Physics-Based Animation

In this article we derive an equation for the velocity of an arbitrary time-evolving implicit surface. Strictly speaking, only the normal component of the velocity is unambiguously defined. This is because an implicit surface does not have a unique parametrization. However, by enforcing a constraint on the evolution of the normal field we obtain a unique tangential component. We apply our formulas to surface tracking and to the problem of computing velocity vectors of a motion blurred blobby surface. Other possible applications are mentioned at the end of the article.

On the Velocity of an Implicit Surface

A new method to simulate deformable objects with heterogeneous material properties and complex geometries is presented. Given a volumetric map of the material properties and an arbitrary number of control nodes, a distribution of the nodes is computed automatically, as well as the associated shape functions. Reference frames attached to the nodes are used to apply skeleton subspace deformation across the volume of the objects. A continuum mechanics formulation is derived from the displacements and the material properties. We introduce novel material-aware shape functions in place of the traditional radial basis functions used in meshless frameworks. In contrast with previous approaches, these allow coarse deformation functions to efficiently resolve non-uniform stiffnesses. Complex models can thus be simulated at high frame rates using a small number of control nodes.

Sparse Meshless Models of Complex Deformable Solids

We present a new type of deformable model which combines the realism of physically based continuum mechanics models and the usability of frame-based skinning methods. The degrees of freedom are coordinate frames. In contrast with traditional skinning, frame positions are not scripted but move in reaction to internal body forces. The displacement field is smoothly interpolated using dual quaternion blending. The deformation gradient and its derivatives are computed at each sample point of a deformed object and used in the equations of Lagrangian mechanics to achieve physical realism. This allows easy and very intuitive definition of the degrees of freedom of the deformable object. The meshless discretization allows on-the-fly insertion of frames to create local deformations where needed. We formulate the dynamics of these models in detail and describe some pre-computations that can be used for speed. We show that our method is effective for behaviors ranging from simple unimodal deformations to complex realistic deformations comparable with Finite Element simulations. To encourage its use, the software will be freely available in the simulation platform SOFA.

Frame-Based Elastic Models

We propose an example-based approach for simulating complex elastic material behavior. Supplied with a few poses that characterize a given object, our system starts by constructing a space of prefered deformations by means of interpolation. During simulation, this example manifold then acts as an additional elastic attractor that guides the object towards its space of prefered shapes. Added on top of existing solid simulation codes, this example potential effectively allows us to implement inhomogeneous and anisotropic materials in a direct and intuitive way. Due to its example-based interface, our method promotes an art-directed approach to solid simulation, which we exemplify on a set of practical examples.

Example-Based Elastic Materials

Cloth often has complicated nonlinear, anisotropic elastic behavior due to its woven pattern and fiber properties. However, most current cloth simulation techniques simply use linear and isotropic elastic models with manually selected stiffness parameters. Such simple simulations do not allow differentiating the behavior of distinct cloth materials such as silk or denim, and they cannot model most materials with fidelity to their real-world counterparts. In this paper, we present a data-driven technique to more realistically animate cloth. We propose a piecewise linear elastic model that is a good approximation to nonlinear, anisotropic stretching and bending behaviors of various materials. We develop new measurement techniques for studying the elastic deformations for both stretching and bending in real cloth samples. Our setup is easy and inexpensive to construct, and the parameters of our model can be fit to observed data with a well-posed optimization procedure. We have measured a database of ten different cloth materials, each of which exhibits distinctive elastic behaviors. These measurements can be used in most cloth simulation systems to create natural and realistic clothing wrinkles and shapes, for a range of different materials.

Data-Driven Elastic Models for Cloth: Modeling and Measurement

We present a general approach to creating realistic swimming behavior for a given articulated creature body. The two main components of our method are creature/fluid simulation and the optimization of the creature motion parameters. We simulate two-way coupling between the fluid and the articulated body by solving a linear system that matches acceleration at fluid/solid boundaries and that also enforces fluid incompressibility. The swimming motion of a given creature is described as a set of periodic functions, one for each joint degree of freedom. We optimize over the space of these functions in order to find a motion that causes the creature to swim straight and stay within a given energy budget. Our creatures can perform path following by first training appropriate turning maneuvers through offline optimization and then selecting between these motions to track the given path. We present results for a clownfish, an eel, a sea turtle, a manta ray and a frog, and in each case the resulting motion is a good match to the real-world animals. We also demonstrate a plausible swimming gait for a fictional creature that has no real-world counterpart.

Articulated Swimming Creatures

Art direction of high resolution naturalistic liquid simulations is notoriously hard, due to both the chaotic nature of the physics and the computational resources required. Resimulating a scene at higher resolution often produces very different results, and is too expensive to allow many design cycles. We present a method of constraining or guiding a high resolution liquid simulation to stay close to a finalized low resolution version (either simulated or directly animated), restricting the solve to a thin outer shell of liquid around a guide shape. Our method is generally faster than an unconstrained simulation and can be integrated with a standard fluid simulator. We demonstrate several applications, with both simulated and hand-animated inputs.

Guide Shapes for High Resolution Naturalistic Liquid Simulation

Ke-Sen Huang’s  list of 2011 SIGGRAPH papers is here.

The physics-related SIGGRAPH papers so far include:

• Efficient Elasticity for Character Skinning with Contact and Collisions
• Data-Driven Elastic Models for Cloth: Modeling and Measurement
• Solid Simulation with Oriented Particles
• Real-Time Eulerian Water Simulation Using a Restricted Tall Cell Grid
• Sparse Meshless Models of Complex Deformable Objects
• Two-Scale Particle Simulation
• Guide Shapes for High Resolution Naturalistic Liquid Simulation
• Physics-inspired Upsampling for Cloth Simulation in Games
• Sensitive Couture for Interactive Garment Editing and Modeling
• Articulated Swimming Creatures
• Example-Based Elastic Materials
• Large-Scale Dynamic Simulation of Highly Constrained Strands
• Eulerian Solid Simulation with Contact
• Real-Time Large-Deformation Substructuring
• HOT: Hodge-Optimized Triangulations

The  TOG papers being presented at SIGGRAPH related to physics:

• Frame-based Elastic Models
• On the Velocity of an Implicit Surface
• A PML-Based Nonreflective Boundary for Free Surface Fluid Animation
• A Nonsmooth Newton Solver for Capturing Exact Coulomb Friction in Fiber Assemblies

We focus on the challenging problem of simulating thin elastic rods in contact, in the presence of friction. Most previous approaches in computer graphics rely on a linear complementarity formulation for handling contact in a stable way, and approximate Coulombs’s friction law for making the problem tractable. In contrast, following the seminal work by Alart and Curnier in contact mechanics, we simultaneously model contact and exact Coulomb friction as a zero finding problem of a nonsmooth function. A semi-implicit time-stepping scheme is then employed to discretizethe dynamics of rods constrained by frictional contact: this leads to a set of linear equations subject to an equality constraint involving a non-differentiable function. To solve this one-step problem we introduce a simple and practical nonsmooth Newton algorithm, which proves to be reasonably efficient and robust for systems that are not over-constrained. We show that our method is able to finely capture the subtle effects that occur when thin elastic rods with various geometries enter into contact, such as stick-slip instabilities in free configurations, entangling curls, resting contacts in braid-like structures, or the formation of tight knots under large constraints. Our method can be viewed as a first step towards the accurate modeling of dynamic fibrous materials.

A Nonsmooth Newton Solver for Capturing Exact Coulomb Friction in Fiber Assemblies

We present a novel approach to fluid simulation, allowing us to take into account the surface energy in a precise manner. This new approach combines a novel, topology-adaptive approach to deformable interface tracking, called the deformable simplicial complexes method (DSC) with an optimization-based, linear finite element method for solving the incompressible Euler equations. The deformable simplicial complexes track the surface of the fluid: the fluid-air interface is represented explicitly as a piecewise linear surface which is a subset of tetrahedralization of the space, such that the interface can be also represented implicitly as a set of faces separating tetrahedra marked as inside from the ones marked as outside. This representation introduces insignificant and controllable numerical diffusion, allows robust topological adaptivity and provides both a volumetric finite element mesh for solving the fluid dynamics equations as well as direct access to the interface geometry data, making inclusion of a new surface energy term feasible. Furthermore, using an unstructured mesh makes it straightforward to handle curved solid boundaries and gives us a possibility to explore several fluid-solid interaction scenarios.

Optimization-based Fluid Simulation on Unstructured Meshes