Adaptively Simulating Inhomogeneous Elastic Deformation

In this paper, we present an adaptive approach for simulating elastic deformation of homogeneous and inhomogeneous objects based on continuum mechanics. In typical adaptive simulation approaches, the deforming elastic object is usually subdivided to form a tree structure on the fly. However, they are not directly applicable for inhomogeneous elastic deformation, since the elasticity matrix, which describes the stiffness, of each element in each resolution is difficult to estimate at runtime. Furthermore, as most multi-resolution approaches, it is usually required that the stiffness of the object should either be uniform all throughout its body or consist of a collection of uniform parts, otherwise the elasticity matrices for the elements in coarse levels cannot be determined. Hence, we propose a bottom-up sampling approach to estimate the elasticity matrices for all elements in all levels based on a given stiffness function. Moreover, the subdivision process is also moved to the off-line preprocessing stage with the elasticity matrix estimation to reduce the runtime computational cost while achieving the adaptive simulation by adaptively selecting the simulation level on the fly. Therefore, we can efficiently simulate the deformation of an elastic object even with spatially varying stiffness.