Deformation simulation based on model reduction with rigidity sampling

Abstract

In computer graphics, model reduction method, which utilizes a low-dimensional subspace to approximate the original high-dimensional deformation space, can simulate deformation well in force-free conditions. However, when external forces are applied to simulated objects, noticeable differences between force-free modal analysis [Barbic and James 2005] and full-scale FEM simulation can be observed (Figure 1). To address this problem, we introduce a data-driven approach that obtains a low-dimensional subspace from pre-computed deformation snapshots by FEM simulation with external forces applied to different parts of an object. In order to significantly reduce pre-computation time without sacrificing deformation quality at run-time, we propose rigidity guided sampling to efficiently select force points for FEM simulation. Our key observation is that the rigidity field of a force point [Au et al. 2007] is related to the potential deformation of an object. By clustering candidate force points according to the similarities of their rigidity fields, we can obtain representative force points that well capture the structural dynamics of an object. As the subspace constructed from these specifically chosen force sample points is more efficient and compact, our results show improved accuracy compared to the results of using only the modal derivative bases [Barbic and James 2005]. Furthermore, faster and more accurate deformations under external forces show great potential in real-time deformation simulation, such as virtual reality surgical simulators and trainers.