Category: Deformables

Accurate Contact Modeling for Multi-rate Single-point Haptic Rendering of Static and Deformable Environments

Thomas Knott, Torsten Kuhlen

Common approaches for the haptic rendering of complex scenarios employ multi-rate simulation schemes. Here, the collision queries or the simulation of a complex deformable object are often performed asynchronously on a lower frequency, while some kind of intermediate contact representation is used to simulate interactions on the haptic rate. However, this can produce artifacts in the haptic rendering when the contact situation quickly changes and the intermediate representation is not able to reflect the changes due to the lower update rate. We address this problem utilizing a novel contact model. It facilitates the creation of contact representations that are accurate for a large range of motions and multiple simulation time-steps.We handle problematic convex contact regions using a local convex decomposition and special constraints for convex areas.We combine our accurate contact model with an implicit temporal integration scheme to create an intermediate mechanical contact representation, which reflects the dynamic behavior of the simulated objects. Moreover, we propose a new iterative solving scheme for the involved constrained dynamics problems.We increase the robustness of our method using techniques from trust region-based optimization. Our approach can be combined with standard methods for the modeling of deformable objects or constraint-based approaches for the modeling of, for instance, friction or joints. We demonstrate its benefits with respect to the simulation accuracy and the quality of the rendered haptic forces in multiple scenarios.

Accurate Contact Modeling for Multi-rate Single-point Haptic Rendering of Static and Deformable Environments

Reconstructing Personalized Anatomical Models for Physics-based Body Animation

Petr Kadlecek, Alexandru-Eugen Ichim, Tiantian Liu, Ladislav Kavan, Jaroslav Krivanek

We present a method to create personalized anatomical models ready for physics-based animation, using only on a set of surface 3D scans. We start by building a template anatomical model of an average male which supports deformations due to both 1) subject-specific variations: shapes and sizes of bones, muscles, and adipose tissues and 2) skeletal poses. Next, we capture a set of 3D scans of an actor in various poses. Our key contribution is formulating and solving a large-scale optimization problem where we solve for both subject-specific and pose-dependent parameters such that our resulting anatomical model explains the captured 3D scans as closely as possible. Compared to data-driven body modeling techniques that focus only on the surface, our approach has the advantage of creating physics-based models, which provide realistic 3D geometry of the bones and muscles, and naturally supports effects such as inertia, gravity, and collisions according to the Newtonian dynamics.

Reconstructing Personalized Anatomical Models for Physics-based Body Animation

Eulerian Solid-Fluid Coupling

Yun Teng, David I.W. Levin, Theodore Kim

We present a new method that achieves a two-way coupling between deformable solids and an incompressible fluid where the underlying geometric representation is entirely Eulerian. Using the recently developed Eulerian Solids approach [Levin et al. 2011], we are able to simulate multiple solids undergoing complex, frictional contact while simultaneously interacting with a fluid. The complexity of the scenarios we are able to simulate surpasses those that we have seen from any previous method. Eulerian Solids have previously been integrated using explicit schemes, but we develop an implicit scheme that allows large time steps to be taken. The incompressibility condition is satisfied in both the solid and the fluid, which has the added benefit of simplifying collision handling.

Eulerian Solid-Fluid Coupling

Vivace: a Practical Gauss-Seidel Method for Stable Soft Body Dynamics

Marco Fratarcangeli, Valentina Tibaldo, Fabio Pellacini

The solution of large sparse systems of linear constraints is at the base of most interactive solvers for physically-based animation of soft body dynamics. We focus on applications with hard and tight per-frame resource budgets, such as video games, where the solution of soft body dynamics needs to be computed in a few milliseconds. Linear iterative methods are preferred in these cases since they provide approximate solutions within a given error tolerance and in a short amount of time. We present a parallel randomized Gauss-Seidel method which can be effectively employed to enable the animation of 3D soft objects discretized as large and irregular triangular or tetrahedral meshes. At the beginning of each frame, we partition the set of equations governing the system using a randomized graph coloring algorithm. The unknowns in the equations belonging to the same partition are independent of each other. Then, all the equations belonging to the same partition are solved at the same time in parallel. Our algorithm runs completely on the GPU and can support changes in the constraints topology. We tested our method as a solver for soft body dynamics within the Projective Dynamics and Position Based Dynamics frameworks. We show how the algorithmic simplicity of this iterative strategy enables great numerical stability and fast convergence speed, which are essential features for physically based animations with fixed and small hard time budgets. Compared to the state of the art, we found our method to be faster and scale better while providing stabler solutions for very small time budgets.

Vivace: a Practical Gauss-Seidel Method for Stable Soft Body Dynamics

Descent Methods for Elastic Body Simulation on the GPU

Huamin Wang, Yin Yang

We show that many existing elastic body simulation approaches can be interpreted as descent methods, under a nonlinear optimization framework derived from implicit time integration. The key question is how to find an effective descent direction with a low computational cost. Based on this concept, we propose a new gradient descent method using Jacobi preconditioning and Chebyshev acceleration. The convergence rate of this method is comparable to that of LBFGS or nonlinear conjugate gradient. But unlike other methods, it requires no dot product operation, making it suitable for GPU implementation. To further improve its convergence and performance, we develop a series of step length adjustment, initialization, and invertible model conversion techniques, all of which are compatible with GPU acceleration. Our experiment shows that the resulting simulator is simple, fast, scalable, memory-efficient, and robust against very large time steps and deformations. It can correctly simulate the deformation behaviors of many elastic materials, as long as their energy functions are second-order differentiable and their Hessian matrices can be quickly evaluated. For additional speedups, the method can also serve as a complement to other techniques, such as multi-grid.

Descent Methods for Elastic Body Simulation on the GPU

High-Resolution Interaction with Corotational Coarsening Models

Rosell Torres, Alejandro Rodríguez, José Miguel Espadero, Miguel A. Otaduy

This paper presents a numerical coarsening method for corotational elasticity, which enables interactive large deformation of high-resolution heterogeneous objects. Our method derives a coarse elastic model from a high-resolution discretization of corotational elasticity with high-resolution boundary conditions. This is in contrast to previous coarsening methods, which derive a coarse elastic model from an unconstrained high-resolution discretization of regular linear elasticity, and then apply corotational computations directly on the coarse setting. We show that previous approaches fail to handle high-resolution boundary conditions correctly, suffering accuracy and robustness problems. Our method, on the other hand, supports efficiently accurate high-resolution boundary conditions, which are fundamental for rich interaction with high-resolution heterogeneous models. We demonstrate the potential of our method for interactive deformation of complex medical imaging data sets.

High-Resolution Interaction with Corotational Coarsening Models

Enriching Triangle Mesh Animations with Physically Based Simulation

Yijing Li, Hongyi Xu, Jernej Barbič

We present a system to combine arbitrary triangle mesh animations with physically based Finite Element Method (FEM) simulation, enabling control over the combination both in space and time. The input is a triangle mesh animation obtained using any method, such as keyframed animation, character rigging, 3D scanning, or geometric shape modeling. The input may be non-physical, crude or even incomplete. The user provides weights, specified using a minimal user interface, for how much physically based simulation should be allowed to modify the animation in any region of the model, and in time. Our system then computes a physically-based animation that is constrained to the input animation to the amount prescribed by these weights. This permits smoothly turning physics on and off over space and time, making it possible for the output to strictly follow the input, to evolve purely based on physically based simulation, and anything in between. Achieving such results requires a careful combination of several system components. We propose and analyze these components, including proper automatic creation of simulation meshes (even for non-manifold and self-colliding undeformed triangle meshes), converting triangle mesh animations into animations of the simulation mesh, and resolving collisions and self-collisions while following the input.

Enriching Triangle Mesh Animations with Physically Based Simulation

Simulating Visual Geometry

Matthias Müller, Nuttapong Chentanez, Miles Macklin

In computer graphics, simulated objects typically have two or three different representations, a visual mesh, a simulation mesh and a collection of convex shapes for collision handling. Using multiple representations requires skilled authoring and complicates object handing at run time. It can also produce visual artifacts such as a mismatch of collision behavior and visual appearance. The reason for using multiple representation has been performance restrictions in real time environments. However, for virtual worlds, we believe that the ultimate goal must be WYSIWYS – what you see is what you simulate, what you can manipulate, what you can touch. In this paper we present a new method that uses the same representation for simulation and collision handling and an almost identical visualization mesh. This representation is very close and directly derived from a visual input mesh which does not have to be prepared for simulation but can be non-manifold, non-conforming and self-intersecting.

Simulating Visual Geometry

XPBD: Position-Based Simulation of Compliant Constrained Dynamics

Miles Macklin, Matthias Muller, Nuttapong Chentanez

We address the long-standing problem of iteration count and time step dependent constraint stiffness in position-based dynamics (PBD). We introduce a simple extension to PBD that allows it to accurately and efficiently simulate arbitrary elastic and dissipative energy potentials in an implicit manner. In addition, our method provides constraint force estimates, making it applicable to a wider range of applications, such those requiring haptic user-feedback. We compare our algorithm to more expensive non-linear solvers and find it produces visually similar results while maintaining the simplicity and robustness of the PBD method.

XPBD: Position-Based Simulation of Compliant Constrained Dynamics

A Robust Method to Extract the Rotational Part of Deformations

Matthias Muller, Jan Bender, Nuttapong Chentanez, Miles Macklin

We present a novel algorithm to extract the rotational part of an arbitrary 3×3 matrix. This problem lies at the core of two popular simulation methods in computer graphics, the co-rotational Finite Element Method and Shape Matching techniques. In contrast to the traditional method based on polar decomposition, degenerate configurations and inversions are handled robustly and do not have to be treated in a special way. In addition, our method can be implemented with only a few lines of code without branches which makes it particularly well suited for GPU-based applications. We demonstrate the robustness, coherence and efficiency of our method by comparing it to stabilized polar decomposition in several simulation scenarios.

A Robust Method to Extract the Rotational Part of Deformations