Physics-Based Animation

Longhua Wu, Botao Wu, Yin Yang, Huamin Wang

Cloth dynamics and collision handling are the two most challenging topics in cloth simulation. While researchers have substantially improved the performance of cloth dynamics solvers recently, their success in fast collision detection and handling is rather limited. In this paper, we focus our research on the safety, efficiency and realism of the repulsion-based collision handling approach, which has demonstrated its potential in existing GPU-based simulators. Our first discovery is the necessary vertex distance conditions for cloth to enter self intersections, the negations of which can be viewed as vertex distance constraints continuous in time for sufficiently avoiding self collisions. Continuous constraints, however, cannot be enforced with ease.Our solution is to convert continuous constraints into three types of constraints: discrete edge length constraints, discrete vertex distance constraints and vertex displacement constraints. Based on this solution, we develop a fast and safe collision handling process for enforcing constraints, a novel splitting method for integrating collision handling with dynamics solvers,and static and adaptive remeshing schemes to further improve the runtime performance. In summary, our cloth simulator is efficient, safe, robust and parallelizable on a GPU. The experiment shows that it runs at least one order of magnitude faster than existing simulators.

A Safe and Fast Repulsion Method for GPU-based Cloth Self Collisions

Syuhei Sato, Yoshinori Dobashi, Theodore Kim

High-resolution fluid simulations are computationally expensive, so many post-processing methods have been proposed to add turbulent details to low-resolution flows. Guiding methods are one promising approach for adding naturalistic, detailed motions as a post-process, but can be inefficient. Thus, we propose a novel, efficient method that formulates fluid guidance as a minimization problem in stream function space. Input flows are first converted into stream functions, and a high resolution flow is then computed via optimization. The resulting problem sizes are much smaller than previous approaches, resulting in faster computation times. Additionally, our method does not require an expensive pressure projection, but still preserves mass. The method is both easy to implement and easy to control, as the user can control the degree of guiding with a single, intuitive parameter. We demonstrate the effectiveness of our method across various examples.

Stream-Guided Smoke Simulations

Ty Trusty, Honglin Chen, David I.W. Levin

We introduce a new method for direct physics-based animation of volumetric curved models, represented using NURBS surfaces. Our technical contribution is the Shape Matching Element Method (SEM). SEM is a completely meshless algorithm, the first to simultaneously be robust to gaps and overlaps in geometry, be compatible with standard constitutive models and time integration schemes, support contact and frictional interactions and to preserve feature correspondence during simulation which enables editable simulated output. We demonstrate the efficacy of our algorithm by producing compelling physics-based animations from a variety of curved input models.

The Shape Matching Element Method: Direct Animation of Curved Surface Models

Lei Lan*, Yin Yang*, Danny M. Kaufman, Junfeng Yao, Minchen Li, Chenfanfu Jiang (*equal contribution)

We propose a framework of efficient nonlinear deformable simulation with both fast continuous collision detection and robust collision resolution. We name this new framework Medial IPC as it integrates the merits from medial elastics, for an efficient and versatile reduced simulation, as well as incremental potential contact, for a robust collision and contact resolution. We leverage medial axis transform to construct a kinematic subspace. Instead of resorting to projective dynamics, we use classic hyperelastics to embrace real-world nonlinear materials. A novel reduced continuous collision detection algorithm is presented based on the medial mesh. Thanks to unique geometric properties of medial axis and medial primitives, we derive closed-form formulations for identifying between-primitive collision within the reduced medial space. In the meantime, the implicit barrier energy that generates necessary repulsion forces for collision resolution is also formulated with the medial coordinate. In other words, Medial IPC exploits a universal reduced coordinate for simulation, continuous self-/collision detection, and IPC-based collision resolution. Continuous collision detection also allows more aggressive time stepping. In addition, we carefully implement our system with a heterogeneous CPU-GPU deployment such that massively parallelizable computations are carried out on the GPU while few sequential computations are on the CPU. Such implementation also frees us from generating training poses for selecting Cubature points and precomputing their weights. We have tested our method on complicated deformable models and collision-rich simulation scenarios. Due to the reduced nature of our system,the computation is faster than fullspace IPC or other fullspace methods using continuous collision detection by at least one order. The simulation remains high-quality as the medial subspace captures intriguing and local deformations with sufficient realism.

Medial IPC: Accelerated Incremental Potential Contact with Medial Elastics

Bolun Wang, Zachary Ferguson, Teseo Schneider, Xin Jiang, Marco Attene, Daniele Panozzo

We introduce a large-scale benchmark for continuous collision detection (CCD) algorithms, composed of queries manually constructed to highlight challenging degenerate cases and automatically generated using existing simulators to cover common cases. We use the benchmark to evaluate the accuracy, correctness, and efficiency of state-of-the-art continuous collision detection algorithms, both with and without minimal separation. We discover that, despite the widespread use of CCD algorithms, existing algorithms are either: (1) correct but impractically slow, (2) efficient but incorrect, introducing false negatives which will lead to interpenetration, or (3) correct but over conservative, reporting a large number of false positives which might lead to inaccuracies when integrated into a simulator. By combining the seminal interval root-finding algorithm introduced by Snyder in 1992 with modern predicate design techniques, we propose a simple and efficient CCD algorithm. This algorithm is competitive with state-of-the-art methods in terms of runtime while conservatively reporting the time of impact and allowing an explicit trade-off between runtime efficiency and the number of false positives reported.

A Large Scale Benchmark and an Inclusion-Based Algorithm for Continuous Collision Detection

Cristian Romero, Dan Casas, Jesús Pérez, Miguel A. Otaduy

This paper introduces a novel subspace method for the simulation of dynamic deformations. The method augments existing linear handle-based subspace formulations with nonlinear learning-based corrections parameterized by the same subspace. Together, they produce a compact nonlinear model that combines the fast dynamics and overall contact-based interaction of subspace methods, with the highly detailed deformations of learning-based methods. We propose a formulation of the model with nonlinear corrections applied on the local undeformed setting, and decoupling internal and external contact-driven corrections. We define a simple mapping of these corrections to the global setting, an efficient implementation for dynamic simulation, and a training pipeline to generate examples that efficiently cover the interaction space. Altogether, the method achieves unprecedented combination of speed and contact-driven deformation detail.

Learningn Contact Corrections for Handle-Based Subspace Dynamics

Minchen Li, Danny M. Kaufman, Chenfanfu Jiang

We extend the incremental potential contact (IPC) model [Li et al. 2020] for contacting elastodynamics to resolve systems composed of arbitrary combinations of codimensional degrees-of-freedoms. This enables a unified, interpenetration-free, robust, and stable simulation framework that couples codimension-0,1,2, and 3 geometries seamlessly with frictional contact. Extending the IPC model to thin structures poses new challenges in computing strain, modeling thickness and determining collisions. To address these challenges we propose three corresponding contributions. First, we introduce a C2 constitutive barrier model that directly enforces strain limiting as an energy potential while preserving rest state. This provides energetically consistent strain limiting models (both isotropic and anisotropic) for cloth that enable strict satisfaction of strain-limit inequalities with direct coupling to both elastodynamics and contact via minimization of the incremental potential. Second, to capture the geometric thickness of codimensional domains we extend IPC to directly enforce distance offsets. Our treatment imposes a strict guarantee that mid-surfaces (respectively mid-lines) of shells (respectively rods) will not move closer than applied thickness values, even as these thicknesses become characteristically small. This enables us to account for thickness in the contact behavior of codimensional structures and so robustly capture challenging contacting geometries; a number of which, to our knowledge, have not been simulated before. Third, codimensional models, especially with modeled thickness, mandate strict accuracy requirements that pose a severe challenge to all existing continuous collision detection (CCD) methods. To address these limitations we develop a new, efficient, simple-to-implement additive CCD (ACCD) method that applies conservative advancement [Mirtich 1996; Zhang et al. 2006] to iteratively refine a lower bound for deforming primitives, converging to time of impact.

Codimensional Incremental Potential Contact

Ante Qu, Doug L James

It is increasingly common to model, simulate, and process complex materials based on loopy structures, such as in yarn-level cloth garments, which possess topological constraints between inter-looping curves. While the input model may satisfy specific topological linkages between pairs of closed loops, subsequent processing may violate those topological conditions. In this paper, we explore a family of methods for efficiently computing and verifying linking numbers between closed curves, and apply these to applications in geometry processing, animation, and simulation, so as to verify that topological invariants are preserved during and after processing of the input models. Our method has three stages: (1) we identify potentially interacting loop-loop pairs, then (2) carefully discretize each loop’s spline curves into line segments so as to enable (3) efficient linking number evaluation using accelerated kernels based on either counting projected segment-segment crossings, or by evaluating the Gauss linking integral using direct or fast summation methods (Barnes-Hut or fast multipole methods). We evaluate CPU and GPU implementations of these methods on a suite of test problems, including yarn-level cloth and chainmail, that involve significant processing: physics-based relaxation and animation, user-modeled deformations, curve compression and reparameterization. We show that topology errors can be efficiently identified to enable more robust processing of loopy structures.

Fast Linking Numbers for Topology Verification
of Loopy Structures

Zachary Ferguson, Minchen Li, Teseo Schneider, Francisca Gil-Ureta, Timothy Langlois, Chenfanfu Jiang, Denis Zorin, Danny M. Kaufman, Daniele Panozzo

We introduce the first implicit time-stepping algorithm for rigid body dynamics, with contact and friction, that guarantees intersection-free configurations at every time step. Our algorithm explicitly models the curved trajectories traced by rigid bodies in both collision detection and response. For collision detection, we propose a conservative narrow phase collision detection algorithm for curved trajectories, which reduces the problem to a sequence of linear CCD queries with minimal separation. For time integration and contact response, we extend the recently proposed incremental potential contact framework to reduced coordinates and rigid body dynamics. We introduce a benchmark for rigid body simulation and show that our approach, while less efficient than alternatives, can robustly handle a wide array of complex scenes, which cannot be simulated with competing methods, without requiring per-scene parameter tuning.

Intersection-free Rigid Body Dynamics

Victor Romero, Mickael Ly, Abdullah Haroon Rasheed, Raphael Charrondiere, Arnaud Lazarus, Sebastian Neukirch, Florence Bertails-Descoubes

We introduce a selected set of protocols inspired from the Soft Matter Physics community in order to validate Computer Graphics simulators of slender elastic structures possibly subject to dry frictional contact. Although these simulators were primarily intended for feature film animation and visual effects, they are more and more used as virtual design tools for predicting the shape and deformation of real objects; hence the need for a careful,quantitative validation. Our tests, experimentally verified, are designed to evaluate carefully the predictability of these simulators on various aspects,such as bending elasticity, bend-twist coupling, and frictional contact. We have passed a number of popular codes of Computer Graphics through our benchmarks by defining a rigorous, consistent, and as fair as possible methodology. Our results show that while some popular simulators for plates/shells and frictional contact fail even on the simplest scenarios, more recent ones, as well as well-known codes for rods, generally perform well and sometimes even better than some reference commercial tools of Mechanical Engineering. To make our validation protocols easily applicable to any simulator, we provide an extensive description of our methodology, and we shall distribute all the necessary model data to be compared against.

Physical validation of simulators in Computer Graphics: A new framework dedicated to slender elastic structures and frictional contact