Physics-Based Animation

Egor Larionov, Christopher Batty, Robert Bridson

We propose a novel unsteady Stokes solver for coupled viscous and pressure forces in grid-based liquid animation which yields greater accuracy and visual realism than previously achieved. Modern fluid simulators treat viscosity and pressure in separate solver stages, which reduces accuracy and yields incorrect free surface behavior. Our proposed implicit variational formulation of the Stokes problem leads to a symmetric positive definite linear system that gives properly coupled forces, provides unconditional stability, and treats difficult boundary conditions naturally through simple volume weights. Surface tension and moving solid boundaries are also easily incorporated. Qualitatively, we show that our method recovers the characteristic rope coiling instability of viscous liquids and preserves fine surface details, while previous grid-based schemes do not. Quantitatively, we demonstrate that our method is convergent through grid refinement studies on analytical problems in two dimensions. We conclude by offering practical guidelines for choosing an appropriate viscous solver, based on the scenario to be animated and the computational costs of different methods.

Variational Stokes: A Unified Pressure-Viscosity Solver for Accurate Viscous Liquids

Yun (Raymond) Fei, Henrique Teles Maia, Christopher Batty, Changxi Zheng, Eitan Grinspun

The diverse interactions between hair and liquid are complex and span multiple length scales, yet are central to the appearance of humans and animals in many situations. We therefore propose a novel multi-component simulation framework that treats many of the key physical mechanisms governing the dynamics of wet hair. The foundations of our approach are a discrete rod model for hair and a particle-in-cell model for fluids. To treat the thin layer of liquid that clings to the hair, we augment each hair strand with a height field representation. Our contribution is to develop the necessary physical and numerical models to evolve this new system and the interactions among its components. We develop a new reduced-dimensional liquid model to solve the motion of the liquid along the length of each hair, while accounting for its moving reference frame and influence on the hair dynamics. We derive a faithful model for surface tension-induced cohesion effects between adjacent hairs, based on the geometry of the liquid bridges that connect them. We adopt an empirically-validated drag model to treat the effects of coarse-scale interactions between hair and surrounding fluid, and propose new volume-conserving dripping and absorption strategies to transfer liquid between the reduced and particle-in-cell liquid representations. The synthesis of these techniques yields an effective wet hair simulator, which we use to animate hair flipping, an animal shaking itself dry, a spinning car wash roller brush dunked in liquid, and intricate hair coalescence effects, among several additional scenarios.

A Multi-Scale Model for Simulating Liquid-Hair Interactions

We present a novel method for posing and animating botanical tree models interactively in real time. Unlike other state of the art methods which tend to produce trees that are overly flexible, bending and deforming as if they were underwater plants, our approach allows for arbitrarily high stiffness while still maintaining real-time frame rates without spurious artifacts, even on quite large trees with over ten thousand branches. This is accomplished by using an articulated rigid body model with as-stiff-as-desired rotational springs in conjunction with our newly proposed simulation technique, which is motivated both by position based dynamics and the typical O(N) algorithms for articulated rigid bodies. The efficiency of our algorithm allows us to pose and animate trees with millions of branches or alternatively simulate a small forest comprised of many highly detailed trees. Even using only a single CPU core, we can simulate ten thousand branches in real time while still maintaining quite crisp user interactivity. This has allowed us to incorporate our framework into a commodity game engine to run interactively even on a low-budget tablet. We show that our method is amenable to the incorporation of a large variety of desirable effects such as wind, leaves, fictitious forces, collisions, fracture, etc.

Real-time Interactive Tree Animation

Christoph Gissler, Stefan Band, Andreas Peer, Markus Ihmsen, Matthias Teschner

Computing the forces acting from a surrounding air phase onto an SPH free-surface fluid is challenging. For full multiphase simulations the computational overhead is significant and stability issues due to the high density ratio may arise. In contrast, the air-fluid interactions can be approximated efficiently by employing a drag equation. Here, for plausible effects, the parameterization is important but challenging. We present an approach to calculate the parameters of the used drag equation in a physically motivated way. We approximate the deformation and occlusion of particles to determine their drag coefficient and exposed surface area. The resulting effects are validated by comparing them to the results of a multiphase SPH simulation. We further show the practicality of our approach by combining it with different types of SPH solvers and by simulating multiple, complex scenes.

Approximate Air-Fluid Interactions for SPH

Stefan Band, Christoph Gissler, Matthias Teschner

The paper shows that the SPH boundary handling of Akinci et al. [AIA∗ 12] suffers from perceivable issues in planar regions due to deviations in the computed boundary normals and due to erroneous oscillations in the distance computation of fluid particles to the boundary. In order to resolve these issues, we propose a novel boundary handling that combines the SPH concept with Moving Least Squares. The proposed technique significantly improves the distance and normal computations in planar boundary regions, while its computational complexity is similar to Akinci’s approach. We embed the proposed boundary handling into Implicit Incompressible SPH in a hybrid setting where it is applied at planar boundaries, while Akinci’s technique is still being used for boundaries with complex shapes. Various benefits of the improved boundary handling are illustrated, in particular a reduced particle leakage and a reduced artificial boundary friction.

Moving Least Squares Boundaries for SPH Fluids

Andreas Peer, Matthias Teschner

Working with prescribed velocity gradients is a promising approach to efficiently and robustly simulate highly viscous SPH fluids. Such approaches allow to explicitly and independently process shear rate, spin, and expansion rate. This can be used to, e.g., avoid interferences between pressure and viscosity solvers. Another interesting aspect is the possibility to explicitly process the vorticity, e.g. to preserve the vorticity. In this context, this paper proposes a novel variant of the prescribed-gradient idea that handles vorticity in a physically motivated way. In contrast to a less appropriate vorticity preservation that has been used in a previous approach, vorticity is diffused. The paper illustrates the utility of the vorticity diffusion. Therefore, comparisons of the proposed vorticity diffusion with vorticity preservation and additionally with vorticity damping are presented. The paper further discusses the relation between prescribed velocity gradients and prescribed velocity Laplacians which improves the intuition behind the prescribed-gradient method for highly viscous SPH fluids. Finally, the paper discusses the relation of the proposed method to a physically correct implicit viscosity formulation.

Prescribed Velocity Gradients for Highly Viscous SPH Fluids with Vorticity Diffusion

• Variational Stokes: A Unified Pressure-Viscosity Solver for Accurate Viscous Liquids
• Power Diagrams and Sparse Paged Grids for High Resolution Adaptive Liquids
• A Multi-Scale Model for Simulating Liquid-Hair Interactions
• A Stiffly Accurate Integrator for Elastodynamic Problems
• Example-Based Damping Design
• Robust eXtended Finite Elements for Complex Cutting of Deformables
• Perceptual Evaluation of Liquid Simulation Methods
• Data-Driven Synthesis of Smoke Flows with CNN-based Feature Descriptors
• Example-Based Expressive Animation of 2D Rigid Bodies
• Phace: Physics-based Face Modeling and Animation
• Multi-species Simulation of Porous Sand and Water Mixtures
• Botanical Materials Based on Biomechanics
• Infinite Continuous Adaptivity for Incompressible SPH
• Bounce Maps: An Improved Restitution Model for Real-Time Rigid Body Impact
• Regularized Kelvinlets: Sculpting Brushes based on Fundamental Solutions of Elasticity
• Authoring Landscapes by Combining Ecosystem and Terrain Erosion Simulation
• Data-Driven Physics for Human Soft Tissue Animation
• Dynamics-Aware Numerical Coarsening for Fabrication Design
• Anisotropic Elastoplasticity for Cloth, Knit, and Hair Frictional Contact
• Fluxed Animated Boundary Method
• Water Wave Packets
• All’s Well That Ends Well: Guaranteed Resolution of Simultaneous Rigid-Body Impact
• Multi-Scale Vorticle Fluids

TOG Papers:

• Interpolations of Smoke and Liquid Simulations
• Fast Weather Simulation for Inverse Procedural Design of 3D Urban Models
• Quasi-Newton Methods for Real-Time Simulation of Hyperelastic Materials
• Efficient Optimal Control of Smoke using Spacetime Multigrid
• A Schur Complement Preconditioner for Scalable Parallel Fluid Simulation
• Improving the GJK Algorithm for Faster and More Reliable Distance Queries Between Convex Objects

Bazin, Jean-Charles; Plüss (Kuster), Claudia; Yu, Guo; Martin, Tobias; Jacobson, Alec; Gross, Markus

Convincing manipulation of objects in live action videos is a difficult and often tedious task. Skilled video editors achieve this with the help of modern professional tools, but complex motions might still lack physical realism since existing tools do not consider the laws of physics. On the other hand, physically based simulation promises a high degree of realism, but typically creates a virtual 3D scene animation rather than returning an edited version of an input live action video. We propose a framework that combines video editing and physics-based simulation. Our tool assists unskilled users in editing an input image or video while respecting the laws of physics and also leveraging the image content. We first fit a physically based simulation that approximates the object’s motion in the input video. We then allow the user to edit the physical parameters of the object, generating a new physical behavior for it. The core of our work is the formulation of an image-aware constraint within physics simulations. This constraint manifests as external control forces to guide the object in a way that encourages proper texturing at every frame, yet producing physically plausible motions. We demonstrate the generality of our method on a variety of physical interactions: rigid motion, multi-body collisions, clothes and elastic bodies.

Physically Based Video Editing

Tongtong Wang, Zhihua Liu, Min Tang, Roufeng Tong, and Dinesh Manocha

We present an efficient and accurate algorithm for self-collision detection in deformable models. Our approach can perform discrete and continuous collision queries on triangulated meshes. We present a simple and linear time algorithm to perform the normal cone test using the unprojected 3D vertices, which reduces to a sequence point-plane classification tests. Moreover, we present a hierarchical traversal scheme that can significantly reduce the number of normal cone tests and the memory overhead using front-based normal cone culling. The overall algorithm can reliably detect all (self) collisions in models composed of hundred of thousands of triangles. We observe considerable performance improvement over prior CCD algorithms.

Efficient and Reliable Self-Collision Culling using Unprojected Normal Cones

• Interactive Paper Tearing
• Geometric Stiffness for Real-time Constrained Multibody Dynamics
• Primal-Dual Optimization for Fluids
• Enriching Facial Blendshape Rigs with Physical Simulation
• Simulation-Ready Hair Capture
• Real-Time Oil Painting on Mobile Hardware (CGF paper)
• Interactive Modeling and Authoring of Climbing Plants
• Parallel Constant Time Collision Detection for Polygonal Objects