Category: Deformables

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

Multi-Resolution Isotropic Strain Limiting

In this paper we describe a fast strain-limiting method that allows stiff, incompliant materials to be simulated efficiently. Unlike prior approaches, which act on springs or individual strain components, this method acts on the strain tensors in a coordinate-invariant fashion allowing isotropic behavior. Our method applies to both two- and three-dimensional strains, and only requires computing the singular value decomposition of the deformation gradient, either a small 2×2 or 3×3 matrix, for each element. We demonstrate its use with triangular and tetrahedral linear-basis elements. For triangulated surfaces in three-dimensional space, we also describe a complementary edge-angle-limiting method to limit out-of-plane bending. All of the limits are enforced through an iterative, non-linear, Gauss-Seidel-like constraint procedure. To accelerate convergence, we propose a novel multi-resolution algorithm that enforces fitted limits at each level of a non-conforming hierarchy. Compared with other constraint-based techniques, our isotropic multi-resolution strain-limiting method is straightforward to implement, efficient to use, and applicable to a wide range of shell and solid materials.

Multi-Resolution Isotropic Strain Limiting

Creature Control in a Fluid Environment

In this paper, we propose a method designed to allow creatures to actively respond to a fluid environment. We explore various objective functions in order to determine ways to direct the behavior of our creatures. Our proposed method works in conjunction with generalized body forces as well as both one-way and two-way coupled fluid forces. As one might imagine, interesting behaviors can be derived from minimizing and maximizing both drag and lift as well as minimizing the effort that a creature’s internal actuators exert. A major application for our work is the automatic specification of secondary motions, for example, certain joints can be animated while others are automatically solved for in order to satisfy the objective function.

Creature Control in a Fluid Environment

A Simple Geometric Model for Elastic Deformations

We advocate a simple geometric model for elasticity: distance between the differential of a deformation and the rotation group. It comes with rigorous differential geometric underpinnings, both smooth and discrete, and is computationally almost as simple and efficient as linear elasticity. Owing to its geometric non-linearity, though, it does not suffer from the usual linearization artifacts. A material model with standard elastic moduli (Lame parameters) falls out naturally, and a minimizer for static problems is easily augmented to construct a fully variational 2nd order time integrator. It has excellent conservation properties even for very coarse simulations, making it very robust. Our analysis was motivated by a number of heuristic, physics-like algorithms from geometry processing (editing, morphing, parameterization, and simulation). Starting with a continuous energy formulation and taking the underlying geometry into account, we simplify and accelerate these algorithms while avoiding common pitfalls. Through the connection with the Biot strain of mechanics, the intuition of previous work that these ideas are “like” elasticity is shown to be spot on.

A Simple Geometric Model for Elastic Deformations

Constraint Based Simulation of Adhesive Contact

Dynamics with contact are often formulated as a constrained optimization problem. This approach allows handling in an integrated manner both non-penetration and frictional constraints. Following developments in the computational mechanics field, we have designed an algorithm for adding the simulation of adhesive contact constraints in the context of state-of-the-art constraint-based contact solvers. We show that implicit adhesion constraints can be handled with minor changes to existing solvers, and we demonstrate our algorithm on a diverse range of objects, including mass-spring cloth, volumetric finite-element models, and rigid bodies.

Constraint Based Simulation of Adhesive Contact

Volume Contact Constraints at Arbitrary Resolution

We introduce a new method for simulating frictional contact between volumetric objects using interpenetration volume constraints. When applied to complex geometries, our formulation results in dramatically simpler systems of equations than those of traditional mesh contact models. Contact between highly detailed meshes can be simplified to a single unilateral constraint equation, or accurately processed at arbitrary geometry-independent resolution with simultaneous sticking and sliding across contact patches.
We exploit fast GPU methods for computing layered depth images, which provides us with the intersection volumes and gradients necessary to formulate the contact equations as linear complementarity problems. Straightforward and popular numerical methods, such as projected Gauss-Seidel, can be used to solve the system.
We demonstrate our method in a number of scenarios and present results involving both rigid and deformable objects at interactive rates.

Volume Contact Constraints at Arbitrary Resolution

Dynamic Local Remeshing for Elastoplastic Simulation

We propose a finite element simulation method that addresses the full range of material behavior, from purely elastic to highly plastic, for physical domains that are substantially reshaped by plastic flow, fracture, or large elastic deformations. To mitigate artificial plasticity, we maintain a simulation mesh in both the current state and the rest shape, and store plastic offsets only to represent the non-embeddable portion of the plastic deformation. To maintain high element quality in a tetrahedral mesh undergoing gross changes, we use a dynamic meshing algorithm that attempts to replace as few tetrahedra as possible, and thereby limits the visual artifacts and artificial diffusion that would otherwise be introduced by repeatedly remeshing the domain from scratch. Our dynamic mesher also locally refines and coarsens a mesh, and even creates anisotropic tetrahedra, wherever a simulation requests it. We illustrate these features with animations of elastic and plastic behavior, extreme deformations, and fracture.

Dynamic Local Remeshing for Elastoplastic Simulation

Unified Simulation of Elastic Rods, Shells, and Solids

We develop an accurate, unified treatment of elastica. Following the method of resultant-based formulation to its logical extreme, we derive a higher-order integration rule, or elaston, measuring stretching, shearing, bending, and twisting along any axis. The theory and accompanying implementation do not distinguish between forms of different dimension (solids, shells, rods), nor between manifold regions and non-manifold junctions. Consequently, a single code accurately models a diverse range of elastoplastic behaviors, including buckling, writhing, cutting and merging. Emphasis on convergence to the continuum sets us apart from early unification efforts.

Unified Simulation of Elastic Rods, Shells, and Solids

Anisotropic Friction for Deformable Surfaces and Solids

This paper presents a method for simulating anisotropic friction for deforming surfaces and solids. Frictional contact is a complex phenomenon that fuels research in mechanical engineering, computational contact mechanics, composite material design and rigid body dynamics, to name just a few. Many real-world materials have anisotropic surface properties. As an example, most textile materials exhibit direction-dependent frictional behavior, but despite its tremendous impact on visual appearance, only simple isotropic models have been considered for cloth and solid simulation so far.
In this work, we propose a simple, application-oriented but physically sound model that extends existing methods to account for anisotropic friction.
The sliding properties of surfaces are encoded in friction tensors, which allows us to model frictional resistance freely along arbitrary directions. We also consider heterogeneous and asymmetric surface roughness and demonstrate the increased simulation quality on a number of two- and three-dimensional examples. Our method is computationally efficient and can easily be integrated into existing systems.

Anisotropic Friction for Deformable Surfaces and Solids