Multi-resolution isotropic strain limiting

In this paper we describe a fast strain-limiting method that allows stiff, incompliant materials to be simulated efficiently. Unlike prior approaches, which act on springs or individual strain components, this method acts on the strain tensors in a coordinate-invariant fashion allowing isotropic behavior. Our method applies to both two-and three-dimensional strains, and only requires computing the singular value decomposition of the deformation gradient, either a small 2x2 or 3x3 matrix, for each element. We demonstrate its use with triangular and tetrahedral linear-basis elements. For triangulated surfaces in three-dimensional space, we also describe a complementary edge-angle-limiting method to limit out-of-plane bending. All of the limits are enforced through an iterative, non-linear, Gauss-Seidel-like constraint procedure. To accelerate convergence, we propose a novel multi-resolution algorithm that enforces fitted limits at each level of a non-conforming hierarchy. Compared with other constraint-based techniques, our isotropic multi-resolution strain-limiting method is straightforward to implement, efficient to use, and applicable to a wide range of shell and solid materials. © 2010 ACM

Hierarchical techniques in collision detection for cloth animation

In the animation of deformable objects, collision detection is crucial for the performance. Contrary to volumetric bodies, the accuracy requirements for the collision treatment of textiles are particularly strict because any overlapping is visible. Therefore, we apply methods speci cally designed for deformable surfaces that speed up the collision detection. In this paper the ef ciency of bounding volume hierarchies is improved by adapted techniques for building and traversing these hierarchies. An extended set of heuristics is described that allows pruning of the hierarchy. Oriented inflation of bounding volumes enables us to detect proximities with a minimum of extra cost