Efficient Example-based Material Simulation in Laplace-Beltrami Shape Space

The existing example-based simulation method generally utilizes Laplace-Beltrami Operator to construct the shape interpolation space for the surface meshes with different topological structures between the simulated objects and their examples. The loss of precision and efficiency will appear during the reconstruction process in the Euclidean space. To tackle the above issues, we present an efficient example-based material simulation method with the help of Laplace-Beltrami shape space. Firstly, we use linear FEM discretization of the Laplace-Beltrami operator to get the eigen-functions on the volumetric meshes. The reconstruction process obtains displacements of the volumetric meshes directly, which avoids the approximate projection process. Secondly, we utilize the simplified linear interpolation method to compute the target shape in the shape space constructed by the eigen-functions, which can improve the simulation efficiency. Finally, we implement the example-based material simulation on the finite element framework with the example-guided force by the target shape. The experiments demonstrate the benefits of our approach with higher efficiency compared with the similar animation results.