Smoothed Aggregation Multigrid for Cloth Simulation

Rasmus Tamstorf, Toby Jones, Stephen F. McCormick

Existing multigrid methods for cloth simulation are based on geometric multigrid. While good results have been reported, geometric methods are problematic for unstructured grids, widely varying material properties, and varying anisotropies, and they often have difficulty handling constraints arising from collisions. This paper applies the algebraic multigrid method known as smoothed aggregation to cloth simulation. This method is agnostic to the underlying tessellation, which can even vary over time, and it only requires the user to provide a fine-level mesh. To handle contact constraints efficiently, a prefiltered preconditioned conjugate gradient method is introduced. For highly efficient preconditioners, like the ones proposed here, prefiltering is essential, but, even for simple preconditioners, prefiltering provides significant benefits in the presence of many constraints. Numerical tests of the new approach on a range of examples confirm 6-8X speedups on a fully dressed character with 371k vertices, and even larger speedups on synthetic examples.

Smoothed Aggregation Multigrid for Cloth Simulation

Posted by christopherbatty on November 2nd, 2015 | Comments Off on Smoothed Aggregation Multigrid for Cloth Simulation Posted in Cloth, Collisions, Deformables

Non-manifold Level Sets: A multivalued implicit surface representation with applications to self-collision processing

Nathan Mitchell, Mridul Aanjaneya, Rajsekhar Setaluri, Eftychios Sifakis

Level sets have been established as highly versatile implicit surface representations, with widespread use in graphics applications including modeling and dynamic simulation. Nevertheless, level sets are often presumed to be limited, compared to explicit meshes, in their ability to represent domains with thin topological features (e.g. narrow slits and gaps) or, even worse, material overlap. Geometries with such features may arise from modeling tools that tolerate occasional self-intersections, fracture modeling algorithms that create narrow or zero-width cuts by design, or as transient states in collision processing pipelines for deformable objects. Converting such models to level sets can alter their topology if thin features are not resolved by the grid size. We argue that this ostensible limitation is not an inherent defect of the implicit surface concept, but a collateral consequence of the standard Cartesian lattice used to store the level set values. We propose storing signed distance values on a regular hexahedral mesh which can have multiple collocated cubic elements and non-manifold bifurcation to accommodate non-trivial topology. We show how such non-manifold level sets can be systematically generated from convenient alternative geometric representations. Finally we demonstrate how this representation can facilitate fast and robust treatment of self-collision in simulations of volumetric elastic deformable bodies.

Non-manifold Level Sets: A multivalued implicit surface representation with applications to self-collision processing

Posted by christopherbatty on October 20th, 2015 | Comments Off on Non-manifold Level Sets: A multivalued implicit surface representation with applications to self-collision processing Posted in Collisions, Deformables

TightCCD: Efficient and Robust Continuous Collision Detection using Tight Error Bounds

Zhendong Wang, Min Tang , Ruofeng Tong, and Dinesh Manocha

We present a realtime and reliable continuous collision detection (CCD) algorithm between triangulated models that exploits the floating point hardware capability of current CPUs and GPUs. Our formulation is based on Bernstein Sign Classification that takes advantage of the geometry properties of Bernstein basis and Bézier curves to perform Boolean collision queries. We derive tight numerical error bounds on the computations and employ those bounds to design an accurate algorithm using finite-precision arithmetic. Compared with prior floatingpoint CCD algorithms, our approach eliminates all the false negatives and 90-95% of the false positives. We integrated our algorithm (TightCCD) with physically-based simulation system and observe speedups in collision queries of 5-15X compared with prior reliable CCD algorithms. Furthermore, we demonstrate its benefits in terms of improving the performance or robustness of cloth simulation systems.

TightCCD: Efficient and Robust Continuous Collision Detection using Tight Error Bounds

Posted by christopherbatty on October 16th, 2015 | Comments Off on TightCCD: Efficient and Robust Continuous Collision Detection using Tight Error Bounds Posted in Cloth, Collisions, Deformables

Deformable Objects Collision Handling with Fast Convergence

Siwang Li, Zherong Pan, Jin Huang,  Hujun Bao, Xiaogang Jin

We present a stable and efficient simulator for deformable objects with collisions and contacts. For stability, an optimization derived from the implicit time integrator is solved in each timestep under the inequality constraints coming from collisions. To achieve fast convergence, we extend the MPRGP based solver from handling boxconstraints only to handling general linear constraints and prove its convergence. This generalization introduces a cost of solving dense linear systems in each step, but these systems can be reduced into diagonal ones for efficiency without affecting the general stability via pruning redundant collisions. Our solver is an order of magnitude faster, especially for elastic objects under large deformation compared with iterative constraint anticipation method (ICA), a typical method for stability. The efficiency, robustness and stability are further verified by our results.

Deformable Objects Collision Handling with Fast Convergence

Posted by christopherbatty on October 16th, 2015 | Comments Off on Deformable Objects Collision Handling with Fast Convergence Posted in Collisions, Deformables

An Efficient Boundary Handling with a Modified Density Calculation for SPH

Makoto Fujisawa, Kenjiro T. Miura

We propose a new boundary handling method for smoothed particle hydrodynamics (SPH). Previous approaches required the use of boundary particles to prevent particles from sticking to the boundary. We address this issue by correcting the fundamental equations of SPH with the integration of a kernel function. Our approach is able to directly handle triangle mesh boundaries without the need for boundary particles. We also show how our approach can be integrated into a position-based fluid framework.

An Efficient Boundary Handling with a Modified Density Calculation for SPH

 

Posted by christopherbatty on October 16th, 2015 | Comments Off on An Efficient Boundary Handling with a Modified Density Calculation for SPH Posted in Fluids

Quadratic Contact Energy Model for Multi-Impact Simulation

Tianxiang Zhang, Sheng Li, Guoping Wang, Dinesh Manocha, Hanqiu Sun

Simultaneous multi-impact simulation is a challenging problem in modeling collision for rigid bodies. There are several physical criteria for an ideal model of rigid body collision, but existing models generally fail to meet one or more of them. In order to reveal the inner process of potential energy variation, which is the physical fundamental of collision in a multi-impact system, we propose a novel quadratic contact energy model for rigid body simulation. Through constructing quadratic energy functions with respect to impulse, post-impact reactions of rigid bodies can be computed efficiently. Our model can fulfil all the physical criteria and can simulate various natural phenomena including wave effect in particular. Besides, our model has high compatibility to be embedded into the Linear Complementary Problem (LCP) easily and can provide feasible results with any restitution coefficient. With a solid physical base, our model can solve the simultaneous multi-impact problem efficiently with high fidelity and robustness, as demonstrated in the experiment results.

Quadratic Contact Energy Model for Multi-Impact Simulation

Posted by christopherbatty on October 16th, 2015 | Comments Off on Quadratic Contact Energy Model for Multi-Impact Simulation Posted in Rigid bodies

Model Reduced Variational Fluid Simulation

Beibei Liu, Gemma Mason, Julian Hodgson, Yiying Tong, Mathieu Desbrun

We present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness of coarse spatial and temporal resolutions of geometric integrators, and the simplicity of sub-grid accurate boundary conditions on regular grids to deal with arbitrarily-shaped domains. At the core of our contributions is a functional map approach to fluid simulation for which scalar- and vector-valued eigenfunctions of the Laplacian operator can be easily used as reduced bases. Using a variational integrator in time to preserve liveliness and a simple, yet accurate embedding of the fluid domain onto a Cartesian grid, our model-reduced fluid simulator can achieve realistic animations in significantly less computational time than full-scale non-dissipative methods but without the numerical viscosity from which current reduced methods suffer. We also demonstrate the versatility of our approach by showing how it easily extends to magnetohydrodynamics and turbulence modeling in 2D, 3D and curved domains.

Model Reduced Variational Fluid Simulation

Posted by christopherbatty on October 9th, 2015 | Comments Off on Model Reduced Variational Fluid Simulation Posted in Fluids

Fast Multiple-Fluid Simulation Using Helmholtz Free Energy

Tao Yang, Jian Chang, Bo Ren, Ming Lin, Jian Jun Zhang, Shi-Min Hu

Multiple-fluid interaction is an interesting and common visual phenomenon we often observe. In this paper, we present an energybased Lagrangian method that expands the capability of existing multiple-fluid methods to handle various phenomena, such as extraction, partial dissolution, etc. Based on our user-adjusted Helmholtz free energy functions, the simulated fluid evolves from high-energy states to low-energy states, allowing flexible capture of various mixing and unmixing processes. We also extend the original Cahn-Hilliard equation to be better able to simulate complex fluid-fluid interaction and rich visual phenomena such as motionrelated mixing and position based pattern. Our approach is easily integrated with existing state-of-the-art smooth particle hydrodynamic (SPH) solvers and can be further implemented on top of the position based dynamics (PBD) method, improving the stability and incompressibility of the fluid during Lagrangian simulation under large time steps. Performance analysis shows that our method is at least 4 times faster than the state-of-the-art multiple-fluid method. Examples are provided to demonstrate the new capability and effectiveness of our approach.

Fast Multiple-Fluid Simulation Using Helmholtz Free Energy

Posted by christopherbatty on September 29th, 2015 | Comments Off on Fast Multiple-Fluid Simulation Using Helmholtz Free Energy Posted in Fluids

Wetbrush: GPU-based 3D painting simulation at the bristle level

Zhili Chen, Byungmoon Kim, Daichi Ito, Huamin Wang

We present a real-time painting system that simulates the interactions among brush, paint, and canvas at the bristle level. The key challenge is how to model and simulate sub-pixel paint details, given the limited computational resource in each time step. To achieve this goal, we propose to define paint liquid in a hybrid fashion: the liquid close to the brush is modeled by particles, and the liquid away from the brush is modeled by a density field. Based on this representation, we develop a variety of techniques to ensure the performance and robustness of our simulator under large time steps, including brush and particle simulations in non-inertial frames, a fixed-point method for accelerating Jacobi iterations, and a new Eulerian-Lagrangian approach for simulating detailed liquid effects. The resulting system can realistically simulate not only the motions of brush bristles and paint liquid, but also the liquid transfer processes among different representations. We implement the whole system on GPU by CUDA. Our experiment shows that artists can use the system to draw realistic and vivid digital paintings, by applying the painting techniques that they are familiar with but not offered by many existing systems.

Wetbrush: GPU-based 3D painting simulation at the bristle level

Posted by christopherbatty on September 29th, 2015 | Comments Off on Wetbrush: GPU-based 3D painting simulation at the bristle level Posted in Collisions, Deformables, Fluids, Hair/Rods/Rope, Rods

A Chebyshev Semi-iterative Approach for Accelerating Projective and Position-based Dynamics

Huamin Wang

In this paper, we study the use of the Chebyshev semi-iterative approach in projective and position-based dynamics. Although projective dynamics is fundamentally nonlinear, its convergence behavior is similar to that of an iterative method solving a linear system. Because of that, we can estimate the “spectral radius” and use it in the Chebyshev approach to accelerate the convergence by at least one order of magnitude, when the global step is handled by the direct solver, the Jacobi solver, or even the Gauss-Seidel solver. Our experiment shows that the combination of the Chebyshev approach and the direct solver runs fastest on CPU, while the combination of the Chebyshev approach and the Jacobi solver outperforms any other combination on GPU, as it is highly compatible with parallel computing. Our experiment further shows position-based dynamics can be accelerated by the Chebyshev approach as well, although the effect is less obvious for tetrahedral meshes. The whole approach is simple, fast, effective, GPU-friendly, and has a small memory cost.

A Chebyshev Semi-iterative Approach for Accelerating Projective and Position-based Dynamics

Posted by christopherbatty on September 29th, 2015 | Comments Off on A Chebyshev Semi-iterative Approach for Accelerating Projective and Position-based Dynamics Posted in Deformables
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