Linear constraints for deformable non-uniform B-spline surfaces
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Perspective on finite elements for shell analysis
Finite Elements in Analysis and Design
Surface Reconstruction with Triangular B-splines
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Isoparametric finite element analysis for Doo-Sabin subdivision models
Proceedings of Graphics Interface 2012
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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.