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A hybrid rotational matrix extraction method for soft tissue deformation modeling

In this paper, we mainly investigated the methods of extracting rotational matrix in co-rotational finite element method (FEM). The matrix is used to perform stiffness warping assembly at every time-step in a soft body deformation simulation procedure. QR decomposition and polar decomposition are two well-known decomposition methods in computer graphics. The former is relative precise but time-consuming, while the latter is less precise but more efficient, and their real-time performances were analyzed in this paper. Our hybrid rotational matrix extraction method with efficient data structure, which combines the two methods mentioned above to make a balance between deformation results and real-time performance. In addition, the specific situation of a virtual surgery system has also been taken into account, in which the deformation usually occurs in a local contacted area, acts as an acceleration factor. The experimental results show that the hybrid rotational matrix extraction method can guarantee both accurate deformation simulation results and fast computation efficiency.