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Xiaohu Guo, Xin Li, Yunfan Bao, Xianfeng Gu, Hong Qin, "Meshless ThinShell Simulation Based on Global Conformal Parameterization," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 3, pp. 375385, May/June, 2006.  
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@article{ 10.1109/TVCG.2006.52, author = {Xiaohu Guo and Xin Li and Yunfan Bao and Xianfeng Gu and Hong Qin}, title = {Meshless ThinShell Simulation Based on Global Conformal Parameterization}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {12}, number = {3}, issn = {10772626}, year = {2006}, pages = {375385}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.52}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Meshless ThinShell Simulation Based on Global Conformal Parameterization IS  3 SN  10772626 SP375 EP385 EPD  375385 A1  Xiaohu Guo, A1  Xin Li, A1  Yunfan Bao, A1  Xianfeng Gu, A1  Hong Qin, PY  2006 KW  Meshless method KW  physicallybased simulation KW  pointbased geometry KW  surface parameterization KW  thinshell. VL  12 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—This paper presents a new approach to the physicallybased thinshell simulation of pointsampled geometry via explicit, global conformal pointsurface parameterization and meshless dynamics. The pointbased global parameterization is founded upon the rigorous mathematics of Riemann surface theory and Hodge theory. The parameterization is globally conformal everywhere except for a minimum number of zero points. Within our parameterization framework, any wellsampled point surface is functionally equivalent to a manifold, enabling popular and powerful surfacebased modeling and physicallybased simulation tools to be readily adapted for point geometry processing and animation. In addition, we propose a meshless surface computational paradigm in which the partial differential equations (for dynamic physical simulation) can be applied and solved directly over point samples via Moving Least Squares (MLS) shape functions defined on the global parametric domain without explicit connectivity information. The global conformal parameterization provides a common domain to facilitate accurate meshless simulation and efficient discontinuity modeling for complex branching cracks. Through our experiments on thinshell elastic deformation and fracture simulation, we demonstrate that our integrative method is very natural, and that it has great potential to further broaden the application scope of pointsampled geometry in graphics and relevant fields.
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