Meshless Thin-shell Simulation Based on Global Conformal Parameterization

Xiaohu Guo, Xin Li, Yunfan Bao, Xianfeng Gu and Hong Qin
IEEE Transactions on Visualization and Computer Graphics, Vol 12, No 3, pp. 375-385 2006

In this paper, we present a new approach to the physics-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. With our parameterization method, any well-sampled point surface is functionally equivalent to a manifold, enabling popular and powerful surface-based modeling and physics-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 in the global parametric domain without the 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 the extensive experiments on the thin-shell elastic deformation and fracture simulation, we demonstrate that our integrative method is both natural and necessary, and it has great potential to further broaden the application scopes of point-sampled geometry in graphics and relevant fields.