Month: June 2014

Adaptive Nonlinearity for Collisions in Complex Rod Assemblies

Danny M. Kaufman, Rasmus Tamstorf, Breannan Smith, Jean-Marie Aubry, Eitan Grinspun

We develop an algorithm for the efficient and stable simulation of large-scale elastic rod assemblies. We observe that the time-integration step is severely restricted by a strong nonlinearity in the response of stretching modes to transversal impact, the degree of this nonlinearity varying greatly with the shape of the rod. Building on these observations, we propose the ADONIS collision response algorithm that adapts the degree of nonlinearity in impact solves. We illustrate the advantages of the ADONIS algorithm by analyzing simulations involving elastic rod assemblies of varying density and scale, with up to 1.7 million individual contacts per time step.

Adaptive Nonlinearity for Collisions in Complex Rod Assemblies

Functional Fluids on Surfaces

Omri Azencot, Steffen Weißmann, Maks Ovsjanikov, Max Wardetzky, Mirela Ben-Chen

Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an incompressible fluid on a curved surface represented as an unstructured triangle mesh. Unlike the commonly used Eulerian description of the fluid using its time-varying velocity field, we propose to model fluids using their vorticity, i.e., by a (time varying) scalar function on the surface. During each time step, we advance scalar vorticity along two consecutive, stationary velocity fields. This approach leads to a variational integrator in the space continuous setting. In addition, using this approach, the update rule amounts to manipulating functions on the surface using linear operators, which can be discretized efficiently using the recently introduced functional approach to vector fields. Combining these time and space discretizations leads to a conceptually and algorithmically simple approach, which is efficient, time-reversible and conserves vorticity by construction. We further demonstrate that our method exhibits no numerical dissipation and is able to reproduce intricate phenomena such as vortex shedding from boundaries.

Functional Fluids on Surfaces

Position-Based Elastic Rods

Nobuyuki Umetani, Ryan Schmidt, Jos Stam

We present a novel method to simulate complex bending and twisting of elastic rods. Elastic rods are commonly simulated using force based methods, such as the finite element method. These methods are accurate, but do not directly fit into the more efficient position-based dynamics framework, since the definition of material frames are not entirely based on positions. We introduce ghost points, which are additional points defined on edges, to naturally endow continuous material frames on discretized rods. We achieve robustness by a novel discretization of the Cosserat theory. The method supports coupling with a frame, a triangle, and a rigid body at the rod’s end point. Our formulation is highly efficient, capable of simulating hundreds of strands in real-time.

Position-Based Elastic Rods

Stable Orthotropic Materials

Yijing Li, Jernej Barbič

Isotropic Finite Element Method (FEM) deformable object simulations are widely used in computer graphics. Several applications (wood, plants, muscles) require modeling the directional dependence of the material elastic properties in three orthogonal directions. We investigate orthotropic materials, a special class of anisotropic materials where the shear stresses are decoupled from normal stresses. Orthotropic materials generalize transversely isotropic materials, by exhibiting different stiffnesses in three orthogonal directions. Orthotropic materials are, however, parameterized by nine values that are difficult to tune in practice, as poorly adjusted settings easily lead to simulation instabilities. We present a user-friendly approach to setting these parameters that is guaranteed to be stable. Our approach is intuitive as it extends the familiar intuition known from isotropic materials. We demonstrate our technique by augmenting linear corotational FEM implementations with orthotropic materials.

Stable Orthotropic Materials

Adaptive Tetrahedral Meshes for Brittle Fracture Simulation

Dan Koschier, Sebastian Lipponer, Jan Bender

We present a method for the adaptive simulation of brittle fracture of solid objects based on a novel reversible tetrahedral mesh refinement scheme. The refinement scheme preserves the quality of the input mesh to a large extent, it is solely based on topological operations, and does not alter the boundary, i.e. any geometric feature. Our fracture algorithm successively performs a stress analysis and increases the resolution of the input mesh in regions of high tensile stress. This results in an accurate location of crack origins without the need of a general high resolution mesh which would cause high computational costs throughout the whole simulation. A crack is initiated when the maximum tensile stress exceeds the material strength. The introduced algorithm then proceeds by iteratively recomputing the changed stress state and creating further cracks. Our approach can generate multiple cracks from a single impact but effectively avoids shattering artifacts. Once the tensile stress decreases, the mesh refinement is reversed to increase the performance of the simulation. We demonstrate that our adaptive method is robust, scalable and computes highly realistic fracture results.

Adaptive Tetrahedral Meshes for Brittle Fracture Simulation

SCA 2014

Physical simulation papers:

 

TVCG Papers appearing at SCA:

Ocean Waves Animation using Boundary Integral Equations and Explicit Mesh Tracking

Todd Keeler, Robert Bridson

We tackle deep water simulation in a scalable way, solving 3D irrotational flow using only variables stored in a mesh of the surface of the water, in time proportional to the rendered mesh. The heart of our method is a novel boundary integral equation formulation that is amenable to explicit mesh tracking with unstructured triangle meshes. Our method complements FFT style waves as it is able to handle solid boundaries. It is less memory intensive than volumetric methods and inherently handles the near-infinite depth of the deep ocean. We demonstrate acceleration techniques using the FMM and GPU computing. The natural Lagrangian motion of our model gives inherent adaptivity to our simulation without the need for direct mesh operations.

Ocean Waves Animation using Boundary Integral Equations and Explicit Mesh Tracking

View-Dependent Adaptive Cloth Simulation

Woojong Koh, Rahul Narain, James F. O’Brien

This paper describes a method for view-dependent cloth simulation using dynamically adaptive mesh refinement and coarsening. Given a prescribed camera motion, the method adjusts the criteria controlling refinement to account for visibility and apparent size in the camera’s view. Objectionable dynamic artifacts are avoided by anticipative refinement and smoothed coarsening. This approach preserves the appearance of detailed cloth throughout the animation while avoiding the wasted effort of simulating details that would not be discernible to the viewer. The computational savings realized by this method increase as scene complexity grows, producing a 2x speed-up for a single character and more than 4x for a small group.

View-Dependent Adaptive Cloth Simulation

From Capture to Simulation – Connecting Forward and Inverse Problems in Fluids

James Gregson, Ivo Irkhe, Nils Thuerey, Wolfgang Heidrich

We explore the connection between fluid capture, simulation and proximal methods, a class of algorithms commonly used for inverse problems in image processing and computer vision. Our key finding is that the proximal operator constraining fluid velocities to be divergence-free is directly equivalent to the pressure-projection methods commonly used in incompressible flow solvers. This observation lets us treat the inverse problem of fluid tracking as a constrained flow problem all while working in an efficient, modular framework. In addition it lets us tightly couple fluid simulation into flow tracking, providing a global prior that significantly increases tracking accuracy and temporal coherence as compared to previous techniques. We demonstrate how we can use these improved results for a variety of applications, such as re-simulation, detail enhancement, and domain modification. We furthermore give an outlook of the applications beyond fluid tracking that our proximal operator framework could enable by exploring the connection of deblurring and fluid guiding.

From Capture to Simulation – Connecting Forward and Inverse Problems in Fluids

Multiple-Fluid SPH Simulation Using a Mixture Model

Bo Reng, Chenfeng Li, Xiao Yan, Ming C. Lin, Javier Bonet, Shi-Min Hu

This paper presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or components is modeled using the volume fraction representation, the dynamics of multiple-fluid flows is captured by using an improved mixture model, and a stable and accurate SPH formulation is rigorously derived to resolve the complex transport and transformation processes encountered in multiple-fluid flows. The new approach can capture a wide range of realworld multiple-fluid phenomena, including mixing/unmixing of miscible and immiscible fluids, diffusion effect and chemical reaction etc. Moreover, the new multiple-fluid SPH scheme can be readily integrated into existing state-of-the-art SPH simulators, and the multiple-fluid simulation is easy to set up. Various examples are presented to demonstrate the effectiveness of our approach.

Multiple-Fluid SPH Simulation Using a Mixture Model