Month: May 2014

Codimensional Surface Tension Flow on Simplicial Complexes

Bo Zhu, Ed Quigley, Matthew Cong, Justin Solomon, and Ron Fedkiw

Many visually interesting natural phenomena are characterized by thin liquid sheets, long filaments, and droplets. We present a new Lagrangian-based numerical method to simulate these codimensional surface tension driven phenomena using non-manifold simplicial complexes. Tetrahedra, triangles, segments, and points are used to model the fluid volume, thin films, filaments, and droplets, respectively. We present a new method for enforcing fluid incompressibility on simplicial complexes along with a physically-guided meshing algorithm to provide temporally consistent information for interparticle forces. Our method naturally allows for transitions between codimensions, either from tetrahedra to triangles to segments to points or vice versa, regardless of the simulation resolution. We demonstrate the efficacy of this method by simulating various natural phenomena that are characterized by thin fluid sheets, filaments, and surface tension effects.

Codimensional Surface Tension Flow on Simplicial Complexes

 

Simulating Articulated Subspace Self-Contact

Yun Teng, Miguel Otaduy, Theodore Kim

We present an efficient new subspace method for simulating the self-contact of articulated deformable bodies, such as characters. Self-contact is highly structured in this setting, as the limited space of possible articulations produces a predictable set of coherent collisions. Subspace methods can leverage this coherence, and have been used in the past to accelerate the collision detection stage of contact simulation. We show that these methods can be used to accelerate the entire contact computation, and allow self-contact to be resolved without looking at all of the contact points. Our analysis of the problem yields a broader insight into the types of nonlinearities that subspace methods can efficiently approximate, and leads us to design a pose-space cubature scheme. Our algorithm accelerates self-contact by up to an order of magnitude over other subspace simulations, and accelerates the overall simulation by two orders of magnitude over full-rank simulations. We demonstrate the simulation of high resolution (100K – 400K elements) meshes
in self-contact at interactive rates (5.8 – 50 FPS).

Simulating Articulated Subspace Self-Contact

Detailed Water with Coarse Grids: Combining Surface Meshes and Adaptive Discontinuous Galerkin

Essex Edwards, Robert Bridson

We present a new adaptive fluid simulation method that captures a high resolution surface with precise dynamics, without an inefficient fine discretization of the entire fluid volume. Prior adap- tive methods using octrees or unstructured meshes carry large over- heads and implementation complexity. We instead stick with coarse regular Cartesian grids, using detailed cut cells at boundaries, and discretize the dynamics with a p-adaptive Discontinuous Galerkin (DG) method. This retains much of the data structure simplicity of regular grids, more efficiently captures smooth parts of the flow, and offers the flexibility to easily increase resolving power where needed without geometric refinement.

Detailed Water with Coarse Grids: Combining Surface Meshes and  Adaptive Discontinuous Galerkin

Animating Deformable Objects using Sparse Spacetime Constraints

Christian Schulz, Christoph von Tycowicz, Hans-Peter Seidel, Klaus Hildebrandt

We propose a scheme for animating deformable objects based on spacetime optimization. The main feature is that it robustly and quickly (within a few seconds) generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and velocities is sufficient. The computed motion satisfies the constraints and the remaining degrees of freedom are determined by physical principles using elasticity and the spacetime constraints paradigm. Our modeling of the spacetime optimization problem combines dimensional reduction, modal coordinates, wiggly splines, and rotation strain warping. Controlling the warped motion requires the derivative of the warp map. We derive a representation of the derivative that can be efficiently and robustly evaluated. Our solver is based on a theorem that characterizes the solutions of the optimization problem and allows us to restrict the optimization to very low-dimensional search spaces. This treatment of the optimization problem avoids a time discretization and the resulting method can robustly deal with sparse input and wiggly motion.

Animating Deformable Objects using Sparse Spacetime Constraints