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Meshless Thin-Shell Simulation Based on Global Conformal Parameterization
May/June 2006 (vol. 12 no. 3)
pp. 375-385
Xiaohu Guo, IEEE
Xin Li, IEEE
Yunfan Bao, IEEE
Hong Qin, IEEE

Abstract—This paper presents a new approach to the physically-based thin-shell simulation of point-sampled geometry via explicit, global conformal point-surface parameterization and meshless dynamics. The point-based 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 well-sampled point surface is functionally equivalent to a manifold, enabling popular and powerful surface-based modeling and physically-based 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 thin-shell 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 point-sampled geometry in graphics and relevant fields.

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Index Terms:
Meshless method, physically-based simulation, point-based geometry, surface parameterization, thin-shell.
Citation:
Xiaohu Guo, Xin Li, Yunfan Bao, Xianfeng Gu, Hong Qin, "Meshless Thin-Shell Simulation Based on Global Conformal Parameterization," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 3, pp. 375-385, May-June 2006, doi:10.1109/TVCG.2006.52
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