Physics-Based Animation

Nuttapong Chentanez, Matthias Müller, Miles Macklin

Shape matching is a popular method for simulating deformable objects in real time as it is fast and stable at large time steps. Although shape matching can simulate large elastic deformation and ductile fracturing, until now, they are limited to scenarios with relatively small plastic deformation. In this work, we present a method for simulating deformable solids undergoing large plastic deformation and topological changes using shape matching within the position based dynamics (PBD) framework. This expands the versatility of PBD which was previously shown to be able to simulate rigid bodies, liquids, gases, cloth, and deformable solids with moderate plastic deformation. Our novel contributions include local particle re-sampling, cluster re-sampling and skinning of an explicitly tracked surface mesh.

Real-time Simulation of Large Elasto-Plastic Deformation with Shape Matching

Sheng Yang Xiaowei He Huamin Wang Sheng Li Guoping Wang Enhua Wu Kun Zhou

Capillary waves are difficult to simulate due to their fast traveling speed and high frequency. In this paper, we propose to approximate capillary wave effects by surface compression waves under the SPH framework. To achieve this goal, we present a method to convert surface tension energy changes measured from SPH simulation into high-frequency density variations. Based on the compression wave propagation model, we present an approximate technique to simulate capillary wave propagation in a high-frequency particle density field. To address noise issues in wave simulation, we develop a simple way to apply the zero pressure condition on free surfaces in projection-based incompressible SPH. Our experiment shows that the developed algorithm can produce realistic capillary wave effects on both thin liquid features and large liquid bodies. Its computational overhead is also small.

Enriching SPH Simulation by Approximate Capillary Waves

Tassilo Kugelstadt, Elmar Schoemer

We present a novel method to simulate bending and torsion of elastic rods within the position-based dynamics (PBD) framework. The main challenge is that torsion effects of Cosserat rods are described in terms of material frames which are attached to the centerline of the rod. But frames or orientations do not fit into the classical position-based dynamics formulation. To solve this problem we introduce new types of constraints to couple orientations which are represented by unit quaternions. For constraint projection quaternions are treated in the exact same way as positions. Unit length is enforced with an additional constraint. This allows us to use the strain measures form Cosserat theory directly as constraints in PBD. It leads to very simple  algebraic expressions for the correction displacements which only contain quaternion products and additions. Our results show that our method is very robust and accurately produces the complex bending and torsion effects of rods. Due to its simplicity our method is very efficient and more than one order of magnitude faster than existing position-based rod simulation methods. It even achieves the same performance as position-based simulations without torsion effects.

Position and Orientation Based Cosserat Rods

Tao Yang, Ming C. Lin, Ralph R. Martin, Jian Chang, and Shi-Min Hu

The realistic capture of various interactions at interfaces is a challenging problem for SPH-based simulation. Previous works have mainly considered a single type of interaction, while real-world phenomena typically exhibit multiple interactions at different interfaces. For instance, when cracking an egg, there are simultaneous interactions between air, egg white, egg yolk, and the shell. To conveniently handle all interactions simultaneously in a single simulation, a versatile approach is critical. In this paper, we present a new approach to the surface tension model based on pairwise interaction forces; its basis is to use a larger number of neighboring particles. Our model is stable, conserves momentum, and furthermore, prevents the particle clustering problem which commonly occurs at the free surface. It can be applied to simultaneous interactions at multiple interfaces (e.g. fluid-solid and fluid-fluid). Our method is versatile, physically plausible and easy-to-implement. We also consider the close connection between droplets and bubbles, and show how to animate bubbles in air as droplets, with the help of a new surface particle detection method. Examples are provided to demonstrate the capabilities and effectiveness of our approach.

Versatile Interactions at Interfaces for SPH-Based Simulations

Simulation-related papers from Symposium on Computer Animation 2016:

• ADMM ⊇ Projective Dynamics: Fast Simulation of General Constitutive Models
• Compressing Fluid Subspaces
• Art-Directed Muscle Simulation for High-End Facial Animation
• Real-time Simulation of Large Elasto-Plastic Deformation with Shape Matching
• Enriching SPH Simulation by Approximate Capillary Waves
• Topology-Aware Neighborhoods for Point-Based Simulation and Reconstruction
• Versatile Interactions at Interfaces for SPH-Based Simulations
• Two-way Coupling of Fluids to Reduced Deformable Bodies
• Hele-Shaw Flow Simulation with Interactive Control using Complex Barycentric Coordinates
• Hierarchical hp-Adaptive Signed Distance Fields
• Asynchronous Implicit Backward Euler Integration
• A macroblock optimization for grid-based nonlinear elasticity
• Accurate Simulation of Wound Healing and Skin Deformation
• Position and Orientation Based Cosserat Rods
• Constrained Neighbor Lists for SPH-based Fluid Simulations

Rahul Narain, Matthew Overby, George E. Brown

We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general-purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constitutive models and hard constraints while retaining the speed, parallelizability, and robustness of projective dynamics. We demonstrate these benefits on several examples that include cloth, collisions, and volumetric deformable bodies with nonlinear elasticity.

ADMM ⊇ Projective Dynamics: Fast Simulation of General Constitutive Models

Dan Koschier, Crispin Deul, Jan Bender

In this paper we propose a novel method to construct hierarchical $hp$-adaptive Signed Distance Fields (SDFs). We discretize the signed distance function of an input mesh using piecewise polynomials on an axis-aligned hexahedral grid. Besides spatial refinement based on octree subdivision to refine the cell size (h), we hierarchically increase each cell’s polynomial degree (p) in order to construct a very accurate but memory-efficient representation. Presenting a novel criterion to decide whether to apply h- or p-refinement, we demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption than previous approaches. Finally, we demonstrate the usage of our representation as collision detector for geometrically highly complex solid objects in the application area of physically-based simulation.

Hierarchical hp-Adaptive Signed Distance Fields

Aviv Segall, Orestis Vantzos, Mirela Ben-Chen

Hele-Shaw flow describes the slow flow of a viscous liquid between two parallel plates separated by a small gap. In some configurations such a flow generates instabilities known as Saffman-Taylor fingers, which form intricate visual patterns. While these patterns have been an inspiration for artists, as well as thoroughly analyzed by mathematicians, efficiently simulating them remains challenging. The main difficulty involves efficiently computing a harmonic function on a time-varying planar domain, a problem which has been recently addressed in the shape deformation literature using a complex-variable formulation of generalized barycentric coordinates. We propose to leverage similar machinery, and show how the model equations for the Hele-Shaw flow can be formulated in this framework. This allows us to efficiently simulate the flow, while allowing interactive user control of the behavior of the fingers. We additionally show that complex barycentric coordinates are applicable to the exterior domain, and use them to simulate two-phase flow, yielding a variety of interesting patterns.

Hele-Shaw Flow Simulation with Interactive Control using Complex Barycentric Coordinates

Vinicius C. Azevedo, Christopher Batty, Manuel M. Oliveira

Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.

Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps

Xiao Yan, Yun-Tao Jiang, Chen-Feng Li, Ralph R. Martin, and Shi-Min Hu

This work extends existing multiphase-fluid SPH frameworks to cover solid phases, including deformable bodies and granular materials. In our extended multiphase SPH framework, the distribution and shapes of all phases, both fluids and solids, are uniformly represented by their volume fraction functions. The dynamics of the multiphase system is governed by conservation of mass and momentum within different phases. The behavior of individual phases and the interactions between them are represented by corresponding constitutive laws, which are functions of the volume fraction fields and the velocity fields. Our generalized multiphase SPH framework does not require separate equations for specific phases or tedious interface tracking. As the distribution, shape and motion of each phase is represented and resolved in the same way, the proposed approach is robust, efficient and easy to implement. Various simulation results are presented to demonstrate the capabilities of our new multiphase SPH framework, including deformable bodies, granular materials, interaction between multiple fluids and deformable solids, flow in porous media, and dissolution of deformable solids.

Multiphase SPH Simulation for Interactive Fluids and Solids