Physics-Based Animation

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

Byungsoo Kim, Vinicius C. Azevedo, Nils Thuerey, Theodore Kim, Markus Gross, Barbara Solenthaler

This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of the data, our generative model is able to accurately approximate the training data set, while providing plausible interpolated in-betweens. The proposed generative model is optimized for fluids by a novel loss function that guarantees divergence-free velocity fields at all times. In addition, we demonstrate that we can handle complex parameterizations in reduced spaces, and advance simulations in time by integrating in the latent space with a second network. Our method models a wide variety of fluid behaviors, thus enabling applications such as fast construction of simulations, interpolation of fluids with different parameters, time re-sampling, latent space simulations, and compression of fluid simulation data. Reconstructed velocity fields are generated up to 700x faster than re-simulating the data with the underlying CPU solver, while achieving compression rates of up to 1300x.

Deep Fluids: A Generative Network for Parameterized Fluid Simulations

Ying Wang, Nicolas J. Weidner, Margaret A. Baxter, Yura Hwang, Danny Kaufman, Shinjiro Sueda

It is well known that the dynamics of articulated rigid bodies can be solved in O(n) time using a recursive method, where n is the number of joints. However, when elasticity is added between the bodies (eg damped springs), with linearly implicit integration, the stiffness matrix in the equations of motion breaks the tree topology of the system, making the recursive O(n) method inapplicable. In such cases, the only alternative has been to form and solve the system matrix, which takes O(n³) time. We propose a new approach that is capable of solving the linearly implicit equations of motion in near linear time. Our method, which we call Red/Max, is built using a combined reduced/maximal coordinate formulation. This hybrid model enables direct flexibility to apply arbitrary combinations of constraints and contact modeling in both reduced and maximal coordinates, as well as mixtures of implicit and explicit forces in either coordinate representation. We highlight Red/Max’s flexibility with seamless integration of deformable objects with two-way coupling, at a standard additional cost. We further highlight its flexibility by constructing an efficient internal (joint) and external (environment) frictional contact solver that can leverage bilateral joint constraints for rapid evaluation of frictional articulated dynamics.

REDMAX: Efficient & Flexible Approach for Articulated Dynamics

Ryan Goldade, Yipeng Wang, Mridul Aanjaneya, Christopher Batty

While pressure forces are often the bottleneck in (near-)inviscid fluid simulations, viscosity can impose orders of magnitude greater computational costs at lower Reynolds numbers. We propose an implicit octree finite difference discretization that significantly accelerates the solution of the free surface viscosity equations using adaptive staggered grids, while supporting viscous buckling and rotation effects, variable viscosity, and interaction with scripted moving solids. In experimental comparisons against regular grids, our method reduced the number of active velocity degrees of freedom by as much as a factor of 7.7 and reduced linear system solution times by factors between 3.8 and 9.4. We achieve this by developing a novel adaptive variational finite difference methodology for octrees and applying it to the optimization form of the viscosity problem. This yields a linear system that is symmetric positive definite by construction, unlike naive finite difference/volume methods, and much sparser than a hypothetical finite element alternative. Grid refinement studies show spatial convergence at first order in L-infinity and second order in L-1, while the significantly smaller size of the octree linear systems allows for the solution of viscous forces at higher effective resolutions than with regular grids. We demonstrate the practical benefits of our adaptive scheme by replacing the regular grid viscosity step of a commercial liquid simulator (Houdini) to yield large speed-ups, and by incorporating it into an existing inviscid octree simulator to add support for viscous flows. Animations of viscous liquids pouring, bending, stirring, buckling, and melting illustrate that our octree method offers significant computational gains and excellent visual consistency with its regular grid counterpart.

An Adaptive Variational Finite Difference Framework for Efficient Symmetric Octree Viscosity

Lawson Fulton, Vismay Modi, David Duvenaud, David I. W. Levin, Alec Jacobson

We propose the first reduced model simulation framework for deformable solid dynamics using autoencoder neural networks.We provide a data-driven approach to generating nonlinear reduced spaces for deformation dynamics. In contrast to previous methods using machine learning which accelerate simulation by approximating the time-stepping function, we solve the true equations of motion in the latent-space using a variational formulation of implicit integration. Our approach produces drastically smaller reduced spaces than conventional linear model reduction, improving performance and robustness. Furthermore,our method works well with existing force-approximation cubature methods.

Latent-space Dynamics for Reduced Deformable Simulation