Interactive Editing of Deformable Simulations

Jernej Barbic, Funshing Sin, Eitan Grinspun

We present an interactive animation editor for complex deformable object animations. Given an existing animation, the artist directly manipulates the deformable body at any time frame, and the surrounding animation immediately adjusts in response. The automatic adjustments are designed to respect physics, preserve detail in both the input motion and geometry, respect prescribed bilateral contact constraints, and controllably and smoothly decay in spacetime. While the utility of interactive editing for rigid body and articulated figure animations is widely recognized, a corresponding approach to deformable bodies has not been technically feasible before. We achieve interactive rates by combining spacetime model reduction, rotation-strain coordinate warping, linearized elasticity, and direct manipulation. This direct editing tool can serve the final stages of animation production, which often call for detailed, direct adjustments that are otherwise tedious to realize by re-simulation or frame-by-frame editing.

Interactive Editing of Deformable Simulations

Data-Driven Estimation of Cloth Simulation Models

Eder Miguel, Derek Bradley, Bernhard Thomaszewski, Bernd Bickel, Wojciech Matusik, Miguel Otaduy, Steve Marschner

Progress in cloth simulation for computer animation and apparel design has led to a multitude of deformation models, each with its own way of relating geometry, deformation, and forces. As simulators improve, differences between these models become more important, but it is difficult to choose a model and a set of parameters to match a given real material simply by looking at simulation results. This paper provides measurement and fitting methods that allow nonlinear models to be fit to the observed deformation of a particular cloth sample. Unlike standard textile testing, our system measures complex 3D deformations of a sheet of cloth, not just one-dimensional force–displacement curves, so it works under a wider range of deformation conditions. The fitted models are then evaluated by comparison to measured deformations with motions very different from those used for fitting.

Data-Driven Estimation of Cloth Simulation Models

Efficient Geometrically Exact Continuous Collision Detection

Tyson Brochu, Essex Edwards, Robert Bridson

Continuous collision detection (CCD) between deforming triangle mesh elements in 3D is a critical tool for many applications. The standard method involving a cubic polynomial solver is vulnerable to rounding error, requiring the use of ad hoc tolerances, and nevertheless is particularly fragile in (near-)planar cases. Even with per-simulation tuning, it may still cause problems by missing collisions or erroneously flagging non-collisions. We present a geometrically exact alternative guaranteed to produce the correct Boolean result (significant collision or not) as if calculated with exact arithmetic, even in degenerate scenarios. Our critical insight is that only the parity of the number of collisions is needed for robust simulation, and this parity can be calculated with simpler non-constructive predicates. In essence we analyze the roots of the nonlinear system of equations defining CCD through careful consideration of the boundary of the parameter domain. The use of new conservative culling and interval filters allows typical simulations to run as fast as with the non-robust version, but without need for tuning or worries about failure cases even in geometrically degenerate scenarios. We demonstrate the effectiveness of geometrically exact detection with a novel adaptive cloth simulation, the first to guarantee to remain intersection-free despite frequent curvature-driven remeshing.

Efficient Geometrically Exact Continuous Collision Detection

Computational Design of Rubber Balloons

Melina Skouras, Bernhard Thomaszewski, Bernd Bickel, Markus Gross

This paper presents an automatic process for fabrication-oriented design of custom-shaped rubber balloons. We cast computational balloon design as an inverse problem: given a target shape, we compute an optimal balloon that, when inflated, approximates the target as closely as possible. To solve this problem numerically, we propose a novel physics-driven shape optimization method, which combines physical simulation of inflatable elastic membranes with a dedicated constrained optimization algorithm. We validate our approach by fabricating balloons designed with our method and comparing their inflated shapes to the results predicted by simulation. An extensive set of manufactured sample balloons demonstrates the shape diversity that can be achieved by our method.

Computational Design of Rubber Balloons

Updated Sparse Cholesky Factors for Corotational Elastodynamics

Florian Hecht, Yeon Jin Lee, Jonathan Shewchuk, James O’Brien

We present warp-canceling corotation, a nonlinear finite element formulation for elastodynamic simulation that achieves fast performance by making only partial or delayed changes to the simulation’s linearized system matrices. Coupled with an algorithm for incremental updates to a sparse Cholesky factorization, the method realizes the stability and scalability of a sparse direct method without the need for expensive refactorization at each time step. This finite element formulation combines the widely used corotational method with stiffness warping so that changes in the per-element rotations are initially approximated by inexpensive per-node rotations. When the errors of this approximation grow too large, the per-element rotations are selectively corrected by updating parts of the matrix chosen according to locally measured errors. These changes to the system matrix are propagated to its Cholesky factor by incremental updates that are much faster than refactoring the matrix from scratch. A nested dissection ordering of the system matrix gives rise to a hierarchical factorization in which changes to the system matrix cause limited, well-structured changes to the Cholesky factor. We show examples of simulations that demonstrate that the proposed formulation produces results that are visually comparable to those produced by a standard corotational formulation. Because our method requires computing only partial updates of the Cholesky factor, it is substantially faster than full refactorization and outperforms widely used iterative methods such as preconditioned conjugate gradients. Our method supports a controlled trade-off between accuracy and speed, and unlike most iterative methods its performance does not slow for stiffer materials but rather it actually improves.

Updated Sparse Cholesky Factors for Corotational Elastodynamics

Asynchronous Integration with Phantom Meshes

David Harmon, Qingnan Zhou, Denis Zorin

Asynchronous variational integration of layered contact models provides a framework for robust collision handling, correct physical behavior, and guaranteed eventual resolution of even the most difficult contact problems. Yet, even for low-contact scenarios, this approach is significantly slower compared to its less robust alternatives — often due to handling of stiff elastic forces in an explicit framework. We propose a method that retains the guarantees, but allows for variational implicit integration of some of the forces, while maintaining asynchronous integration needed for contact handling. Our method uses phantom meshes for calculations with stiff forces, which are then coupled to the original mesh through constraints. We use the augmented discrete Lagrangian of the constrained system to derive a variational integrator with the desired conservation properties.

Asynchronous Integration with Phantom Meshes

Sensitive Couture for Interactive Garment Editing and Modeling

Nobuyuki Umetani, Danny M. Kaufman, Takeo Igarashi, Eitan Grinspun

We present a novel interactive tool for garment design that enables, for the first time, interactive bidirectional editing between 2D patterns and 3D high-fidelity simulated draped forms. This provides a continuous, interactive, and natural design modality in which 2D and 3D representations are simultaneously visible and seamlessly maintain correspondence. Artists can now interactively edit 2D pattern designs and immediately obtain stable accurate feedback online, thus enabling rapid prototyping and an intuitive understanding of complex drape form.

Sensitive Couture for Interactive Garment Editing and Modeling

Physics-inspired Upsampling for Cloth Simulation in Games

Ladislav Kavan, Dan Gerszewski, Peter-Pike Sloan, Adam W. Bargteil

We propose a method for learning linear upsampling operators for physically-based cloth simulation, allowing us to enrich coarse meshes with mid-scale details in minimal time and memory budgets, as required in computer games. In contrast to classical subdivision schemes, our operators adapt to a specific context (e.g. a flag flapping in the wind or a skirt worn by a character), which allows them to achieve higher detail. Our method starts by pre-computing a pair of coarse and fine training simulations aligned with tracking constraints using harmonic test functions. Next, we train the upsampling operators with a new regularization method that enables us to learn mid-scale details without overfitting. We demonstrate generalizability to unseen conditions such as different wind velocities or novel character motions. Finally, we discuss how to re-introduce high frequency details not explainable by the coarse mesh alone using oscillatory modes.

Physics-inspired Upsampling for Cloth Simulation in Games

Data-Driven Elastic Models for Cloth: Modeling and Measurement

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

Fast and Scalable CPU/GPU Collision Detection for Rigid and Deformable Surfaces

We present a new hybrid CPU/GPU collision detection technique for rigid and deformable objects based on spatial subdivision. Our approach efficiently exploits the massive computational capabilities of modern CPUs and GPUs commonly found in off-the-shelf computer systems. The algorithm is specifically tailored to be highly scalable on both the CPU and the GPU sides. We can compute discrete and continuous external and self-collisions of non-penetrating rigid and deformable objects consisting of many tens of thousands of triangles in few milliseconds on a modern PC. Our approach is orders of magnitude faster than earlier CPU-based approaches and up to twice as fast as the most recent GPU-based techniques.

Fast and Scalable CPU/GPU Collision Detection for Rigid and Deformable Surfaces