An efficient rotational matrix extraction scheme for finite element method-based deformation

Abstract

With the development of computer science and mechanical engineering, advanced and stable soft tissue deformation modelling methods have been employed, such as mass-spring model, finite element method and meshless method. The co-rotational finite element method (co-rotational FEM), which was first introduced in physics-based computer animations, has shown its strengths to be a feasible approach to modelling the process of soft tissue deformation in a virtual surgery simulation system. In this study, we mainly investigated the method of extracting the rotational matrix which is used to perform stiffness warping assembly at each simulation time step. We first introduced and compared the time-consuming polar decomposition method and the efficient QR decomposition method, and then our hybrid rotational matrix extraction method is described. The final experimental results show that our efficient rotational matrix extraction method can improve the computation efficiency greatly without deformation accuracy losing.