Physics-Based Animation

Hossein Baktash, Nicholas Sharp, Qingnan Zhou, Keenan Crane, Alec Jacobson

This paper explores the analysis and design of the resting configurations of a rigid body, without the use of physical simulation. In particular, given a rigid body in ℝ³, we identify all possible stationary points, as well as the probability that the body will stop at these points, assuming a random initial orientation and negligible momentum. The forward version of our method can hence be used to automatically orient models, to provide feedback about object stability during the design process, and to furnish plausible distributions of shape orientation for natural scene modeling. Moreover, a differentiable inverse version of our method lets us design shapes with target resting behavior, such as dice with target, nonuniform probabilities. Here we find solutions that would be nearly impossible to find using classical techniques, such as dice with additional unstable faces that provide more natural overall geometry.

Putting Rigid Bodies to Rest

Magí Romanyà Serrasolsas, Juan J. Casafranca, Miguel A. Otaduy

We propose the formulation of forward and differentiable rigid-body dynamics using Lie-algebra rotation derivatives. In particular, we show how this approach can easily be applied to incremental-potential formulations of forward dymamics, and we introduce a novel definition of adjoints for differentiable dynamics. In contrast to other parameterizations of rotations (notably the popular rotation-vector parameterization), our approach leads to painlessly simple and compact derivatives, better conditioning, and higher runtime efficiency. We demonstrate our approach on fundamental rigid-body problems, but also on Cosserat rods as an example of multi-rigid-body dynamics.

Painless Differentiable Rotation Dynamics

David Algis, Bérenger Bramas, Emmanuelle Darles, Lilian Aveneau

The oceans cover the vast majority of the Earth. Therefore, their simulation has many scientific, industrial and military interests, including computer graphics domain. By fully exploiting the multi-threading power of GPU and CPU, current state-of-the-art tools can achieve real-time ocean simulation, even if it is sometimes needed to reduce the physical realism for large scenes. Although most of the building blocks for implementing an ocean simulator are described in the literature, a clear explanation of how they interconnect is lacking. Hence, this paper proposes to bring all these components together, detailing all their interactions, in a comprehensive and fully described real-time framework that simulates the free ocean surface and the coupling between solids and fluid. This article also presents several improvements to enhance the physical realism of our model. The two main ones are: calculating the real-time velocity of ocean fluids at any depth; computing the input of the solid to fluid coupling algorithm.

Arc Blanc: a real time ocean simulation framework

Tianchen Hao, Jinxian Pan, Yangcheng Xiang, Xiangda Shen, Xinsheng Li, Yanci Zhang

A Mesoscale Convective System (MCS) is a collection of thunderstorms operating as a unified system, showcasing nature’s untamed power. They represent a phenomenon widely referenced in both the natural sciences and the visual effects (VFX) industries. However, in computer graphics, visually accurate simulation of MCS dynamics remains a significant challenge due to the inherent complexity of atmospheric microphysical processes. To achieve a high level of visual quality while ensuring practical performance, we introduce Thunderscapes, the first physically based simulation framework for visually realistic MCS tailored to graphical applications. Our model integrates mesoscale cloud microphysics with hydrometeor electrification processes to simulate thunderstorm development and lightning flashes. By capturing various thunderstorm types and their associated lightning activities, Thunderscapes demonstrates the versatility and physical accuracy of the proposed approach.

Thunderscapes: Simulating the Dynamics of Mesoscale Convective System

Huanbo Zhou, Zhenyu Xu, Xijun Liu, Xinyu Zhang

Simulating multi-object collisions in real-time environments remains a significant challenge, particularly when handling simultaneous collisions in a physically accurate manner. Traditional Gauss-Seidel solvers, widely employed in physics engines, often fail to preserve the symmetry and consistency of multi-object interactions that are often observed in physics. In this paper, we present a generalized and robust Gauss-Seidel solver to overcome the difficulties in simultaneous collisions. Using spatial and temporal collision states to classify and resolve constraints, our algorithm ensures correct collision propagation and symmetry, addressing the limitations commonly found in existing solvers. Moreover, our algorithm can mitigate jitters caused by floating-point errors, ensuring smooth and stable collision responses. Our approach demonstrates fast convergence and improved accuracy in scenarios involving complex multi-object collisions.

A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions

Shiguang Liu, Maolin Wu, Chenfanfu Jiang, Yisheng Zhang

This paper proposes a novel method to simulate the dynamic fracture effect of elastoplastic objects. Our method is based on the continuum damage mechanics (CDM) theory and uses the material point method (MPM) to discretize the governing equations. Our proposed approach distinguishes itself from previous works by incorporating a novel method for modeling decohesion, which preserves the incompressibility of the cracks. In contrast to existing methods that rely on material stiffness degradation, our approach leverages carefully crafted constitutive models for both fully and partially damaged materials. We further introduce a novel granular material model that effectively captures the physical behavior of fully damaged debris. This is augmented by a volume-aware deformation gradient tensor designed to evaluate and stabilize material expansion. We conduct a comprehensive evaluation of our proposed method on multiple dynamic fracturing scenarios and demonstrate its effectiveness in producing visually richer and more realistic behaviors compared to previous state-of-the-art MPM approaches.

An Incompressible Crack Model for Volume Preserving MPM Fracture

Jiong Chen, Florian T. Schäfer, Mathieu Desbrun

Boundary element methods (BEM) for solving linear elliptic partial differential equations have gained traction in a wide range of graphics applications: they eliminate the need for volumetric meshing by solving for variables exclusively on the domain boundary through a linear boundary integral equation (BIE). However, BEM often generate dense and ill-conditioned linear systems that lead to poor computational scalability and substantial memory demands for large-scale problems, limiting their applicability and efficiency in practice. In this paper, we address these limitations by generalizing the Kaporin-based approach to asymmetric preconditioning: we construct a sparse approximation of the inverse-LU factorization of arbitrary BIE matrices in a massively parallel manner. Our sparse inverse-LU factorization, when employed as a preconditioner for the generalized minimal residual (GMRES) method, significantly enhances the efficiency of BIE solves, often yielding orders-of-magnitude speedups in solving times.

Lightning-fast Boundary Element Method

Bosheng Li, Nikolas A. Schwarz, Wojtek Pałubicki, Sören Pirk, Dominik L. Michels, Bedrich Benes

We propose a novel approach for the computational modeling of lignified tissues, such as those found in tree branches and timber. We leverage a state-of-the-art strand-based representation for tree form, which we extend to describe biophysical processes at short and long time scales. Simulations at short time scales enable us to model different breaking patterns due to branch bending, twisting, and breaking. On long timescales, our method enables the simulation of realistic branch shapes under the influence of plausible biophysical processes, such as the development of compression and tension wood. We specifically focus on computationally fast simulations of woody material, enabling the interactive exploration of branches and wood breaking. By leveraging Cosserat rod physics, our method enables the generation of a wide variety of breaking patterns. We showcase the capabilities of our method by performing and visualizing numerous experiments.

Stressful Tree Modeling: Breaking Branches with Strands

Filipe Nascimento, Fabricio S. Sousa, Afonso Paiva

Powder-snow avalanches are natural phenomena that result from an instability in the snow cover on a mountain relief. It begins with a dense avalanche core moving fast down the mountain. During its evolution, the snow particles in the avalanche front mix with the air, forming a suspended turbulent cloud of snow dust surrounding the dense snow avalanche. This paper introduces a physically-based framework using the Finite Volume Method to simulate powder-snow avalanches under complex terrains. Specifically, the primary goal is to simulate the turbulent snow cloud dynamics within the avalanche in a visually realistic manner. Our approach relies on a multi-layer model that splits the avalanche into two main layers: dense and powder-snow. The dense-snow layer flow is simulated by solving a type of Shallow Water Equations suited for intricate basal surfaces, known as the Savage-Hutter model. The powder-snow layer flow is modeled as a two-phase mixture of miscible fluids and simulated using Navier-Stokes equations. Moreover, we propose a novel model for the transition layer, which is responsible for coupling the avalanche main layers, including the snow mass injected into the powder-snow cloud from the snow entrainment processes and its injection velocity. In brief, our framework comprehensively simulates powder-snow avalanches, allowing us to render convincing animations of one of the most complex gravity-driven flows.

Digital Animation of Powder-Snow Avalanches