Stable real-time deformations

Abstract

The linear strain measures that are commonly used in real-time animations of deformable objects yield fast and stable simulations. However, they are not suitable for large deformations. Recently, more realistic results have been achieved in computer graphics by using Green's non-linear strain tensor, but the non-linearity makes the simulation more costly and introduces numerical problems.In this paper, we present a new simulation technique that is stable and fast like linear models, but without the disturbing artifacts that occur with large deformations. As a precomputation step, a linear stiffness matrix is computed for the system. At every time step of the simulation, we compute a tensor field that describes the local rotations of all the vertices in the mesh. This field allows us to compute the elastic forces in a non-rotated reference frame while using the precomputed stiffness matrix. The method can be applied to both finite element models and mass-spring systems. Our approach provides robustness, speed, and a realistic appearance in the simulation of large deformations.

CPU–GPU mixed implementation of virtual node method for real-time interactive cutting of deformable objects using OpenCL

“…Due to complexity of fully nonlinear FEM, we choose corotational linear FEM [4] for deformation. Bounding volume tree with AABB is used to detect collision between surgical tools and deformable objects.…”

“…For more realistic behavior under large-scale rotation and extension, nonlinear FEM with much higher computational cost has to be used. A simple compromise is co-rotational linear FEM [4], which constructs local rotation of deformation gradient and uses linear FEM equations in rotated local coordinate frame.…”

Real-time finite element structural analysis in augmented reality

“…The approximation is considered reasonable to speed up the solution processes. Some real-time deformation models can handle geometry nonlinearity by extracting local material rotations from co-rotational models [29], and many studies employed explicit integration schemes to develop real-time methodologies for nonlinear models [30]. However, these methods are only applicable to models that allow large time integration steps.…”

An iterative predictor–corrector approach for modeling static and kinetic friction in interactive simulations

“…However, simulations using linear formulations can show visual artifacts such as unrealistic expansion in situations involving small strains and large rotations. Muller et al proposed a co-rotational formulation [22] that can account for large rotations. In this formulation, a rotation matrix is computed for each element at the end of each time step based on updated displacements.…”