Point-Based Surface Filtering Based on Meshless Local Petrov-Galerkin Method

Abstract

Abstract: This paper presented a meshless approach for pointbased surface filtering based on meshless local PetrovGalerkin method. For the approach, there is neither need to construct local or global triangular meshes, nor need of global parameterization. By computing local tangent space, local symmetric weak form for every point is constructed in terms of anisotropic diffusion equation. Then PDEspecific mass and stiffness matrices are constructed. The corresponding sparse linear system is solved with an iterative solver. The obtained results show that the approach can smooth noises on pointbased surfaces while preserving geometric feature. Its efficiency is comparable with that of the traditional finite element method.

Key words: point-based surface, anisotropic diffusion equation, meshless local Petrov-Galerkin method, finite element method

CLC Number:

TP 391.41

QIN Hong-Xing-1, YANG Jie-2. Point-Based Surface Filtering Based on Meshless Local Petrov-Galerkin Method[J]. Journal of Shanghai Jiaotong University, 2012, 46(04): 584-590.

References

［1］Alexa M, Behr J, CoherOr D， et al. Computing and rendering point set surfaces［J］. IEEE Transactions on Visualization and Computer Graphics, 2003, 9(1): 315.

［2］Fleishman S, Drori I, CohenOr D. Bilateral mesh denoising［J］. ACM Transactions on Graphics, 2003， 22(3): 950953.

［3］Jones T R, Durand F, Desbrun M. Noniterative, featurepreserving mesh smoothing［J］. ACM Transactions on Graphics (TOG), 2003， 22(3): 943949.

［4］Hu G, Peng Q, Forrest A B. Mean shift denoising of pointsampled surfaces［J］. The Visual Computer, 2006， 22(3): 147157.

［5］Qin Hongxing, Yang Jie, Zhu Yuemin. Nonuniform bilateral filtering for point sets and surface attributes［J］. The Visual Computer， 2008, 24(12), 10671074.

［6］Taubin G. A signal processing approach to fair surface design［C］//Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM Press, 1995: 351358.

［7］Desbrun M, Meyer M, Schrder P, et al. Implicit fairing of irregular meshes using diffusion and curvature flow［C］// Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM Press, 1999: 317324.

［8］Clarenz U, Diewald U, Rumpf M. Anisotropic geometric diffusion in surface processing［C］//Proceedings of the Conference on Visualization’00. Salt Lake City, Utah, United States: IEEE CS Press, 2000: 397405.

［9］Bajaj C L, Xu G. Anisotropic diffusion of surfaces and functions on surfaces［J］. ACM Transactions on Graphics (TOG), 2003, 22(1): 432.

［10］Clarenz U, Rumpf M, Telea A. Finite elements on point based surfaces［C］// Proc of Symposium on PointBased Graphics. Zurich: Blackwell, 2004：201211.

［11］Pauly M, Keiser R, Adams B, et al. Meshless animation of fracturing solids［J］. ACM Transactions on Graphics (TOG), 2005， 24(3): 957964.

［12］Guo X, Bao Y, Gu X, et al. Meshless thinshell simulation based on global conformal parameterization［J］. IEEE Transaction on Visualization and Computer Graphics, 2006, 12(3): 375385.

［13］Belytschko T, Lu Y Y, Gu L. Elementfree Galerkin methods［J］. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229256.

［14］Atluri S N，Shen S. The meshless local PetrovGalerkin(MLPG) method: A simple and lesscostly alternative to the finite element and boundary element methods［J］. CMES Computer Modeling in Engineering and Sciences, 2002, 3(1): 1151.

[1]	WANG Rui, HU Zhiping, YIN Ke, MA Jiakuan, REN Xiang. Dynamic Responses Law of Subgrade of a Special Railway Line in Loess Region [J]. Journal of Shanghai Jiao Tong University, 2022, 56(7): 908-918.
[2]	ZHANG Peizhen, LIN Fang. Sound Scattering Characteristics of Oxygen Cylinder for Open Breathing Diver [J]. Journal of Shanghai Jiao Tong University, 2022, 56(6): 764-771.
[3]	MA Zunnong, ZHANG Yansong, ZHAO Yixi. Mechanism and Influencing Factors of Frictional Energy Dissipation in Multilayer Ultrasonic Welding [J]. Journal of Shanghai Jiao Tong University, 2022, 56(6): 772-783.
[4]	TANG Genglin, LI Jianjun, LI Yuanhui, ZHANG Longyao, ZHU Wenfeng. Numerical Simulation and Experimental Research of Sheet Hemming Forming Based on Adhesive Filling [J]. Journal of Shanghai Jiao Tong University, 2022, 56(4): 523-531.
[5]	LI Yuanhui, LI Jianjun, WANG Shunchao, ZHANG Longyao, ZHU Wenfeng. Modeling and Experiment on Roll-Hemming Forming Process of Aluminum Alloy Sheet with Adhesive [J]. Journal of Shanghai Jiao Tong University, 2022, 56(4): 532-542.
[6]	ZHU Hanhao, XIAO Rui, ZHU Jun, TANG Jun. Propagation Characteristics of Low Frequency Sound Energy in Range-Dependent Shallow Water Waveguides [J]. Journal of Shanghai Jiao Tong University, 2021, 55(8): 958-967.
[7]	ZHANG Yu, LIU Haiting, WENG Lin, SHEN Yao. Extraction of Fracture Toughness Parameters by Ring-Notched Small Punch Specimen Using Cohesive Model [J]. Journal of Shanghai Jiao Tong University, 2021, 55(7): 850-857.
[8]	ZHAO Pengfei, XUE Xin, YANG Cheng. Simulation of Influence of End Anchorage Degradation of Stirrups Caused by Alkali Aggregate Reaction on Shear Performance of Reinforced Concrete Beams [J]. Journal of Shanghai Jiao Tong University, 2021, 55(6): 681-688.
[9]	GUO Deping, LI Zheng, PENG Senlin, ZENG Zhikai, WU Daifeng. Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme [J]. Journal of Shanghai Jiao Tong University, 2021, 55(6): 689-697.
[10]	ZHANG Yuan, LI Fanchun, JIA Dejun. Design and 3D Printing Simulation of a Lattice Compressor Impeller [J]. Journal of Shanghai Jiao Tong University, 2021, 55(6): 729-740.
[11]	ZHOU Bo∗ (周博), KANG Zetian (康泽天), WANG Zhiyong (王志勇), XUE Shifeng (薛世峰). Nonlinear Finite Element Method Considering Martensite Plasticity for Shape Memory Alloy Structure [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(6): 774-785.
[12]	JING Mengjie (荆梦杰), CUI Zhixin(崔志鑫), FU Hang (傅航), CHEN Xiaojun (陈晓军). Real-Time Deformation Simulation of Kidney Surgery Based on Virtual Reality [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(3): 290-297.
[13]	ZHENG Changlong, DING Xiaohong, SHEN Hong, ZHAO Lijuan. Dynamic Topology Optimization of Rudder Structure Based on Adaptive Growth Method [J]. Air & Space Defense, 2021, 4(2): 7-.
[14]	WANG Feng, CHEN Jiali, CHEN Denghong, FAN Yong, LI Zhiyuan, HE Weiping. Element-Free Galerkin Scaled Boundary Method Based on Moving Kriging Interpolation for Steady Heat Conduction Analysis with Temperatures on Side-Faces [J]. Journal of Shanghai Jiao Tong University, 2021, 55(11): 1483-1492.
[15]	JIANG Qianqian,WANG Jiaxu,LI Junyang,XIAO Ke,TANG Ting,WANG Cheng. Influence of Double Circular Arc Harmonic Transmission Profile Parameters on Flexspline Stress [J]. Journal of Shanghai Jiaotong University, 2020, 54(2): 167-175.