Deformable objects modeling with iterative updates of local positions

Deformation of elastic material such as soft tissues of human body in the virtual environment is computed based on actual material properties. But this often leads to computational overhead hindering real-time simulation. This paper proposes a new modeling method of deformable objects for real-time simulation, using iterative updates of local positions, and control of the desired behavior by material properties.

The Saint Venant-Kirchhoff model is used to form the governing equation to express and control the nonlinear behavior and properties of the material. This governing equation is combined with a local iterative solver using position-based dynamics framework. The proposed method updates the local positions iteratively by finding the solution to minimize the energy of related elements surrounding the target nodes. A grouping method is devised to determine the optimal order of computation.

Various dynamic behaviors can be simulated using the proposed method corresponding to different Young's modulus. Maximum deformations simulated by the proposed method are compared with those results from commercial ANSYS. Relative errors of the real-time simulation results are less than 15% when Young's modulus ranges from 4 kPa to 10 kPa. Real-time performance is evaluated using a liver model composed of 596 tetrahedral elements.

Simulation results show that the proposed method can simulate, in real-time, the stiffness of the model faithfully according to their material properties.