Multi-Resolution meshless method for real-time cutting simulation of deformable object

Abstract

This dissertation presents a novel method for a real-time and stable cutting simulation of deformable objects using meshless method. Three major issues in the meshless cutting simulation, i.e. real-time computa-tion, topology change management, and contact and intersection processing are addressed in this dissertation. Element-free Galerkin (EFG) method is employed as a numerical model of the deformable object. The multi-resolution technique is introduced to improve the computational performance of the conventional EFG. Two different resolutions of uniformly placed simulation nodes, i.e. sparse and dense nodes, are employed for one deformable object. In this approach, first we define the surface layer as a region extended from the surface to certain depth into the internal part of the object. Deformation of the surface layer is precisely computed using the dense nodes placed in this region which is called active nodes. The deformation of the other dense nodes placed in the internal part of object that is called passive nodes is computed by interpolating the displacement field computed using the sparse nodes. The multi-resolution approach reduces tremendous computation by replacing the computation required to compute deformation of the passive nodes with that of the sparse nodes while maintaining details of the deformation near the surface. Topology change of the meshless object arisen in the cutting procedure is managed using visibility cri-terion. Topological relation among simulation nodes is defined as an undirected graph which connects the nearby nodes placed inside of the support. This graph is called connectivity graph. The connectivity graph is refined by testing intersections between the edges of the graph and the cut surface, and related variables with the intersected edge such as neighbor node relation, shape function values are locally updated. Our approach utilizes the BVH to accelerate the computation of the intersection test. The real-time recon...