Joshua A. Levine, Adam W. Bargteil, Christopher Corsi, Jerry Tessendorf, Robert Geist
The application of spring-mass systems to the animation of brittle fracture is revisited. The motivation arises from the recent popularity of peridynamics in the computational physics community. Peridynamic systems can be regarded as spring-mass systems with two specific properties. First, spring forces are based on a simple strain metric, thereby decoupling spring stiffness from spring length. Second, masses are connected using a distance-based criterion. The relatively large radius of influence typically leads to a few hundred springs for every mass point. Spring-mass systems with these properties are shown to be simple to implement, trivially parallelized, and well-suited to animating brittle fracture.
A Peridynamic Perspective on Spring-Mass Fracture
Saket Patkar, Mridul Aanjaneya, Aric Bartle, Minjae Lee, Ronald Fedkiw
We present a novel method for the efficient denting and bending of rigid bodies without the need for expensive finite element simulations. Denting is achieved by deforming the triangulated surface of the target body based on a dent map computed on-the-fly from the projectile body using a Z-buffer algorithm with varying degrees of smoothing. Our method accounts for the angle of impact, is applicable to arbitrary shapes, readily scales to thousands of rigid bodies, is amenable to artist control, and also works well in combination with prescoring algorithms for fracture. Bending is addressed by augmenting a rigid body with an articulated skeleton which is used to drive skinning weights for the bending deformation. The articulated skeleton is simulated to include the effects of both elasticity and plasticity. Furthermore, we allow joints to be added dynamically so that bending can occur in a nonpredetermined way and/or as dictated by the artist. Conversely, we present an articulation condensation method that greatly simplifies large unneeded branches and chains on-the-fly for increased efficiency.
Efﬁcient Denting and Bending of Rigid Bodies
Zhili Chen, Miaojun Yao, Renguo Feng, Huamin Wang
Physically based animation of detailed fracture effects is not only computationally expensive, but also difficult to implement due to numerical instability. In this paper, we propose a physics-inspired approach to enrich low-resolution fracture animation by realistic fracture details. Given a custom-designed material strength field, we adaptively refine a coarse fracture surface into a detailed one, based on a discrete gradient descent flow. Using the new fracture surface, we then generate a high-resolution fracture animation with details on both the fracture surface and the exterior surface. Our experiment shows that this approach is simple, fast, and friendly to user design and control. It can generate realistic fracture animations within a few seconds.
Physics-Inspired Adaptive Fracture Refinement
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