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Meshless
Thin-shell Simulation Based on Global Conformal Parameterization |
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Project Members |
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Xiaohu
Guo, Xin
Li, Yunfan
Bao, Xianfeng
Gu, Hong
Qin
Center for Visual Computing
Department of Computer
Science
State University of New
York at Stony Brook |
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Abstract: |
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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. |
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Keywords:
meshless
method, physically-based simulation, point-based geometry, surface
parameterization, thin-shell |
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Screenshots: |
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Video:
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Publication: |
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- Xiaohu
Guo, Xin Li, Yunfan Bao, Xianfeng Gu, Hong Qin, "Meshless
Thin-shell Simulation Based on Global Conformal Parameterization",
in IEEE Transactions on Visualization and Computer Graphics
(TVCG), Vol. 12, No. 3, pp. 375-385, 2006.
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