Four-Order Superconvergent Weak Galerkin Methods for the Biharmonic Equation on Triangular Meshes

A stabilizer-free weak Galerkin(SFWG)finite element method was introduced and analyzed in Ye and Zhang(SIAM J.Numer.Anal.58:2572–2588,2020)for the biharmonic equation,which has an ultra simple finite element formulation.This work is a continuation of our investigation of the SFWG method for the biharmonic equation.The new SFWG method is highly accurate with a convergence rate of four orders higher than the optimal order of convergence in both the energy norm and the L^(2)norm on triangular grids.This new method also keeps the formulation that is symmetric,positive definite,and stabilizer-free.Four-order superconvergence error estimates are proved for the corresponding SFWG finite element solutions in a discrete H^(2)norm.Superconvergence of four orders in the L^(2)norm is also derived for k≥3,where k is the degree of the approximation polynomial.The postprocessing is proved to lift a P_(k)SFWG solution to a P_(k+4)solution elementwise which converges at the optimal order.Numerical examples are tested to verify the theor ies.

A Novel VOF-Type Volume-Tracking Method for Free-Surface Flows Based on Unstructured Triangular Mesh

A novel VOF-type volume-tracking method for two-dimensional free-surface flows based on the unstructured triangular mesh is presented. Owing to the inherent merit of the unstructured triangular mesh in fitting curved boundaries, this method can handle the free-surface problems with complex geometries accurately and directly, without introducing any complicated boundary treatment or artificial diffusion. The method solves the volume transport equation geometrically through the Modified Lagrangian-Eulerian Re-map （MLER） method, which is applied to advective fluid volumes. Moreover, the PLIC method is adopted to give a second-order reconstructed interface approximation. To validate this method, two advection tests were performed for the establishment of the accuracy and convergence rate of the solutions. Numerical results for these complex tests provide convincing evidence for the excellent solution quality and fidelity of the method.

Curvatures estimation on triangular mesh

Curvatures are important geometric attributes of surfaces. There are many applications that require as a first step the accurate estimation of curvatures at arbitrary vertices on a triangulated surface. Chen and Schmitt (1992) and Taubin (1995) presented two simple methods to estimate principal curvatures. They used circular arcs to approximate the normal curvature. We find this may cause large error in some cases. In this paper, we describe a more accurate method to estimate the normal curvature, and present a novel algorithm to estimate principal curvatures by simplifying the Chen and Schmitt’s method. Some comparison results are also shown in this paper.

An Algorithm of Neighbor Finding on Sphere Triangular Meshes with Quaternary Code

The characteristic of Quaternary codes is analyzed. The rule of distinguishing triangle direction is given out. An algorithm of neighbor finding by decomposing the Quaternary code from back to front is presented in this paper. The contrastive analysis of time complexity between this algorithm and Bartholdi＇s algorithm is approached. The result illustrates that the average consumed time of this algorithm is about 23.66% of Bartholdi＇s algorithm.

基于改进MeshCNN的机械零件加工特征识别方法

为了解决传统CAPP系统中特征识别效率低且智能化程度不高的问题,将原始的MeshCNN与Faster RCNN相结合,提出一种基于Mesh-Faster RCNN的机械零件加工特征识别方法,该方法通过将自定义的加工数据集作为神经网络的输入端,获得最优的神经网络模型;然后利用MBD技术对加工模进行标注,通过PMI的信息标注获取待加工特征,将其转化为三角网格数据;在此基础上结合三角网格数据处理的算法,将处理好的加工特征数据导入最优神经网络模型中,完成特征识别过程。最后以某型号船用柴油机部分关键件为例,验证了所提方法的可行性和有效性。

Algorithm of Detecting and Filling Small Holes in Triangular Mesh Surface

In some scattered point cloud triangular mesh restoration algorithm, small triangular mesh holes problem will often affect the quality of the model. For small holes at the details, this paper propose a method for identifying and extracting hollow edge,and use a triangle growth way based on boundary edge angle to fill the empty void. First, according the relationship of the point, side and face of the triangle mesh model to identify the hole, then extracting the holes boundary edge and classifying it. Finally, using a triangle growth method based on holes boundary edge angle to fill each small holes separated from the boundary. Compared with other algorithm of filling holes, this method is high efficiency for small holes of smooth surface,and itimprovesthe quality of the triangular mesh model.

Fast view prediction for stereo images based on Delaunay triangular mesh model

The view prediction is an important step in stereo/multiview video coding, wherein, disparity estil mation （DE） is a key and difficult operation. DE algorithms usually require enormous computing power. A fast DE algorithm based on Delaunay triangulation （DT） is proposed. First, a flexible and content adaptive DT mesh is established on a target frame by an iterative split-merge algorithm. Second, DE on DT nodes are performed in a three-stage algorithm, which gives the majority of nodes a good estimate of the disparity vectors （DV）, by removing unreliable nodes due to occlusion, and forcing the minority of ＇problematic nodes＇ to be searched again, within their umbrella-shaped polygon, to the best. Finally, the target view is predicted by using affine transformation. Experimental results show that the proposed algorithm can give a satisfactory DE with less computational cost.

Improving the Quality of Conforming Triangular Meshes by Topological Clean up and DSI

A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. This method can improve the angle distribution of mesh element. while keeping the resulting meshes conform to the predefined constraints which are inputted as a PSLG.

Method of triangular mesh modeling in numerical control machining simulation

In the process of numerical control machining simulation,the workpiece surface is usually described with the uniform triangular mesh model.To alleviate the contradiction between the simulation speed and accuracy in this model,two improved methods,i.e.,the local refinement triangular mesh modeling method and the adaptive triangular mesh modeling method were presented.The simulation results show that when the final shape of the workpiece is known and its mathematic representation is simple,the local refinement triangular mesh modeling method is preferred;when the final shape of the workpiece is unknown and its mathematic description is complicated,the adaptive triangular mesh modeling method is more suitable.The experimental results show that both methods are more targeted and practical and can meet the requirements of real-time and precision in simulation.

PARAMETERIZATION OF TRIANGULAR MESHES

A new algorithm called the weighted least square discrete parameterization (WLSDP) is presented for the parameterization of triangular meshes over a convex planar region. This algorithm is the linear combination of the discrete Conformal mapping(DCM) and the discrete Authalic mapping(DAM). It provides the good properties of both DCM and DAM, such as robustness and low distortion. By adjusting the scaling factor q embedded in the WLSDP, satisfactory parameterizations in different special applications can be achieved.

面向机械零件三角网格模型自动配准中增强特征的分割方法

三角网格模型配准是工业自动化检测软件中的重要一环,其配准精度对检测机械零件的形位公差有重要影响。针对三角网格模型的自动配准精度低、鲁棒性差的问题,本文提出一种面向机械零件三角网格模型自动配准中增强特征的分割方法。首先,确定三角网格模型特征分割的K值,通过拉普拉斯矩阵确定种子点进行迭代初始化。其次,本文采用合适的区域形状代理和代价函数以加速该过程,并通过多源迭代聚类得到特征分割结果。最终,在三角网格模型特征分割结果的基础上进行基于奇异值分解法的粗配准,之后再根据EM-ICP进行精配准。与传统的特征描述子粗配准结合ICP精配准的方法进行对比,结果表明,本文方法的配准误差下降了25.2%,自动配准时间缩短了62.6%,有效地提高了三角网格模型自动配准的精度和效率。

静态爆轰试验后带破片穿孔靶板形变恢复方法

针对静态爆轰试验后发生形变的靶板,提出一种新的参数化方法,在三角网格模型下解决了靶板上孔洞部分参数化形变大以及边界角度形变、面积形变和拉伸形变大的问题。该方法首先通过拟合变分隐式曲面修补孔洞,接着采用基于虚拟边界的ABF++方法进行参数化,然后根据试验前靶板的网格能量,优化整体的靶板点云,进一步减少形变,最后去除附加的修补点和虚拟边界点,得到参数化后的靶板点云。实验选取了LSCM、ABF++方法来直接对两个经典人脸三角网格模型和靶板三角网格模型及其对应带孔洞的模型进行形变恢复,并与所提方法进行了对比,实验结果表明所提方法在三个模型的外边界角度畸变、外边界面积畸变,含孔洞三个模型的内边界角度畸变、内边界面积畸变,四项指标上相较于LSCM和ABF++平均降低了31.10%、23.76%、19.60%、10.08%,因此可以更好地减少参数化曲面上的内外边界形变,为带破片穿孔的靶板提供一种有效的参数化方法。

基于网格模型的自动铺丝路径规划方法

针对复合材料自动铺丝工艺,研究基于网格模型的自动铺丝路径规划方法。梳理了自动铺丝路径规划的业务流程,对三角网格拓扑关系进行重建,节省数据存储空间;提出了基于给定点与方向的定向延伸算法,用于精确计算网格模型的线型路径点;对路径等距后的点集进行优化,避免了等距后的线型自交以及凸边现象,保证了线型的准确;对所规划路径的压辊可铺放性分析方法进行研究,并基于分析结果提出了路径优化策略。结合CATIA二次开发工具CAA在VS平台对自动铺丝路径规划模块进行开发,并通过实例验证了本文所研究方法的可行性与可靠性。

基于Transformer的三角形网格分类分割网络

三角形网格是一种重要的几何数据结构,能有效地表达三维模型的形状细节,但三角形网格面元素的分布并不规则,因此将现有的深度神经网络直接应用到网格上较为困难。针对三角形网格不规则的结构问题,直接将网格的面作为Token,提出一种将Transformer应用于三角形网格的深度神经网络。首先,将面的重心坐标或谱域特征作为位置信息,融合其内蕴特征作为输入特征,并对输入特征位置嵌入;其次,利用自注意力模块提取全局特征,利用面卷积模块提取局部特征,以增强网络局部特征的提取能力;最后,融合局部特征和全局特征构建应用于三角形网格上的分类和分割深度神经网络。在SHREC分类数据集和COSEG分割数据集上的实验结果表明,该方法准确率较高且可以有效地提升训练速度。

RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

Frame interpolation with pixel-level motion vector field and mesh based hole filling

Most of the traditional methods are based on block motion compensation tending to involve heavy blocking artifacts in the interpolated frames. In this paper, a new frame interpolation method with pixel-level motion vector field （MVF） is proposed. Our method consists of the following four steps： （i） applying the pixel-level motion vectors （MVs） estimated by optical flow algorithm to eliminate blocking artifacts （ii） motion post-processing and super-sampling anti-aliasing to solve the problems caused by pixel-level MVs （iii） robust warping method to address collisions and holes caused by occlusions （iv） a new holes filling method using triangular mesh （HFTM） to reduce the artifacts caused by holes. Experimental results show that the proposed method can effectively alleviate the holes and blocking artifacts in interpolated frames, and outperforms existing methods both in terms of objective and subjective performances, especially for sequences with complex motions.

保留STL模型特征细节的3D打印自适应分层算法

针对传统的3D打印自适应分层算法存在计算过程复杂、无法消除阶梯效应影响、不能保留模型特征以及特征容易丢失等问题,提出了一种改进的保留STL模型特征细节的自适应分层算法。该算法首先判断模型当前层是否含有显著特征边;然后针对当前层含有显著特征边的情况,通过相邻2个三角网格法矢量的夹角来适应性确定层厚,对不含显著特征边的情况,利用三角网格法矢量与成型方向的夹角来自适应确定层厚,对于模型存在特征偏移的情况,则通过相邻切平面封闭曲线个数变化来适应性地确定层厚;最后将上述3种情况下自适应层厚的最小值作为当前分层的依据。研究结果表明:对于所采用的恐龙模型,所提算法不仅很好地保留了模型的细节特征,而且显著提升了模型成型质量;与基于三角面片法的矢量自适应分层算法和仅保留模型特征的自适应分层算法相比,所提算法的模型精度分别提升了28.6%和31.7%。该算法减小了阶梯效应以及模型特征丢失和偏移对打印质量的影响,提高了模型的打印精度。

基于实测载荷谱的三维路面重构方法

针对三维路面重构时路面不平度难以描述的问题,提出一种利用实测载荷谱反求路面的方法。在建立采集方法和测试系统基础上采集某车实际行驶载荷谱,以3种典型路面下的直线匀速行驶工况为例进行三维路面重构。基于BP神经网络建立路面反求模型,使用车辆7自由度路面输入振动模型在标准等级路面输入下的输出响应,对BP神经网络进行训练和验证。以实测和积分后的载荷谱为输入,反求得到二维路面并进行验证,在此基础上,使用三角网格法对三维路面进行重构。研究结果表明:反求出的路面作为激励输入至7自由度路面输入振动模型中,输出的簧上及簧下加速度与实测相对误差在8%以内,验证了路面反求结果的有效性,为三维路面重构提供了一种切实可行的方法。

一种保细节特征的点云多尺度三角网格重建算法

点云三角网格重建是逆向工程领域重要的研究内容。网格模型的细节特征是评判三角网格重建算法的重要指标,如何通过点云数据重建完整的网格模型并保证模型表面的细节特征不丢失是点云重建的难点。为了解决这一问题,引入多尺度概念,在点云数据的低频尺度空间中进行网格重建,保证点云数据的重建率,从而保证有高质量的重建结果。在进行网格重建过程中,采用自适应半径搜索策略进行邻域点搜索,减少了网格模型的孔洞。实验结果表明,所提算法三角网格重建质量较高,具有较高的点云数据重建率,有效保证了重建结果细节特征的完整性。

基于三角形网格的无量纲最小二乘有限元法及其应用

利用最小二乘有限元法计算二维流体场需要采用四边形网格,而仅采用四边形单元剖分含有角环、圆角和尖角等复杂结构的电力装备二维仿真模型时往往出现网格畸变。为此,提出了一种基于三角形网格实现最小二乘有限元的方法,即在三角形剖分网格上再处理得到四边形网格,从而实现最小二乘有限元法计算流体场。为验证所提方法的有效性,分别对方腔模型和带有角环等复杂结构的变压器单分区模型进行了数值计算,并分别与规则四边形网格下的最小二乘有限元法和Fluent计算结果进行对比。对比结果表明所提出的网格处理方法可以实现含有复杂结构电力装备的二维流体场仿真。