Physics-Based Animation

Huamin Wang

Numerical errors and rounding errors in continuous collision detection (CCD) can easily cause collision detection failures if they are not handled properly. A simple and effective approach is to use error tolerances, as shown in many existing CCD systems. Unfortunately, finding the optimal tolerance values is a difficult problem for users. Larger tolerance values will introduce false positive artifacts, while smaller tolerance values may cause collisions to be undetected. The biggest issue here is that we do not know whether or when CCD will fail, even though failures are extremely rare. In this paper, we demonstrate a set of simple modifications to make a basic CCD implementation failure-proof. Using error analysis, we prove the safety of this method and we formulate suggested tolerance values to reduce false positives. The resulting algorithms are safe, automatic, efficient, and easy to implement.

Defending Continuous Collision Detection against Errors

Ye Fan, Joshua Litven, Dinesh Pai

We introduce a new framework for simulating the dynamics of musculoskeletal systems, with volumetric muscles in close contact and a novel data-driven muscle activation model. Muscles are simulated using an Eulerian-on-Lagrangian discretization that handles volume preservation, large deformation, and close contact between adjacent tissues. Volume preservation is crucial for accurately capturing the dynamics of muscles and other biological tissues. We show how to couple the dynamics of soft tissues with Lagrangian multibody dynamics simulators, which are widely available. Our physiologically based muscle activation model utilizes knowledge of the active shapes of muscles, which can be easily obtained from medical imaging data or designed to meet artistic needs. We demonstrate results with models derived from MRI data and models designed for artistic effect.

Active Volumetric Musculoskeletal Systems

Florian Reichl,  Matthäus G. Chajdas,  Jens Schneider, and  Rüdiger Westermann

We describe the design of an interactive rendering system for particle-based fluid simulations comprising hundreds of millions of particles per time step. We present a novel binary voxel representation for particle positions in combination with random jitter to drastically reduce memory and bandwidth requirements. To avoid a time-consuming preprocess and restrict the workload to what is seen, the construction of this representation is embedded into front-to-back GPU ray-casting. For high speed rendering, we ray-cast spheres and extend on total-variation-based image de-noising models to smooth the fluid surface according to data specific boundary conditions. The regular voxel structure permits highly efficient ray-sphere intersection testing as well as classification of foam particles at runtime on the GPU. Foam particles are rendered volumetrically by reconstructing densities from the binary representation on-the-fly. The particular design of our system allows scrubbing through high-resolution animated fluids at interactive rates.

Interactive Rendering of Giga-Particle Fluid Simulations

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

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

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

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

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

Physical simulation papers:

• Ocean Waves Animation using Boundary Integral Equations and Explicit Mesh Tracking
• View-Dependent Adaptive Cloth Simulation
• Adaptive Tetrahedral Meshes for Brittle Fracture Simulation
• Strain Based Dynamics
• Coupling 3D Eulerian, Height Field and Particle Methods for the Simulation of Large Scale Liquid Phenomena
• Position-based Elastic Rods
• Optimization Integrator for Large Time Steps
• Stable Orthotropic Materials
• A Peridynamic Perspective on Spring-Mass Fracture
• An Adaptive Virtual Node Algorithm with Robust Mesh Cutting
• Efficient Denting and Bending of Rigid Bodies
• Fast Grid-Based Nonlinear Elasticity for 2D Deformations
• Steklov-Poincare Skinning

TVCG Papers appearing at SCA:

• Implicit Incompressible SPH
• Implicit Multibody Penalty-based Distributed Contact
• Large-Scale Liquid Simulation on Adaptive Hexahedral Grids

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