is reduced, the frame rate is improved, and the integrity of the geometric features and triangular facets is effectively preserved.

High-performance simplification of triangular surfaces using a GPU

Due to advances in high-performance computing technologies, computer graphics techniques—especially those related to mesh simplification—have been noticeably improved. These techniques, which have a strong impact on many applications, such as geometric modeling and visualization, have been well studied for more than two decades. Recent advances in GPUs have led to significant improvements in terms of speed and interactivity. In this paper, we present a mesh simplification algorithm that benefits from the parallel framework provided by recent GPUs. We customize the halfedge data structure for adaption with the dynamic memory restrictions of CUDA. The proposed algorithm is fully parallelized by employing a lock-free skip priority queue and a set of disjoint regions of the mesh. The proposed technique accelerates the simplification process while preserving the topological properties of the mesh. Some results and comparisons are provided to verify the efficiency of the proposed algorithm.

An effective energy-conserving contact modelling strategy for spherical harmonic particles represented by surface triangular meshes with automatic simplification

An effective discrete element modelling strategy for triangular mesh represented spherical harmonic particles is proposed. It features: (1) using a golden spiral lattice on the unit sphere to generate an initial triangular mesh with any number of vertices/triangles for a star-shaped surface; (2) applying an edge contraction mesh simplification algorithm to reduce the mesh size to any desired level; and (3) adopting an energy-conserving linear normal contact model to compute the contact geometric and force features of contacting particles. In particular, the edge contraction algorithm is applicable to any triangular mesh. It is algorithmically very simple and highly effective, and can be easily incorporated into existing discrete element frameworks. Numerical experiments are conducted to demonstrate that the simplified mesh by the edge contraction can not only have a very low geometric approximation error but also achieve expected mechanical responses. Thus this mesh simplification approach can serve as an ideal pre-processing tool to optimise a large input triangular mesh in order to significantly reduce the computational cost associated with discrete element simulations without compromising the modelling accuracy.

RETRACTED ARTICLE: Urban Landscape Ecological Design and Stereo Vision Based on 3D Mesh Simplification Algorithm and Artificial Intelligence

With the development of urban road construction in China, urban road landscape design is also making progress. Aesthetic design is a kind of behavior that does not depend on the subjectivity of science. When this process is going on, we need to consider the various components of landscape, that is, landscape elements. Only in this way, works of art that conform to the aesthetic concept of a specific group of people can be created. The landscape ecological design of urban road is guided by the ecological theory, which can meet the normal traffic function of the road and realize the beautiful green landscape. This paper introduces three-dimensional network reconstruction method and three-dimensional vision technology, and puts forward the visualization scheme of urban landscape ecological design. Based on the model design and simulations, the perfomance of the proposed framework is validated. Compared with the state-of-the-art models, the proposed outperforms.

Mesh Simplification Algorithms for Rendering Performance

Mesh Simplification Algorithms for Rendering Performance

Mesh simplification algorithm based on edge curvature metrics and local optimization

Aiming at the problem that the mesh simplification algorithm loses the geometric features of the model in large-scale simplification, an improved half-edge collapse mesh simplification algorithm is proposed. The concept of approximate measurement of edge curvature is introduced, and the edge curvature is added to the error measure, so that the order of half-edge collapse of the mesh is changed, and the simplified details of the mesh model can be preserved accurately. At the same time, by analyzing the quality of simplified triangular mesh, optimizing triangular mesh locally, reducing the amount of narrow triangles, the quality of the simplified model is improved. The proposed algorithm was tested on Cow model, Car model and Bunny model, and compared with another three algorithms, one of them is a classical mesh simplification algorithm based on edge collapse, the other is an improved algorithm of the classical one. The experimental results show that the improved algorithm can better retain the detail features of the original model at the same reduction ratio, and has reasonable mesh allocation, fast execution speed and small error.

Mesh Simplification Algorithm Based on the Quadratic Error Metric and Triangle Collapse

Triangular mesh is a commonly used method for representing 3D models. With the continuous development of 3D modeling and scanning technologies, the complexity of the mesh is increasing. The greater the density of the mesh is, the higher the representation quality of the model. However, a higher mesh density also results in greater storage and time costs. Mesh simplification is a basic research topic in the fields of computer graphics and virtual reality. This paper implements a mesh simplification algorithm based on triangle collapse. The algorithm uses a half-edge data structure to record the mesh information, obtains the folding point by minimizing the sum of squares of the spatial distances from the folding point to all adjacent surfaces, and then calculates the folding cost and folding order. The algorithm iteratively folds the triangular faces with the smallest folding costs to achieve mesh simplification. By processing a large number of models, it is proven that the algorithm in this paper can retain the original model features during the simplification process.

The simulation of flight trajectory based on quasi-Newton and mesh simplification

To address the problem of low accuracy of aircraft flight trajectory, a new prediction method for flight trajectory is proposed based on the quasi-Newton and mesh simplification algorithm. This method firstly proposes the calculation method of 3D aircraft flight trajectory, and simplifies the calculation process with mesh simplification algorithm. At the same time, the prediction accuracy is further improved with the quasi-Newton algorithm. At last, through the simulation experiment, we have made a deep study of the key factors influencing the prediction method. The result has shown that the method has good adaptability.

Geometric optimization of building information models in MEP projects: Algorithms and techniques for improving storage, transmission and display

Abstract Mechanical, Electrical and Plumbing (MEP) models are generally characterized by information redundancy and a high density of irregularly shaped components. Consequently, they require large storage spaces and are not conducive for interchange purposes. Geometric optimization of MEP models can play a significant role in facilitating model exchange and handover by increasing storage, transmission and display efficiency. To date, the body of knowledge on such geometric optimization, unfortunately, is still very narrow. This paper presents and tests a solution for the optimization of storage, transmission, and display of MEP models. Storage optimization was achieved through a mapping-based model description method and a novel Quadric-Error-Metric (QEM) mesh simplification algorithm, reducing required storage while maintaining the contour of components. For transmission optimization, a normal vector compression algorithm and a fixed-dictionary specific compression algorithm were proposed to achieve efficient compression of data thus, fulfilling the need for cross-platform interchange. Display optimization was obtained through a normal vector regeneration algorithm for clustering triangle meshes to improve 3D display effects. The evaluation of the solution, performed for each individual component separately as well as for an entire solution, proved successful. Volume of storage data was reduced by 40% to 50% through mesh simplification. Data transmission volume was reduced by more than 80% for components with complicated geometry without affecting the topology of the components. Finally, the display process was capable of decreasing the number of triangles and delivering very good quality of displayed models.

Animated mesh simplification based on motion features in visual sensor networks

The three-dimensional animated model is widely used in scientific visualization, entertainment, and virtual applications, especially in visual sensor networks. The main purpose of simplification is to capture the shape sequence of an object with very few elements while preserving the overall shape. As three-dimensional animated mesh is time-varying in all frames, the trade-off between the temporal coherence and geometric distortion must be considered to develop simplification algorithm. In this article, a novel three-dimensional animated mesh simplification algorithm based on motion features is presented. Here, motion features are the connection areas of the relative movement consisted of vertices and edges. Motion feature extraction is to find a subgraph that has movement property. Dihedral angle of the edge through all frames is used to determine whether an edge is connected or not to the movement parts. Then, a rotation connected graph is defined to extract motion features. Traveling this graph, all motion features can be extracted. Based on the motion features, animated quadric error metric is created and quadric error matrix is built through all frames. Compared with the other methods, the important advantages of this method are high-efficiency simplification process and smoother simplification effects. It is suitable to be used in real-time applications. Experiment results show that the 3D animated mesh simplification effects by our method are satisfactory.

Exploring the efficiency of image metric for assessing the visual quality of 3D mesh model

Recent developments in 3D graphics technology have led to extensive processes on 3D meshes (e.g., compression, simplification, transmission and watermarking), these processes unavoidably cause the visual perceptual degradation of the 3D objects. The existing mesh visual quality evaluation metrics either require topology constrain or fail to reflect the perceived visual quality. Meanwhile, for the 3D objects that are observed on 2D screens by the users, it is reasonable to apply image metric to assess the distortion caused by mesh simplification. We attempt to explore the efficiency of image metric for assessing the visual fidelity of the simplified 3D model in this paper. For this purpose, several latest and most effective image metrics, 2D snapshots, number and pooling algorithms are involved in our study, and finally tested on the IEETA simplification database. The statistical data allow the researcher to select the optimal parameter for this image-based mesh visual quality assessment and provide a new perspective for the design and performance assessment of mesh simplification algorithms.

Designing and Evaluating a Mesh Simplification Algorithm for Virtual Reality

With the increasing accessibility of the mobile head-mounted displays (HMDs), mobile virtual reality (VR) systems are finding applications in various areas. However, mobile HMDs are highly constrained with limited graphics processing units (GPUs) and low processing power and onboard memory. Hence, VR developers must be cognizant of the number of polygons contained within their virtual environments to avoid rendering at low frame rates and inducing simulator sickness. The most robust and rapid approach to keeping the overall number of polygons low is to use mesh simplification algorithms to create low-poly versions of pre-existing, high-poly models. Unfortunately, most existing mesh simplification algorithms cannot adequately handle meshes with lots of boundaries or nonmanifold meshes, which are common attributes of many 3D models. In this article, we present QEM 4VR , a high-fidelity mesh simplification algorithm specifically designed for VR. This algorithm addresses the deficiencies of prior quadric error metric (QEM) approaches by leveraging the insight that the most relevant boundary edges lie along curvatures while linear boundary edges can be collapsed. Additionally, our algorithm preserves key surface properties, such as normals, texture coordinates, colors, and materials, as it preprocesses 3D models and generates their low-poly approximations offline. We evaluated the effectiveness of our QEM 4VR algorithm by comparing its simplified-mesh results to those of prior QEM variations in terms of geometric approximation error, texture error, progressive approximation errors, frame rate impact, and perceptual quality measures. We found that QEM 4VR consistently yielded simplified meshes with less geometric approximation error and texture error than the prior QEM variations. It afforded better frame rates than QEM variations with boundary preservation constraints that create unnecessary lower bounds on overall polygon count reduction. Our evaluation revealed that QEM 4VR did not fair well in terms of existing perceptual distance measurements, but human-based inspections demonstrate that these algorithmic measurements are not suitable substitutes for actual human perception. In turn, we present a user-based methodology for evaluating the perceptual qualities of mesh simplification algorithms.

Synchronizing Parallel Geometric Algorithms on Multi-Core Machines

A thread synchronization mechanism dubbed Spatial Locks for parallel geometric algorithms is presented. We show that Spatial Locks ensure thread synchronization on geometric algorithms that perform concurrent operations on geometric surfaces in two-dimensional or three-dimensional space. The proposed technique respects the fact that these operations follow a certain order of processing, i.e. priorities. Parallelizing these kinds of geometric algorithms using Spatial Locks requires only a simple parameter initialization, rather than modifying the algorithms themselves together with their internal data structures. A parallel algorithm for mesh simplification is chosen to show the Spatial Locks usefulness when parallelizing geometric algorithms with ease on multi-core machines. Experimental results illustrate the advantage of using this synchronization mechanism where significant computational improvement can be achieved compared to alternative approaches.

Autonomous positioning control of manipulator and fast surface fitting based on particle filter and point cloud library technology

The real-time calculations of the positioning error, error correction, and state analysis have always been a difficult challenge in the process of autonomous positioning. In order to solve this problem, a simple depth imaging equipment (Kinect) is used, and a particle filter based on three-frame subtraction to capture the end-effector’s motion is proposed in this article. Further, a back-propagation neural network is adopted to recognize targets. The point cloud library technology is used to collect the space coordinates of the end-effector and target. Finally, a three-dimensional mesh simplification algorithm based on the density analysis and average distance between points is proposed to carry out data compression. Accordingly, the target point cloud is fitted quickly. The experiments conducted in the article demonstrate that the proposed algorithm can detect and track the end-effector in real time. The recognition rate of 99% is achieved for a cylindrical object. The geometric center of all particles is regarded as the end-effector’s center. Furthermore, the gradual convergence of the end-effector center to the target centroid shows that the autonomous positioning is successful. Compared to traditional algorithms, both moving the end-effector and a stationary object can be extracted from image frames using a thesis. The thesis presents a simple and convenient positioning method, which adjusts the motion of the manipulator according to the error between the end-effector’s center and target centroid. The computational complexity is reduced and the camera calibration is eliminated.