Spline Thin-Shell Simulation of Manifold Surfaces
KexiangWang, Ying He, Xiaohu Guo, Xianfeng Gu, and Hong Qin
Computer Graphics International 2006.
It has been technically challenging to effectively model and simulate
elastic deformation of spline-based, thin-shell objects of complicated topology.
This is primarily because traditional FEM are typically defined upon planar domain,
therefore incapable of constructing complicated, smooth spline surfaces
without patching/trimming. Moreover, at least C1 continuity is required for the
convergence of FEM solutions in thin-shell simulation. In this paper, we develop
a new paradigm which elegantly integrates the thin-shell FEM simulation with
geometric design of arbitrary manifold spline surfaces. In particular, we systematically
extend the triangular B-spline FEM from planar domains to manifold
domains. The deformation is represented as a linear combination of triangular
B-splines over shell surfaces, then the dynamics of thin-shell simulation is computed
through the minimization of Kirchhoff-Love energy. The advantages given
by our paradigm are: FEM simulation of arbitrary manifold without meshing
and data conversion, and the integrated approach for geometric design and dynamic
simulation/analysis. Our system also provides a level-of-detail sculpting
tool to manipulate the overall shapes of thin-shell surfaces for effective design.
The proposed framework has been evaluated on a set of spline models of various
topologies, and the results demonstrate its efficacy in physics-based modeling,
interactive shape design and finite-element simulation.