Category: Uncategorized

Floyd M. Chitalu, Christophe Dubach, Taku Komura

We present a simple, efficient and low-memory technique, targeting fast construction of bounding volume hierarchies (BVH) for broad-phase collision detection. To achieve this, we devise a novel representation of BVH trees in memory. We develop a mapping of the implicit index representation to compact memory locations, based on simple bit-shifts, to then construct andevaluate bounding volume test trees (BVTT) during collision detection with real-time performance. We model the topology of the BVH tree implicitly as binary encodings which allows us to determine the nodes missing from a complete binary tree using the binary representation of the number of missing nodes. The simplicity of our technique allows for fast hierarchy construction achieving over6×speedup over the state-of-the-art. Making use of these characteristics, we show that not only it is feasible to rebuild the BVH at every frame, but that using our technique, it is actually faster than refitting and more memory efficient.

Binary Ostensibly-Implicit Trees for Fast Collision Detection

Camille Schreck, Chris Wojtan

This paper introduces a simple method for simulating highly anisotropic elastoplastic material behaviors like the dissolution of fibrous phenomena (splintering wood, shredding bales of hay) and materials composed of large numbers of irregularly-shaped bodies (piles of twigs, pencils, or cards). We introduce a simple transformation of the anisotropic problem into an equivalent isotropic one, and we solve this new “fictitious’’ isotropic problem using an existing simulator based on the material point method. Our approach results in minimal changes to existing simulators, and it allows us to re-use popular isotropic plasticity models like the Drucker-Prager yield criterion instead of inventing new anisotropic plasticity models for every phenomenon we wish to simulate.

A Practical Method for Animating Anisotropic Elastoplastic Materials

Ran Luo, Weiwei Xu, Tianjia Shao, Hongyi Xu, Yin Yang

In deformable simulation, an important computing task is to calculate the gradient and derivative of the strain energy function in order to infer the corresponding internal force and tangent stiffness matrix. The standard numerical routine is the finite difference method, which evaluates the target function multiple times under a small real-valued perturbation. Unfortunately, the subtractive cancellation prevents us from setting this perturbation sufficiently small, and the regular finite difference is doomed for computing problems requiring a high-accuracy derivative evaluation. In this paper, we graft a new finite difference scheme, namely the complex finite difference(CFD), with physics-based animation. CFD is based on the complex Taylor series expansion, which avoids the subtraction for the first-order derivative approximation. As a result, one can use a very small perturbation to calculate the numerical derivative that is as accurate as its analytic counterpart. We significantly accelerate the original CFD method so that it is also as efficient as the analytic derivative. This is achieved by discarding high-order error terms, decoupling real and imaginary calculations, replacing costly functions based on the theory of equivalent infinitesimal, and isolating the propagation of the perturbation in composite/nesting functions. CFD can be further augmented with the multicomplex Taylor expansion and Cauchy-Riemann formula to handle higher-order derivatives and tensor-valued functions. We demonstrate the accuracy, convenience, and efficiency of this new numerical routine in the context of deformable simulation – one can easily deploy a robust simulator for general hyperelastic materials, including user-crafted ones to cater to specific needs in different applications. Higher-order derivatives of the energy can be readily computed to construct modal derivative bases for reduced real-time simulation. Inverse simulation problems can also be conveniently solved using gradient/Hessian based optimization procedures.

Accelerated complex-step finite difference for expedient deformable simulation

Tetsuya Takahashi, Ming C. Lin

In physically-based simulation, it is essential to choose appropriate material parameters to generate desirable simulation results. In many cases, however, choosing appropriate material parameters is very challenging, and often tedious trial-and-error parameter tuning steps are inevitable. In this paper, we propose a real-to-virtual parameter transfer framework that identifies material parameters of viscous fluids with example video data captured from real-world phenomena. Our method first extracts positional data of fluids and then uses the extracted data as a reference to identify the viscosity parameters, combining forward viscous fluid simulations and parameter optimization in an iterative process. We evaluate our method with a range of synthetic and real-world example data, and demonstrate that our method can identify the hidden physical variables and viscosity parameters. This set of recovered physical variables and parameters can then be effectively used in novel scenarios to generate viscous fluid behaviors visually consistent with the example videos.

Video-Guided Real-to-Virtual Parameter Transfer for Viscous Fluids

We present a novel and general framework for the design and control of underwater soft-bodied animals. The whole body of an animal consisting of soft tissues is modeled by tetrahedral and triangular FEM meshes. The contraction of muscles embedded in the soft tissues actuates the body and limbs to move. We present a novel muscle excitation model that mimics the anatomy of muscular hydrostats and their muscle excitation patterns. Our deep reinforcement learning algorithm equipped with the muscle excitation model successfully learned the control policy of soft-bodied animals, which can be physically simulated in real-time, controlled interactively, and resilient to external perturbations. We demonstrate the effectiveness of our approach with various simulated animals including octopuses, lampreys, starfishes, stingrays, and cuttlefishes. They learn diverse behaviors such as swimming, grasping, and escaping from a bottle. We also implemented a simple user interface system that allows the user to easily create their creatures.

SoftCon: Simulation and Control of Soft-Bodied Animals with Biomimetic Actuators

Christian Hafner, Christian Schumacher, Espen Knoop, Thomas Auzinger, Bernd Bickel, Moritz Bächer

We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models.

X-CAD: Optimizing CAD Models with Extended Finite Elements

Albert Peiret, Sheldon Andrews, József Kövecses, Paul G. Kry, Marek Teichmann

Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on non-overlapping domain decomposition with the Schur complement method, which we extend to systems involving contact formulated as a mixed bounds linear complementarity problem. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the active constraints to compute the effective mass of subsystems within the interface solve, we obtain an exact solution. We demonstrate that our simulations have preferable behavior compared to standard iterative solvers and substructuring techniques based on the exchange of forces at interface bodies. We observe considerable speedups for structured simulations where a user-defined partitioning can be applied, and moderate speedups for unstructured simulations, such as piles of bodies. In the latter case, we propose an automatic partitioning strategy based on the degree of bodies in the constraint graph. Because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.

Schur Complement-based Substructuring of Stiff Multibody Systems with Contact

Tassilo Kugelstadt, Andreas Longva, Nils Thuerey, Jan Bender

We propose a novel implicit density projection approach for hybrid Eulerian/Lagrangian methods like FLIP and APIC to enforce volume conservation of incompressible liquids. Our approach is able to robustly recover from highly degenerate configurations and incorporates volume-conserving boundary handling. A problem of the standard divergence-free pressure solver is that it only has a differential view on density changes. Numerical volume errors, which occur due to large time steps and the limited accuracy of pressure projections, are invisible to the solver and cannot be corrected. Moreover, these errors accumulate over time and can lead to drastic volume changes, especially in long-running simulations or interactive scenarios. Therefore, we introduce a novel method that enforces constant density throughout the fluid. The density itself is tracked via the particles of the hybrid Eulerian/Lagrangian simulation algorithm. To achieve constant density, we use the continuous mass conservation law to derive a pressure Poisson equation which also takes density deviations into account. It can be discretized with standard approaches and easily implemented into existing code by extending the regular pressure solver. Our method enables us to relax the strict time step and solver accuracy requirements of a regular solver, leading to significantly higher performance. Moreover, our approach is able to push fluid particles out of solid obstacles without losing volume and generates more uniform particle distributions, which makes frequent particle resampling unnecessary. We compare the proposed method to standard FLIP and APIC and to previous volume correction approaches in several simulations and demonstrate significant improvements in terms of incompressibility, visual realism and computational performance.

Implicit Density Projection for Volume Conserving Liquids

Jan Bender, Tassilo Kugelstadt, Marcel Weiler, Dan Koschier

In this paper, we present a novel method for the robust handling of static and dynamic rigid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. We build upon the ideas of the density maps approach which has been introduced recently by Koschier and Bender. They precompute the density contributions of solid boundaries and store them on a spatial grid which can be efficiently queried during runtime. This alleviates the problems of commonly used boundary particles, like bumpy surfaces and inaccurate pressure forces near boundaries. Our method is based on a similar concept but we precompute the volume contribution of the boundary geometry and store it on a grid. This maintains all benefits of density maps but offers a variety of advantages which are demonstrated in several experiments. Firstly, in contrast to the density maps method we can compute derivatives in the standard SPH manner by differentiating the kernel function. This results in smooth pressure forces, even for lower map resolutions, such that precomputation times and memory requirements are reduced by more than two orders of magnitude compared to density maps. Furthermore, this directly fits into the SPH concept so that volume maps can be seamlessly combined with existing SPH methods. Finally, the kernel function is not baked into the map such that the same volume map can be used with different kernels. This is especially useful when we want to incorporate common surface tension or viscosity methods that use different kernels than the fluid simulation.

Volume Maps: An Implicit Boundary Representation for SPH

Michael Tao, Christopher Batty, Eugene Fiume, David IW Levin

Although geometry arising “in the wild” most often comes in the form of a surface representation, a plethora of geometrical and physical applications require the construction of volumetric embeddings either of the geometry itself or the domain surrounding it. Cartesian cut-cell-based mesh generation provides an attractive solution in which volumetric elements are constructed from the intersection of the input surface geometry with a uniform or adaptive hexahedral grid. This choice, especially common in computational fluid dynamics, has the potential to efficiently generate accurate, surface-conforming cells; unfortunately, current solutions are often slow, fragile, or cannot handle many common topological situations. We therefore propose a novel, robust cut-cell construction technique for triangle surface meshes that explicitly computes the precise geometry of the intersection cells, even on meshes that are open or non-manifold. Its fundamental geometric primitive is the intersection of an arbitrary segment with an axis-aligned plane. Beginning from the set of intersection points between triangle mesh edges and grid planes, our bottom-up approach robustly determines cut-edges, cut-faces, and finally cut-cells, in a manner designed to guarantee topological correctness. We demonstrate its effectiveness and speed on a wide range of input meshes and grid resolutions, and make the code available as open source.

Mandoline: Robust Cut-Cell Generation for Arbitrary Triangle Meshes