Category: Deformables

Interactive Two-Way Shape Design of Elastic Bodies

Rajaditya Mukherjee, Longhua Wu, Huamin Wang
We present a novel system for interactive elastic shape design in both forward and inverse fashions. Using this system, the user can choose to edit the rest shape or the quasistatic shape of an elastic solid, and obtain the other shape that matches under the quasistatic equilibrium condition at the same time. The development of this system is based on the discovery that inverse quasistatic simulation can be immediately solved by Newton’s method with a direct solver. To implement our simulator, we propose a Jacobian matrix evaluation scheme for the inverse elastic problem and we present step length and matrix evaluation techniques that improve the simulation performance. While our simulator is efficient, it is still not fast enough for the system to generate the result in real time. Our solution is a shape initialization method using the recent projective dynamics technique. Shape initialization not only works as a fast preview function during the user editing process, but also speeds up the convergence of quasistatic or inverse quasistatic simulation afterwards. The use of a heterogeneous algorithm structure allows the system to further reduce its preview cost, by utilizing the power of both the CPU and the GPU. Our experiment demonstrates that the whole system is fast, robust, and convenient for the designer to use in both forward and inverse elastic shape design. It can handle a variet of nonlinear elastic material models, and its runtime performance has space for more improvement.

Learning Nonlinear Soft-Tissue Dynamics for Interactive Avatars

Dan Casas, Miguel Otaduy

We present a novel method to enrich existing vertex-based human body models by adding soft-tissue dynamics. Our model learns to predict per-vertex 3D offsets, referred to as dynamic blendshapes, that reproduce nonlinear mesh deformation effects as a function of pose information. This enables the synthesis of realistic 3D mesh animations, including soft-tissue effects, using just skeletal motion. At the core of our method there is a neural network regressor trained on high-quality 4D scans from which we extract pose, shape and soft-tissue information. Our regressor uses a novel nonlinear subspace, which we build using an autoencoder, to efficiently compact soft-tissue dynamics information. Once trained, our method can be plugged to existing vertex-based skinning methods with little computational overhead (<10ms), enabling real-time nonlinear dynamics. We qualitatively and quantitatively evaluate our method, and show compelling animations with soft-tissue effects, created using publicly available motion capture datasets

Learning Nonlinear Soft-Tissue Dynamics for Interactive Avatars

A Material Point Method for Thin Shells with Frictional Contact

Qi Guo, Xuchen Han, Chuyuan Fu, Theodore Gast, Rasmus Tamstorf, Joseph Teran

We present a novel method for simulation of thin shells with frictional contact using a combination of the Material Point Method (MPM) and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. Furthermore we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials.

A Material Point Method for Thin Shells with Frictional Contact

Eulerian-on-Lagrangian Cloth Simulation

Nicholas J. Weidner, Kyle Piddington, David I. W. Levin, Shinjiro Sueda

We resolve the long-standing problem of simulating the contact-mediated interaction of cloth and sharp geometric features by introducing an Eulerian-on-Lagrangian (EOL) approach to cloth simulation. Unlike traditional Lagrangian approaches to cloth simulation, our EOL approach permits bending exactly at and sliding over sharp edges, avoiding parasitic locking caused by over-constraining contact constraints. Wherever the cloth is in contact with sharp features, we insert EOL vertices into the cloth, while the rest of the cloth is simulated in the standard Lagrangian fashion. Our algorithm manifests as new equations of motion for EOL vertices, a contact-conforming remesher, and a set of simple constraint assignment rules, all of which can be incorporated into existing state-of-the-art cloth simulators to enable smooth, inequality-constrained contact between cloth and objects in the world.

Eulerian-on-Lagrangian Cloth Simulation

A Moving Least Squares Material Point Method with Displacement Discontinuity and Two-Way Rigid Body Coupling

Yuanming Hu, Yu Fang, Ziheng Ge, Ziyin Qu, Yixin Zhu, Andre Pradhana, Chenfanfu Jiang

In this paper, we introduce the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM naturally leads to the formulation of Affine Particle-In-Cell (APIC) [Jiang et al. 2015] and Polynomial Particle-In-Cell [Fu et al. 2017] in a way that is consistent with a Galerkin-style weak form discretization of the governing equations. Additionally, it enables a new stress divergence discretization that eortlessly allows all MPM simulations to run two times faster than before. We also develop a Compatible Particle-In-Cell (CPIC) algorithm on top of MLS-MPM. Utilizing a colored distance field representation and a novel compatibility condition for particles and grid nodes, our framework enables the simulation of various new phenomena that are not previously supported by MPM, including material cutting, dynamic open boundaries, and two-way coupling with rigid bodies. MLS-MPM with CPIC is easy to implement and friendly to performance optimization.

A Moving Least Squares Material Point Method with Displacement Discontinuity and Two-Way Rigid Body Coupling

Animating Fluid Sediment Mixture in Particle-Laden Flows

Ming Gao, Andre Pradhana-Tampubolon, Xuchen Han, Qi Guo, Grant Kot, Eftychios Sifakis, Chenfanfu Jiang

In this paper, we present a mixed explicit and semi-implicit Material Point Method for simulating particle-laden flows. We develop a Multigrid Preconditioned fluid solver for the Locally Averaged Navier-Stokes equation. This is discretized purely on a semi-staggered standard MPM grid. Sedimentation is modeled with the Drucker-Prager elastoplasticity flow rule, enhanced by a novel particle density estimation method for converting particles between representations of either continuum or discrete points. Fluid and sediment are two-way coupled through a momentum exchange force that can be easily resolved with two MPM background grids. We present various results to demonstrate the efficacy of our method.

Animating Fluid Sediment Mixture in Particle-Laden Flows

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

Andreas Peer, Christoph Gissler, Stefan Band, Matthias Teschner
We propose a novel SPH formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation-aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first-order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure-based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self-collisions are implicitly handled by the pressure solver.

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

A Skinned Tetrahedral Mesh for Hair Animation and Hair-Water Interaction

Minjae Lee, David Hyde, Michael Bao, Ronald Fedkiw

We propose a novel framework for hair animation as well as hair-water interaction that supports millions of hairs. First, we develop a hair animation framework that embeds hair into a tetrahedralized volume mesh that we kinematically skin to deform and follow the exterior of an animated character. Allowing the hairs to follow their precomputed embedded locations in the kinematically deforming skinned mesh already provides visually plausible behavior. Creating a copy of the tetrahedral mesh, endowing it with springs, and attaching it to the kinematically skinned mesh creates more dynamic behavior. Notably, the springs can be quite weak and thus efficient to simulate because they are structurally supported by the kinematic mesh. If independent simulation of individual hairs or guide hairs is desired, they too benefit from being anchored to the kinematic mesh dramatically increasing efficiency as weak springs can be used while still supporting interesting and dramatic hairstyles. Furthermore, we explain how to embed these dynamic simulations into the kinematically deforming skinned mesh so that they can be used as part of a blendshape system where an artist can make many subsequent iterations without requiring any additional simulation. Although there are many applications for our newly proposed approach to hair animation, we mostly focus on the particularly challenging problem of hair-water interaction. While doing this, we discuss how porosities are stored in the kinematic mesh, how the kinematically deforming mesh can be used to apply drag and adhesion forces to the water, etc.

A Skinned Tetrahedral Mesh for Hair Animation and Hair-Water Interaction

Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation

Yu Ju Chen, Uri M. Ascher, Dinesh K. Pai

High quality simulations of the dynamics of soft flexible objects can be rather costly, because the assembly of internal forces through an often nonlinear stiffness at each time step is expensive. Many standard implicit integrators introduce significant, time-step dependent artificial damping. Here we propose and demonstrate the effectiveness of an exponential Rosenbrock-Euler (ERE) method which avoids discretization-dependent artificial damping. The method is relatively inexpensive and works well with the large time steps used in computer graphics. It retains correct qualitative behaviour even in challenging circumstances involving non-convex elastic energies. Our integrator is designed to handle and perform well even in the important cases where the symmetric stiffness matrix is not positive definite at all times. Thus we are able to address a wider range of practical situations than other related solvers. We show that our system performs efficiently for a wide range of soft materials.

Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation

Stabilizing Integrators for Real-Time Physics

Dimitar Dinev, Tiantian Liu, Ladislav Kavan

We present a new time integration method featuring excellent stability and energy conservation properties, making it particularly suitable for real-time physics. The commonly used backward Euler method is stable but introduces artificial damping. Methods such as implicit midpoint do not suffer from artificial damping but are unstable in many common simulation scenarios. We propose an algorithm that blends between the implicit midpoint and forward/backward Euler integrators such that the resulting simulation is stable while introducing only minimal artificial damping. We achieve this by tracking the total energy of the simulated system, taking into account energy-changing events: damping and forcing. To facilitate real-time simulations, we propose a local/global solver, similar to Projective Dynamics, as an alternative to Newton’s method. Compared to the original Projective Dynamics, which is derived from backward Euler, our final method introduces much less numerical damping at the cost of minimal computing overhead. Stability guarantees of our method are derived from the stability of backward Euler, whose stability is a widely accepted empirical fact. However, to our knowledge, theoretical guarantees have so far only been proven for linear ODEs. We provide preliminary theoretical results proving the stability of backward Euler also for certain cases of nonlinear potential functions.

Stabilizing Integrators for Real-Time Physics