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.