Physics-Based Animation

Rosa M. Sánchez-Banderas, Alejandro Rodríguez, Héctor Barreiro, Miguel A. Otaduy

This paper introduces a method to simulate complex rod assemblies and stacked layers with implicit contact handling, through Eulerian-on-Lagrangian (EoL) discretizations. Previous EoL methods fail to handle such complex situations, due to ubiquitous and intrinsic degeneracies in the contact geometry, which prevent the use of remeshing and make simulations unstable. We propose a novel mixed Eulerian-Lagrangian discretization that supports accurate and efficient contact as in EoL methods, but is transparent to internal rod forces, and hence insensitive to degeneracies. By combining the standard and novel EoL discretizations as appropriate, we derive mixed statics-dynamics equations of motion that can be solved in a unified manner with standard solvers. Our solution is simple and elegant in practice and produces robust simulations on large-scale scenarios with complex rod arrangements and pervasive degeneracies. We demonstrate our method on multi-layer yarn-level cloth simulations, with implicit handling of both intra- and inter-layer contacts.

Robust Eulerian-on-Lagrangian Rods

José A. Canabal, Miguel A. Otaduy, Byungmoon Kim, Jose Echevarria

We present a new system for interactive dendritic painting. Dendritic painting is characterized by the unique and intricate branching patterns that grow from the interaction of inks, solvents and medium. Painting sessions thus become very dynamic and experimental. To achieve a compelling simulation of this painting technique we introduce a new Reaction-Diffusion model with carefully designed terms to allow natural interactions in a painting context. We include additional user control not possible in the real world to guide and constrain the growth of the patterns in expressive ways. Our multi-field model is able to capture and simulate all these complex phenomena efficiently in real-time, expanding the tools available to the digital artist, while producing compelling animations for motion graphics.

Simulation of Dendritic Painting

• Local Bases for Model-Reduced Smoke Simulation
• Displacement-Correlated XFEM for Simulating Brittle Fracture
• Mixing Yarns and Triangles in Cloth Simulation
• Binary Ostensibly-Implicit Trees for Fast Collision Detection
• A Practical Method for Animating Anisotropic Elastoplastic Materials
• Fast and Scalable Solvers for the Fluid Pressure Equations with Separating Solid Boundary Conditions
• Simulation of Dendritic Painting
• SoftSMPL: Data-driven Modeling of Nonlinear Soft-tissue Dynamics for Parametric Humans
• Modeling and Estimation of Nonlinear Skin Mechanics for Animated Avatars
• Interactive Meso-scale Simulation of Skyscapes
• Asynchronous Eulerian Liquid Simulation

Olivier Mercier, Derek Nowrouzezahrai

We present a flexible model reduction method for simulating incompressible fluids. We derive a novel vector field basis composed of localized basis flows that have simple analytic forms and can be tiled on regular lattices, avoiding the use of complicated data structures or neighborhood queries. Local basis flow interactions can be precomputed and reused to simulate fluid dynamics on any simulation domain without additional overhead. We introduce heuristic simulation dynamics tailored to our basis and derived from a projection of the Navier-Stokes equations to produce physically plausible motion, exposing intuitive parameters to control energy distribution across scales. Our basis can adapt to curved simulation boundaries, can be coupled with dynamic obstacles, and offers simple adjustable trade-offs between speed and visual resolution.

Local Bases for Model-reduced Smoke Simulations

Floyd M. Chitalu, Qinghai Miao, Kartic Subr, Taku Komura

We present a remeshing-free brittle fracture simulation method under the assumption of quasi-static linear elastic fracture mechanics (LEFM). To achieve this, we devise two algorithms. First, we develop an approximate volumetric simulation, based on the extended Finite Element Method (XFEM), to initialize and propagate Lagrangian crack-fronts. We model the geometry of fracture explicitly as a surface mesh, which allows us to generate high-resolution crack surfaces that are decoupled from the resolution of the deformation mesh. Our second contribution is a mesh cutting algorithm, which produces fragments of the input mesh using the fracture surface. We do this by directly operating on the half-edge data structures of two surface meshes, which enables us to cut general surface meshes including those of concave polyhedra and meshes with abutting concave polygons. Since we avoid triangulation for cutting, the connectivity of the resulting fragments is identical to the (uncut) input mesh except at edges introduced by the cut. We evaluate our simulation and cutting algorithms and show that they outperform state-of-the-art approaches both qualitatively and quantitatively.

Displacement-Correlated XFEM for Simulating Brittle Fracture

Juan J. Casafranca, Gabriel Cirio, Alejandro Rodríguez, Eder Miguel, Miguel A. Otaduy

This paper presents a method to combine triangle and yarn models in cloth simulation, and hence leverage their best features. The majority of a garment uses a triangle-based model, which reduces the overall computational and memory cost. Key areas of the garment use a yarn-based model, which elicits rich effects such as structural nonlinearity and plasticity. To combine both models in a seamless and robust manner, we solve two major technical challenges. We propose an enriched kinematic representation that augments triangle-based deformations with yarn-level details. Naive enrichment suffers from kinematic redundancy, but we devise an optimal kinematic filter that allows a smooth transition between triangle and yarn models. We also introduce a preconditioner that resolves the poor conditioning produced by the extremely different inertia of triangle and yarn nodes. This preconditioner deals effectively with rank deficiency introduced by the kinematic filter. We demonstrate that mixed yarns and triangles succeed to efficiently capture rich effects in garment fit and drape.

Mixing Yarns and Triangles in Cloth Simulation

Floyd M. Chitalu, Christophe Dubach, Taku Komura

We present a simple, efficient and low-memory technique, targeting fast construction of bounding volume hierarchies (BVH) for broad-phase collision detection. To achieve this, we devise a novel representation of BVH trees in memory. We develop a mapping of the implicit index representation to compact memory locations, based on simple bit-shifts, to then construct andevaluate bounding volume test trees (BVTT) during collision detection with real-time performance. We model the topology of the BVH tree implicitly as binary encodings which allows us to determine the nodes missing from a complete binary tree using the binary representation of the number of missing nodes. The simplicity of our technique allows for fast hierarchy construction achieving over6×speedup over the state-of-the-art. Making use of these characteristics, we show that not only it is feasible to rebuild the BVH at every frame, but that using our technique, it is actually faster than refitting and more memory efficient.

Binary Ostensibly-Implicit Trees for Fast Collision Detection

Camille Schreck, Chris Wojtan

This paper introduces a simple method for simulating highly anisotropic elastoplastic material behaviors like the dissolution of fibrous phenomena (splintering wood, shredding bales of hay) and materials composed of large numbers of irregularly-shaped bodies (piles of twigs, pencils, or cards). We introduce a simple transformation of the anisotropic problem into an equivalent isotropic one, and we solve this new “fictitious’’ isotropic problem using an existing simulator based on the material point method. Our approach results in minimal changes to existing simulators, and it allows us to re-use popular isotropic plasticity models like the Drucker-Prager yield criterion instead of inventing new anisotropic plasticity models for every phenomenon we wish to simulate.

A Practical Method for Animating Anisotropic Elastoplastic Materials

Ran Luo, Weiwei Xu, Tianjia Shao, Hongyi Xu, Yin Yang

In deformable simulation, an important computing task is to calculate the gradient and derivative of the strain energy function in order to infer the corresponding internal force and tangent stiffness matrix. The standard numerical routine is the finite difference method, which evaluates the target function multiple times under a small real-valued perturbation. Unfortunately, the subtractive cancellation prevents us from setting this perturbation sufficiently small, and the regular finite difference is doomed for computing problems requiring a high-accuracy derivative evaluation. In this paper, we graft a new finite difference scheme, namely the complex finite difference(CFD), with physics-based animation. CFD is based on the complex Taylor series expansion, which avoids the subtraction for the first-order derivative approximation. As a result, one can use a very small perturbation to calculate the numerical derivative that is as accurate as its analytic counterpart. We significantly accelerate the original CFD method so that it is also as efficient as the analytic derivative. This is achieved by discarding high-order error terms, decoupling real and imaginary calculations, replacing costly functions based on the theory of equivalent infinitesimal, and isolating the propagation of the perturbation in composite/nesting functions. CFD can be further augmented with the multicomplex Taylor expansion and Cauchy-Riemann formula to handle higher-order derivatives and tensor-valued functions. We demonstrate the accuracy, convenience, and efficiency of this new numerical routine in the context of deformable simulation – one can easily deploy a robust simulator for general hyperelastic materials, including user-crafted ones to cater to specific needs in different applications. Higher-order derivatives of the energy can be readily computed to construct modal derivative bases for reduced real-time simulation. Inverse simulation problems can also be conveniently solved using gradient/Hessian based optimization procedures.

Accelerated complex-step finite difference for expedient deformable simulation

Tetsuya Takahashi, Ming C. Lin

In physically-based simulation, it is essential to choose appropriate material parameters to generate desirable simulation results. In many cases, however, choosing appropriate material parameters is very challenging, and often tedious trial-and-error parameter tuning steps are inevitable. In this paper, we propose a real-to-virtual parameter transfer framework that identifies material parameters of viscous fluids with example video data captured from real-world phenomena. Our method first extracts positional data of fluids and then uses the extracted data as a reference to identify the viscosity parameters, combining forward viscous fluid simulations and parameter optimization in an iterative process. We evaluate our method with a range of synthetic and real-world example data, and demonstrate that our method can identify the hidden physical variables and viscosity parameters. This set of recovered physical variables and parameters can then be effectively used in novel scenarios to generate viscous fluid behaviors visually consistent with the example videos.

Video-Guided Real-to-Virtual Parameter Transfer for Viscous Fluids