Meshless thin-shell simulation based on global conformal parameterization

IEEE Transactions on Visualization and Computer Graphics
Xiaohu GuoHong Qin

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...Continue Reading

References

Jan 9, 1998·Progress in Neurobiology·P Duchamp-Viret, A Duchamp
Jan 5, 2005·IEEE Computer Graphics and Applications·Xiaohu GuoHong Qin

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Citations

Jul 5, 2008·IEEE Transactions on Visualization and Computer Graphics·Hongwei LiChi-Wing Fu
Jun 16, 2010·IEEE Transactions on Visualization and Computer Graphics·Nan ZhangRobert Sweet

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