Physics-Based Animation

Ryan Goldade, Mridul Aanjaneya, Christopher Batty

We propose to enhance the capability of standard free-surface flow simulators with efficient support for immersed bubbles through two new models: constraint-based bubbles and affine fluid regions. Unlike its predecessors, our constraint-based model entirely dispenses with the need for advection or projection inside zero-density bubbles, with extremely modest additional computational overhead that is proportional to the surface area of all bubbles. This surface-only approach is easy to implement, realistically captures many familiar bubble behaviors, and even allows two or more distinct liquid bodies to correctly interact across completely unsimulated air. We augment this model with a per-bubble volume-tracking and correction framework to minimize the cumulative effects of gradual volume drift. To support bubbles with non-zero densities, we propose a novel reduced model for an irregular fluid region with a single pointwise incompressible affine vector field. This model requires only 11 interior velocity degrees of freedom per affine fluid region in 3D, and correctly reproduces buoyant, stationary, and sinking behaviors of a secondary fluid phase with non-zero density immersed in water. Since the pressure projection step in both the above schemes is a slightly modified Poisson-style system, we propose novel Multigrid-based preconditioners for Conjugate Gradients for fast numerical solutions of our new discretizations. Furthermore, we observe that by enforcing an incompressible affine vector field over a coalesced set of grid cells, our reduced model is effectively an irregular coarse super-cell. This offers a convenient and flexible adaptive coarsening strategy that integrates readily with the standard staggered grid approach for fluid simulation, yet supports coarsened regions that are arbitrary voxelized shapes, and provides an analytically divergence-free interior. We demonstrate its effectiveness with a new adaptive liquid simulator whose interior regions are coarsened into a mix of tiles with regular and irregular shapes.

Constraint Bubbles and Affine Regions: Reduced Fluid Models for Efficient Immersed Bubbles and Flexible Spatial Coarsening

Lei Lan, Ran Luo, Marco Fratarcangeli, Weiwei Xu, Huamin Wang, Xiaohu Guo, Junfeng Yao, Yin Yang

We propose a framework for the interactive simulation of nonlinear de-formable objects. The primary feature of our system is the seamless integration of deformable simulation and collision culling, which are often independently handled in existing animation systems. The bridge connect-ing them is the medial axis transform or MAT, a high-fidelity volumetric approximation of complex 3D shapes. From the physics simulation perspective, MAT leads to an expressive and compact reduced nonlinear model. We employ a semi-reduced projective dynamics formulation, which well captures high-frequency local deformations of high-resolution models while retaining a low computation cost. Our key observation is that the most compelling (nonlinear) deformable effects are enabled by the local constraint projection, which should not be aggressively reduced, and only apply model reduction at the global stage. From the collision detection/culling perspective, MAT is geometrically versatile using linear-interpolated spheres (i.e.the so-called medial primitives) to approximate the boundary of the input model. The intersection test between two medial primitives is formulated as a quadratically constrained quadratic program problem. We give an algorithm to solve this problem exactly, which returns the deepest penetration between a pair of intersecting medial primitives. When coupled with spatial hashing, collision (including self-collision) can be efficiently identified on the GPU within few milliseconds even for massive simulations. We have tested our system on a variety of geometrically complex and high-resolution deformable objects, and our system produces convincing animations with all the collisions/self-collisions well handled at an interactive rate.

Medial Elastics: Efficient and Collision-ready Deformation via Medial Axis Transform

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