Physics-Based Animation

Marco Romeo, Carlos Monteagudo, Daniel Sánchez‐Quirós

Recent research on muscle and fascia simulation for visual effects relies on numerical methods such as the finite element method or finite volume method. These approaches produce realistic results, but require high computational time and are complex to set up. On the other hand, position‐based dynamics offers a fast and controllable solution to simulate surfaces and volumes, but there is no literature on how to implement constraints that could be used to realistically simulate muscles and fascia for digital creatures with this method. In this paper, we extend the current state‐of‐the‐art in Position‐Based Dynamics to efficiently compute realistic skeletal muscle and superficial fascia simulation. In particular, we embed muscle fibres in the solver by adding an anisotropic component to the distance constraints between mesh points and apply overpressure to realistically model muscle volume changes under contraction. In addition, we also define a modified distance constraint for the fascia that allows compression and enables the user to scale the constraint’s original distance to gain elastic potential at rest. Finally, we propose a modification of the extended position‐based dynamics algorithm to properly compute different sets of constraints and describe other details for proper simulation of character’s muscle and fascia dynamics.

Muscle and Fascia Simulation with Extended Position Based Dynamics

Mridul Aanjaneya, Chengguizi Han, Ryan Goldade, Christopher Batty

We present an efficient geometric Multigrid solver for simulating viscous liquids based on the variational approach of [Batty and Bridson 2008]. Although the governing equations for viscosity are elliptic, the strong coupling between different velocity components in the discrete stencils mandates the use of more exotic smoothing techniques to achieve textbook Multigrid efficiency. Our key contribution is the design of a novel box smoother involving small and sparse systems (at most 9×9 in 2D and 15×15 in 3D), which yields excellent convergence rates and performance improvements of 3.5x – 13.8x over a naïve Multigrid approach. We employ a hybrid approach by using a direct solver only inside the box smoother and keeping the remaining pipeline assembly-free, allowing our solver to efficiently accommodate more than 194 million degrees of freedom, while occupying a memory footprint of less than 16 GB. To reduce the computational overhead of using the box smoother, we precompute the Cholesky factorization of the subdomain system matrix for all interior degrees of freedom. We describe how the variational formulation, which requires volume weights computed at the centers of cells, edges, and faces, can be naturally accommodated in the Multigrid hierarchy to properly enforce boundary conditions. Our proposed Multigrid solver serves as an excellent preconditioner for Conjugate Gradients, outperforming existing state-of-the-art alternatives. We demonstrate the efficacy of our method on several high resolution examples of viscous liquid motion including two-way coupled interactions with rigid bodies.

An Efficient Geometric Multigrid Solver for Viscous Liquids

Maximilian Werhahn, You Xie, Mengyu Chu, Nils Thuerey

We propose a novel method to up-sample volumetric functions with generative neural networks using several orthogonal passes. Our method decomposes generative problems on Cartesian field functions into multiple smaller sub-problems that can be learned more efficiently. Specifically, we utilize two separate generative adversarial networks: the first one up-scales slices which are parallel to the XY- plane, whereas the second one refines the whole volume along the Z- axis working on slices in the YZ- plane. In this way, we obtain full coverage for the 3D target function and can leverage spatio-temporal supervision with a set of discriminators. Additionally, we demonstrate that our method can be combined with curriculum learning and progressive growing approaches. We arrive at a first method that can up-sample volumes by a factor of eight along each dimension, i.e., increasing the number of degrees of freedom by 512. Large volumetric up-scaling factors such as this one have previously not been attainable as the required number of weights in the neural networks renders adversarial training runs prohibitively difficult. We demonstrate the generality of our trained networks with a series of comparisons to previous work, a variety of complex 3D results, and an analysis of the resulting performance.

A Multi-Pass GAN for Fluid Flow Super-Resolution

• Fast Simulation of Deformable Characters with Articulated Skeletons in Projective Dynamics
• VIPER: Volume Invariant Position-based Elastic Rods
• A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects
• Small Steps in Physics Simulation
• Building Accurate Physics-based Face Models from Data
• A Robust Volume Conserving Method for Character-Water Interaction
• An Efficient Geometric Multigrid Solver for Viscous Liquids
• A Second-Order Advection-Reflection Solver
• A Hybrid Material Point Method for Frictional Contact with Diverse Materials
• Simulation and Visualization of Ductile Fracture with the Material Point Method
• EigenFit for Consistent Elastodynamic Simulation Across Mesh Resolution
• Subspace Neural Physics: Fast Data-Driven Interactive Simulation
• A Multi-Pass GAN for Fluid Flow Super-Resolution
• Fluid Simulation with Adaptive Staggered Power Particles on GPUs (TVCG)
• Flexible Use of Temporal and Spatial Reasoning for Fast and Scalable CPU Broad Phase Collision Detection using KD-Trees (CGF)

Bohan Wang, George Matcuk, Jernej Barbič

We demonstrate how to acquire complete human hand bone anatomy (meshes) in multiple poses using magnetic resonance imaging (MRI). Such acquisition was previously difficult because MRI scans must be long for high-precision results (over 10 minutes) and because humans cannot hold the hand perfectly still in non-trivial and badly supported poses. We invent a manufacturing process whereby we use lifecasting materials commonly employed in film special effects industry to generate hand molds, personalized to the subject, and to each pose. These molds are both ergonomic and encasing, and they stabilize the hand during scanning. We also demonstrate how to efficiently segment the MRI scans into individual bone meshes in all poses, and how to correspond each bone’s mesh to same mesh connectivity across all poses. Next, we interpolate and extrapolate the MRI-acquired bone meshes to the entire range of motion of the hand, producing an accurate data-driven animation-ready rig for bone meshes. We also demonstrate how to acquire not just bone geometry (using MRI) in each pose, but also a matching highly accurate surface geometry (using optical scanners) in each pose, modeling skin pores and wrinkles. We also give a soft tissue Finite Element Method simulation “rig”, consisting of novel tet meshing for stability at the joints, spatially varying geometric and material detail, and quality constraints to the acquired skeleton kinematic rig. Given an animation sequence of hand joint angles, our FEM soft tissue rig produces quality hand surface shapes in arbitrary poses in the hand range of motion. Our results qualitatively reproduce important features seen in the photographs of the subject’s hand, such as similar overall organic shape and fold formation.

Hand Modeling and Simulation Using Stabilized Magnetic Resonance Imaging

Marc Alexa

We introduce the notion of harmonic triangulations: a harmonic triangulation simultaneously minimizes the Dirichlet energy of all piecewise linear functions. By a famous result of Rippa, Delaunay triangulations are the harmonic triangulations of planar point sets. We prove by explicit counterexample that in 3D a harmonic triangulation does not exist in general. However, we show that bistellar flips are harmonic: if they decrease Dirichlet energy for one set of function values, they do so for all. This observation gives rise to the notion of locally harmonic triangulations. We demonstrate that locally harmonic triangulations can be efficiently computed, and efficiently reduce sliver tetrahedra. The notion of harmonic triangulation also gives rise to a scalar measure of the quality of a triangulation, which can be used to prioritize flips and optimize the position of vertices. Tetrahedral meshes generated by optimizing this function generally show better quality than Delaunay-based optimization techniques. 

Harmonic Triangulations

Thomas Buffet, Damien Rohmer, Loïc Barthe, Laurence Boissieux, Marie-Paule Cani

We propose a robust method for untangling an arbitrary number of cloth layers, possibly exhibiting deep interpenetrations, to a collision-free state, ready for animation. Our method relies on an intermediate, implicit representation to solve the problem: the user selects a few garments stored in a library together with their implicit approximations, and places them over a mannequin while specifying the desired order between layers. The intersecting implicit surfaces are then combined using a new family of N-ary composition operators, specially designed for untangling layers. Garment meshes are finally projected to the deformed implicit surfaces in linear time, while best preserving triangles and avoiding loss of details. Each of the untangling operators computes the target surface for a given garment in a single step, while accounting for the order between cloth layers and their individual thicknesses. As a group, they guarantee an intersection-free output configuration. Moreover, a weight can be associated with each layer to tune their relative influence during untangling, such as leather being less deformed than cloth. Results for each layer then reflect the combined effect of the other layers, enabling us to output a plausible configuration in contact regions. As our results show, our method can be used to generate plausible, new static shapes of garments when underwear has been added, as well as collision-free configurations enabling a user to safely launch animations of arbitrarily complex layered clothing.

Implicit Untangling: A Robust Solution for Modeling Layered Clothing

Teseo Schneider, Jérémie Dumas, Xifeng Gao, Mario Botsch, Daniele Panozzo, Denis Zorin

We introduce an integrated meshing and finite element method pipeline enabling solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order bases on its elements, combining triquadratic B-splines, triquadratic hexahedra, and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson’s equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.

Poly-Spline Finite Element Method

Bowen Yang, William Corse, Jiecong Lu, Joshuah Wolper, Chenfanfu Jiang

We present a novel approach for animating incompressible fluids with Eulerian advection-projection solvers on the surface of a sphere by extending the recent work by Hill and Henderson [2016] with a staggered spherical grid discretization. By doing so, we avoid the infamous checkerboard null modes. We additionally introduce new, straightforward polar singularity treatments that avoid the previous need for any spectral filtering of high-frequency noise at the poles. Lastly, we enforce incompressibility with a fast Fourier solution to Poisson’s equation for pressure in spherical coordinates. Our high-performance GPU-based framework combines scalability, art-directability, and ease of implementation, and reaches real-time speeds for various practical scenarios.

Real-Time Fluid Simulation on the Surface of a Sphere

Mickeal Verschoor, Andrei C. Jalba

Simulating (elastically) deformable models that can collide with each other and with the environment remains a challenging task. The resulting contact problems can be elegantly approached using Lagrange multipliers to represent the unknown magnitude of the response forces. Typical methods construct and solve a Linear Complementarity Problem (LCP) to obtain the response forces. This requires the inverse of the generalized mass matrix, which is generally hard to obtain for deformable-body problems. In this article, we tackle such contact problems by directly solving the Mixed Linear Complementarity Problem (MLCP) and omitting the construction of an LCP matrix. Since a convex quadratic program with linear constraints is equivalent to an MLCP, we propose to use a Conjugate Residual (CR) solver as the backbone of our collision response system. By dynamically updating the set of active constraints, the MLCP with inequality constraints can be solved efficiently. We also propose a simple yet efficient preconditioner that ensures faster convergence. Finally, our approach is faster than existing methods (at the same accuracy), and it allows accurate treatment of friction.

Efficient and Accurate Collision Response for Elastically Deformable Models