Modal warping: real-time simulation of large rotational deformation and manipulation

This paper proposes a real-time simulation technique for large deformations. Green's nonlinear strain tensor accurately models large deformations; however, time stepping of the resulting nonlinear system can be computationally expensive. Modal analysis based on a linear strain tensor has been shown to be suitable for real-time simulation, but is accurate only for moderately small deformations. In the present work, we identify the rotational component of an infinitesimal deformation and extend traditional linear modal analysis to track that component. We then develop a procedure to integrate the small rotations occurring at the nodal points. An interesting feature of our formulation is that it can implement both position and orientation constraints in a straightforward manner. These constraints can be used to interactively manipulate the shape of a deformable solid by dragging/twisting a set of nodes. Experiments show that the proposed technique runs in real-time, even for a complex model, and that it can simulate large bending and/or twisting deformations with acceptable realism.