Month: December 2010

A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects

We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into a geometric multigrid solver. Starting with a coarse hexahedral simulation grid, this grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is modeled by separating elements along the cell faces at this level. To represent the induced discontinuities on successive multigrid levels, the affected coarse grid cells are duplicated and the resulting connectivity components are distributed to either side of the cut. Drawing upon recent work on octree and multigrid schemes for the numerical solution of partial differential equations, we develop efficient algorithms for updating the systems of equations of the adaptive finite element discretization and the multigrid hierarchy. To construct a surface that accurately aligns with the cuts, we adapt the splitting cubes algorithm to the specific linked voxel representation of the simulation domain we use. The paper is completed by a convergence analysis of the finite element solver and a performance comparison to alternative numerical solution methods. These investigations show that our approach offers high computational efficiency and physical accuracy, and that it enables cutting of deformable bodies at very high resolutions.

A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects

Physics-Animation Forum?

I was recently asked whether there exists any internet forum dedicated to physics-based animation. The two that came to mind are Gamedev’s Math & Physics forum and Bullet’s physics simulation forums (both linked in the right column of the page), though my impression is that these naturally tend to be focused towards games, and with somewhat greater emphasis on rigid bodies and collision detection. So I wanted to pose some questions to you…

  1. Are there other forum sites that focus on physical simulation for computer graphics? If so please post a link in the comments.
  2. Would a dedicated physics-based animation forum be of genuine use to you? (Alternatively, do existing forums already serve this purpose, or do you not see a need for such a forum?)

Feel free to share any other thoughts you have on the subject.

Iso-geometric Analysis Based on Catmull-Clark Subdivision Solids

We present a volumetric iso-geometric finite element analysis based on Catmull-Clark solids. This concept allows one to use the same representation for the modeling, the physical simulation, and the visualization, which optimizes the design process and narrows the gap between CAD and CAE. In our method the boundary of the solid model is a Catmull-Clark surface with optional corners and creases to support the modeling phase. The crucial point in the simulation phase is the need to perform efficient  integration for the elements. We propose a method similar to the standard subdivision surface evaluation technique, such that numerical quadrature can be used.
Experiments show that our approach converges faster than methods based on tri-linear and tri-quadratic elements. However, the topological structure of Catmull-Clark elements is as simple as the structure of linear elements. Furthermore, the Catmull-Clark elements we use are C2-continuous on the boundary and in the interior except for irregular vertices and edges.

Iso-geometric Analysis Based on Catmull-Clark Subdivision Solids

Fast and Scalable CPU/GPU Collision Detection for Rigid and Deformable Surfaces

We present a new hybrid CPU/GPU collision detection technique for rigid and deformable objects based on spatial subdivision. Our approach efficiently exploits the massive computational capabilities of modern CPUs and GPUs commonly found in off-the-shelf computer systems. The algorithm is specifically tailored to be highly scalable on both the CPU and the GPU sides. We can compute discrete and continuous external and self-collisions of non-penetrating rigid and deformable objects consisting of many tens of thousands of triangles in few milliseconds on a modern PC. Our approach is orders of magnitude faster than earlier CPU-based approaches and up to twice as fast as the most recent GPU-based techniques.

Fast and Scalable CPU/GPU Collision Detection for Rigid and Deformable Surfaces