A Skinned Tetrahedral Mesh for Hair Animation and Hair-Water Interaction

Minjae Lee, David Hyde, Michael Bao, Ronald Fedkiw

We propose a novel framework for hair animation as well as hair-water interaction that supports millions of hairs. First, we develop a hair animation framework that embeds hair into a tetrahedralized volume mesh that we kinematically skin to deform and follow the exterior of an animated character. Allowing the hairs to follow their precomputed embedded locations in the kinematically deforming skinned mesh already provides visually plausible behavior. Creating a copy of the tetrahedral mesh, endowing it with springs, and attaching it to the kinematically skinned mesh creates more dynamic behavior. Notably, the springs can be quite weak and thus efficient to simulate because they are structurally supported by the kinematic mesh. If independent simulation of individual hairs or guide hairs is desired, they too benefit from being anchored to the kinematic mesh dramatically increasing efficiency as weak springs can be used while still supporting interesting and dramatic hairstyles. Furthermore, we explain how to embed these dynamic simulations into the kinematically deforming skinned mesh so that they can be used as part of a blendshape system where an artist can make many subsequent iterations without requiring any additional simulation. Although there are many applications for our newly proposed approach to hair animation, we mostly focus on the particularly challenging problem of hair-water interaction. While doing this, we discuss how porosities are stored in the kinematic mesh, how the kinematically deforming mesh can be used to apply drag and adhesion forces to the water, etc.

A Skinned Tetrahedral Mesh for Hair Animation and Hair-Water Interaction

Posted by christopherbatty on February 24th, 2018 | Comments Off on A Skinned Tetrahedral Mesh for Hair Animation and Hair-Water Interaction Posted in Deformables, Fluids, Hair/Rods/Rope

Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation

Yu Ju Chen, Uri M. Ascher, Dinesh K. Pai

High quality simulations of the dynamics of soft flexible objects can be rather costly, because the assembly of internal forces through an often nonlinear stiffness at each time step is expensive. Many standard implicit integrators introduce significant, time-step dependent artificial damping. Here we propose and demonstrate the effectiveness of an exponential Rosenbrock-Euler (ERE) method which avoids discretization-dependent artificial damping. The method is relatively inexpensive and works well with the large time steps used in computer graphics. It retains correct qualitative behaviour even in challenging circumstances involving non-convex elastic energies. Our integrator is designed to handle and perform well even in the important cases where the symmetric stiffness matrix is not positive definite at all times. Thus we are able to address a wider range of practical situations than other related solvers. We show that our system performs efficiently for a wide range of soft materials.

Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation

Posted by christopherbatty on February 22nd, 2018 | Comments Off on Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation Posted in Deformables

Efficient BVH-based Collision Detection Scheme with Ordering and Restructuring

X. L. Wang, M. Tang, D. Manocha, Ruo-Feng Tong

Bounding volume hierarchy (BVH) has been widely adopted as the acceleration structure in broad-phase collision detection. Previous state-of-the-art BVH-based collision detection approaches exploited the spatio-temporal coherence of simulations by maintaining a bounding volume test tree (BVTT) front. A major drawback of these algorithms is that large deformations in the scenes decrease culling efficiency and slow down collision queries. Moreover, for front-based methods, the inefficient caching on GPU caused by the arbitrary layout of BVH and BVTT front nodes becomes a critical performance issue. We present a fast and robust BVH-based collision detection scheme on GPU that addresses the above problems by ordering and restructuring BVHs and BVTT fronts. Our techniques are based on the use of histogram sort and an auxiliary structure BVTT front log, through which we analyze the dynamic status of BVTT front and BVH quality. Our approach efficiently handles inter- and intra-object collisions and performs especially well in simulations where there is considerable spatio-temporal coherence. The benchmark results demonstrate that our approach is significantly faster than the previous BVH-based method, and also outperforms other state-of-the-art spatial subdivision schemes in terms of speed.

Efficient BVH-based Collision Detection Scheme with Ordering and Restructuring

Posted by christopherbatty on February 16th, 2018 | Comments Off on Efficient BVH-based Collision Detection Scheme with Ordering and Restructuring Posted in Collisions

Stabilizing Integrators for Real-Time Physics

Dimitar Dinev, Tiantian Liu, Ladislav Kavan

We present a new time integration method featuring excellent stability and energy conservation properties, making it particularly suitable for real-time physics. The commonly used backward Euler method is stable but introduces artificial damping. Methods such as implicit midpoint do not suffer from artificial damping but are unstable in many common simulation scenarios. We propose an algorithm that blends between the implicit midpoint and forward/backward Euler integrators such that the resulting simulation is stable while introducing only minimal artificial damping. We achieve this by tracking the total energy of the simulated system, taking into account energy-changing events: damping and forcing. To facilitate real-time simulations, we propose a local/global solver, similar to Projective Dynamics, as an alternative to Newton’s method. Compared to the original Projective Dynamics, which is derived from backward Euler, our final method introduces much less numerical damping at the cost of minimal computing overhead. Stability guarantees of our method are derived from the stability of backward Euler, whose stability is a widely accepted empirical fact. However, to our knowledge, theoretical guarantees have so far only been proven for linear ODEs. We provide preliminary theoretical results proving the stability of backward Euler also for certain cases of nonlinear potential functions.

Stabilizing Integrators for Real-Time Physics

Posted by christopherbatty on February 7th, 2018 | Comments Off on Stabilizing Integrators for Real-Time Physics Posted in Cloth, Deformables

Fast Fluid Simulations with Sparse Volumes on the GPU

Kui Wu, Nghia Truong, Cem Yuksel, Rama Hoetzlein

We introduce efficient, large scale fluid simulation on GPU hardware using the fluid-implicit particle (FLIP) method over a sparse hierarchy of grids represented in NVIDIA GVDB Voxels. Our approach handles tens of millions of particles within a virtually unbounded simulation domain. We describe novel techniques for parallel sparse grid hierarchy construction and fast incremental updates on the GPU for moving particles. In addition, our FLIP technique introduces sparse, work efficient parallel data gathering from particle to voxel, and a matrix-free GPU-based conjugate gradient solver optimized for sparse grids. Our results show that our method can achieve up to an order of magnitude faster simulations on the GPU as compared to FLIP simulations running on the CPU.

Fast Fluid Simulations with Sparse Volumes on the GPU

Posted by christopherbatty on February 1st, 2018 | Comments Off on Fast Fluid Simulations with Sparse Volumes on the GPU Posted in Fluids

Eurographics 2018

Posted by christopherbatty on January 30th, 2018 | Comments Off on Eurographics 2018 Posted in Uncategorized

Direct Position-Based Solver for Stiff Rods

Crispin Deul, Tassilo Kugelstadt, Marcel Weiler, Jan Bender

In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the Position-Based Dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of non-linear equations using a non-linear Gauss-Seidel solver. However, this solver requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast we use Newton iterations in combination with our direct solver to solve the non-linear equations which significantly improves convergence by solving all constraints of an acyclic structure (tree), simultaneously. Our solver only requires a few Newton iterations to achieve high stiffness and inextensibility. We model inextensible rods and trees using rigid segments connected by constraints. Bending and twisting constraints are derived from the well-established Cosserat model. The high performance of our solver is demonstrated in highly realistic simulations of rods consisting of multiple ten-thousand segments. In summary, our method allows the efficient simulation of stiff rods in the Position-Based Dynamics framework with a speedup of two orders of magnitude compared to the original XPBD approach.

Direct Position-Based Solver for Stiff Rods

Posted by christopherbatty on January 30th, 2018 | Comments Off on Direct Position-Based Solver for Stiff Rods Posted in Hair/Rods/Rope, Rods

A Physically Consistent Implicit Viscosity Solver for SPH Fluids

Marcel Weiler, Dan Koschier, Magnus Brand, Jan Bender

In this paper, we present a novel physically consistent implicit solver for the simulation of highly viscous fluids using the Smoothed Particle Hydrodynamics (SPH) formalism. Our method is the result of a theoretical and practical in-depth analysis of the most recent implicit SPH solvers for viscous materials. Based on our findings, we developed a list of requirements that are vital to produce a realistic motion of a viscous fluid. These essential requirements include momentum conservation, a physically meaningful behavior under temporal and spatial refinement, the absence of ghost forces induced by spurious viscosities and the ability to reproduce complex physical effects that can be observed in nature. On the basis of several theoretical analyses, quantitative academic comparisons and complex visual experiments we show that none of the recent approaches is able to satisfy all requirements. In contrast, our proposed method meets all demands and therefore produces realistic animations in highly complex scenarios. We demonstrate that our solver outperforms former approaches in terms of physical accuracy and memory consumption while it is comparable in terms of computational performance. In addition to the implicit viscosity solver, we present a method to simulate melting objects. Therefore, we generalize the viscosity model to a spatially varying viscosity field and provide an SPH discretization of the heat equation.

A Physically Consistent Implicit Viscosity Solver for SPH Fluids

Posted by christopherbatty on January 30th, 2018 | Comments Off on A Physically Consistent Implicit Viscosity Solver for SPH Fluids Posted in Fluids

Stable Neo-Hookean Flesh Simulation

Breannan Smith, Fernando de Goes, Theodore Kim

Non-linear hyperelastic energies play a key role in capturing the fleshy appearance of virtual characters. Real-world, volume-preserving biological tissues have Poisson’s ratios near 1/2, but numerical simulation within this regime is notoriously challenging. In order to robustly capture these visual characteristics, we present a novel version of Neo-Hookean elasticity. Our model maintains the fleshy appearance of the Neo-Hookean model, exhibits superior volume preservation, and is robust to extreme kinematic rotations and inversions. We obtain closed-form expressions for the eigenvalues and eigenvectors of all of the system’s components, which allows us to directly project the Hessian to semi-positive-definiteness, and also leads to insights into the numerical behavior of the material. These findings also inform the design of more sophisticated hyperelastic models, which we explore by applying our analysis to Fung and Arruda-Boyce elasticity. We provide extensive comparisons against existing material models.

Stable Neo-Hookean Flesh Simulation

Posted by christopherbatty on December 14th, 2017 | Comments Off on Stable Neo-Hookean Flesh Simulation Posted in Deformables

A Polynomial Particle-In-Cell Method

Chuyuan Fu, Qi Guo, Theodore Gast, Chenfanfu Jiang, Joseph Teran

Recently the Affine Particle-In-Cell (APIC) Method was proposed by Jiang et al.[2015; 2017b] to improve the accuracy of the transfers in Particle-In-Cell (PIC) [Harlow 1964] techniques by augmenting each particle with a locally
affine, rather than locally constant description of the velocity. This reduced the dissipation of the original PIC without suffering from the noise present in the historic alternative, Fluid-Implicit-Particle (FLIP) [Brackbill and Ruppel 1986]. We present a generalization of APIC by augmenting each particle with a more general local function. By viewing the grid-to-particle transfer as a linear and angular momentum conserving projection of the particle-wise local grid velocities onto a reduced basis, we greatly improve the energy and vorticity conservation over the original APIC. Furthermore, we show that the cost of the generalized projection is negligible over APIC when using a particular class of local polynomial functions. Lastly, we note that our method retains the filtering property of APIC and PIC and thus has similar robustness to noise.

A Polynomial Particle-In-Cell Method

Posted by christopherbatty on December 14th, 2017 | Comments Off on A Polynomial Particle-In-Cell Method Posted in Deformables, Fluids
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