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This paper introduces Claycode, a novel 2D scannable code designed for extensive stylization and deformation. Unlike traditional matrix-based codes (e.g., QR codes), Claycodes encode their message in a tree structure. During the encoding process, bits are mapped into a topology tree, which is then depicted as a nesting of color regions drawn within the boundaries of a target polygon shape. When decoding, Claycodes are extracted and interpreted in real-time from a camera stream. We detail the end-to-end pipeline and show that Claycodes allow for extensive stylization without compromising their functionality. We then empirically demonstrate Claycode's high tolerance to heavy deformations, outperforming traditional 2D scannable codes in scenarios where they typically fail.
We present a novel contact model, termed Offset Geometric Contact (OGC), for guaranteed penetration-free simulation of codimensional objects with minimal computational overhead. Our method is based on constructing a volumetric shape by offsetting each face along its normal direction, ensuring orthogonal contact forces, thus allows large contact radius without artifacts. We compute vertex-specific displacement bounds to guarantee penetration-free simulation, which improves convergence and avoids the need for expensive continuous collision detection. Our method relies solely on massively parallel local operations, avoiding global synchronization and enabling efficient GPU implementation. Experiments demonstrate real-time, large-scale simulations with performance more than two orders of magnitude faster than prior methods while maintaining consistent computational budgets.
In physics-based simulation of rigid or nearly rigid objects, collisions often become the primary performance bottleneck, particularly when enforcing intersection-free constraints. Previous simulation frameworks rely on primitive-level CCD algorithms. Due to the large number of colliding surface primitives to process, those methods are computationally intensive and heavily dependent on advanced parallel computing resources such as GPUs, which are often inaccessible due to competing tasks or capped threading capacity in applications like policy training for robotics. To address these limitations, we propose a sequential CCD algorithm for convex shapes undergoing constant affine motion. This approach uses the conservative advancement method to iteratively refine a lower-bound estimate of the TOI, exploiting the linearity of affine motion and the efficiency of convex shape distance computation. Our CCD algorithm integrates seamlessly into the ABD framework, achieving a 10-fold speed-up over primitive-level CCD. Its high single-threaded efficiency further enables significant throughput improvements via scene-level parallelism, making it well-suited for resource-constrained environments.
Barrier potentials gained popularity as a means for robust contact handling in physical modeling and for modeling self-avoiding shapes. The key to the success of these approaches is adherence to geometric constraints, i.e., avoiding intersections, which are the cause of most robustness problems in complex deformation simulation with contact. However, existing barrier-potential methods may lead to spurious forces and imperfect satisfaction of the geometric constraints. They may have strong resolution dependence, requiring careful adaptation of the potential parameters to the object discretizations. We present a systematic derivation of a continuum potential defined for smooth and piecewise smooth surfaces, starting from identifying a set of natural requirements for contact potentials, including the barrier property, locality, differentiable dependence on shape, and absence of forces in rest configurations. Our potential is formulated independently of surface discretization and addresses the shortcomings of existing potential-based methods while retaining their advantages. We present a discretization of our potential that is a drop-in replacement for the potential used in the incremental potential contact formulation [Li et al. 2020], and compare its behavior to other potential formulations, demonstrating that it has the expected behavior. The presented formulation connects existing barrier approaches, as all recent existing methods can be viewed as a variation of the presented potential, and lays a foundation for developing alternative (e.g., higher-order) versions.
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.
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. From a technical point of view, our key observation is that rolling equilibria can be extracted from the Morse-Smale complex of the support function over the Gauss map. Our method is hence purely geometric, and does not make use of random sampling, or numerical time integration. Yet surprisingly, this purely geometric model makes extremely accurate predictions of rest behavior, which we validate both numerically, and via physical experiments. Moreover, for computing rest statistics, it is orders of magnitude faster than state of the art rigid body simulation, opening the door to inverse design—rather than just forward analysis.
Hand shadow art is a captivating art form, creatively using hand shadows to reproduce expressive shapes on the wall. In this work, we study an inverse problem: given a target shape, find the poses of left and right hands that together best produce a shadow resembling the input. This problem is nontrivial, since the design space of 3D hand poses is huge while being restrictive due to anatomical constraints. Also, we need to attend to the input's shape and crucial features, though the input is colorless and textureless. To meet these challenges, we design Hand-Shadow Poser, a three-stage pipeline, to decouple the anatomical constraints (by hand) and semantic constraints (by shadow shape): (i) a generative hand assignment module to explore diverse but reasonable left/right-hand shape hypotheses; (ii) a generalized hand-shadow alignment module to infer coarse hand poses with a similarity-driven strategy for selecting hypotheses; and (iii) a shadow-feature-aware refinement module to optimize the hand poses for physical plausibility and shadow feature preservation. Further, we design our pipeline to be trainable on generic public hand data, thus avoiding the need for any specialized training dataset. For method validation, we build a benchmark of 210 diverse shadow shapes of varying complexity and a comprehensive set of metrics, including a novel DINOv2-based evaluation metric. Through extensive comparisons with multiple baselines and user studies, our approach is demonstrated to effectively generate bimanual hand poses for a large variety of hand shapes for over 85% of the benchmark cases.
The Material Point Method (MPM) has become a cornerstone of physics-based simulation, widely used in geomechanics and computer graphics for modeling phenomena such as granular flows, viscoelasticity, fracture mechanics, etc. Despite its versatility, the original MPM suffers from cell-crossing instabilities caused by discontinuities in particle-grid transfer kernels. Existing solutions mostly mitigate these issues by adopting smoother shape functions, but at the cost of increased numerical diffusion and computational overhead due to larger kernel support. In this paper, we propose a novel C2-continuous compact kernel for MPM that achieves a unique balance in terms of stability, accuracy, and computational efficiency. Our method integrates seamlessly with Affine Particle-In-Cell (APIC) and Moving Least Squares (MLS) MPM, while only doubling the number of grid nodes associated with each particle compared to linear kernels. At its core is an innovative dual-grid framework, which associates particles with grid nodes exclusively within the cells they occupy on two staggered grids, ensuring consistent and stable force computations. We demonstrate that our method can be conveniently implemented using a domain-specific language, Taichi, or based on open-source GPU MPM frameworks, achieving faster runtime and less numerical diffusion compared to quadratic B-spline MPM. Comprehensive validation through unit tests, comparative studies, and stress tests demonstrates the efficacy of our approach in conserving both linear and angular momentum, handling stiff materials, and scaling efficiently for large-scale simulations. Our results highlight the transformative potential of compact, high-order kernels in advancing MPM's capabilities for stable, accurate, and high-performance simulations.
We introduce Arenite, a novel physics-based approach for modeling sandstone structures. The key insight of our work is that simulating a combination of stress and multi-factor erosion enables the generation of a wide variety of sandstone structures observed in nature. We isolate the key shape-forming phenomena: multi-physics fabric interlocking, wind and fluvial erosion, and particle-based deposition processes. Complex 3D structures such as arches, alcoves, hoodoos, or buttes can be achieved by creating simple 3D structures with user-painted erodable areas and vegetation and running the simulation. We demonstrate the algorithm on a wide variety of structures, and our GPU-based implementation achieves the simulation in less than 5 minutes on a desktop computer for our most complex example.
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.
Turbulent boundary layer represents one of the most complex but interesting phenomena in fluid flows. While the generation and alteration of sheared vortices in various interacting scales near the boundary are visually appealing, it is difficult to correctly replicate such phenomena by simulation, especially at high Reynolds numbers. Practical methodologies typically incorporate empirical wall modeling to substantially curtail the computational expenses while retaining physical consistency. Nevertheless, these are predominantly applicable to steady-state flow solvers. While complex scenarios involving dynamic fluid-solid interaction and its application to create time-dependent flow phenomena invariably necessitate unsteady flow solvers, the underlying wall modeling techniques are imprecise, leading to a different formation of near-wall vortices, especially for the highly efficient lattice Boltzmann solver operating on Cartesian grids. In this paper, we propose a novel hybrid near-wall model for the lattice Boltzmann solver, which can handle turbulent boundary layer flows in a simple and efficient manner, inspired by measuring the degree of boundary layer separation. Our model comprises both macroscopic and mesoscopic algebraic models, which collaborate to let the low dissipation lattice Boltzmann solver naturally form the turbulent boundary layer appropriately. By leveraging the multi-resolution technique, accurate simulation outcomes can be obtained. Our model is parameterized to approximate different physical attributes of the solid surface that can potentially influence the boundary layer distribution, and comparable boundary layer flow behaviors can be simulated at various grid resolutions. Rigorous benchmark tests are carried out to validate our model at different grid resolutions by comparing with experimental data and visualizations. We showcase the applications of our new model in both facilitating computational design and generating visual animations, accompanied by specific examples and comparisons with actual experimental setups and photographic images. All demonstrations affirm the physical consistency of our solver even when simulated with a relatively coarse grid resolution.
Modern hexahedral mesh generation relies on integer-grid maps (IGM), which map the Cartesian grid of integer iso-surfaces to a structure-aligned and conforming hexahedral cell complex discretizing the target shape. The hexahedral mesh is formed by iso-surfaces of the map such that an extraction algorithm is needed to convert the implicit map representation into an explicit mesh. State-of-the-art algorithms have been designed with two goals in mind, i.e., (i) unconditional robustness and (ii) tolerance to map defects in the form of inverted or degenerate tetrahedra. Because of significant advancements in the generation of locally injective maps, the tolerance to map defects has become irrelevant. At the same time, there is a growing demand for efficiently handling significantly larger mesh complexities, unfortunately not well served by the state-of-the-art since the tolerance to map defects induces a high runtime cost. Consequently, we present HexHex, a novel (unconditionally robust) hexahedral mesh extraction algorithm for locally injective integer-grid maps designed for maximal performance and scalability. Key contributions include a novel and highly compact mesh data structure based on so-called propellers and a conservative rasterization technique, significantly reducing the number of required exact predicate tests. HexHex not only offers lower asymptotic runtime complexities from a theoretical perspective but also lower constants, enabling in practice a 30x speedup for medium-sized examples and a larger speedup for more complex inputs, specifically when the hex-to-tet ratio is large. We provide a C++ reference implementation, supporting multi-core parallelization and the extraction of curved (piecewise-linear) hexahedral mesh edges and faces, e.g., valuable for subsequent higher-order mesh generation.
We introduce TetWeave, a novel isosurface representation for gradient-based mesh optimization that jointly optimizes the placement of a tetrahedral grid used for Marching Tetrahedra and a novel directional signed distance at each point. TetWeave constructs tetrahedral grids on-the-fly via Delaunay triangulation, enabling increased flexibility compared to predefined grids. The extracted meshes are guaranteed to be watertight, two-manifold and intersection-free. The flexibility of TetWeave enables a resampling strategy that places new points where reconstruction error is high and allows to encourage mesh fairness without compromising on reconstruction error. This leads to high-quality, adaptive meshes that require minimal memory usage and few parameters to optimize. Consequently, TetWeave exhibits near-linear memory scaling relative to the vertex count of the output mesh — a substantial improvement over predefined grids. We demonstrate the applicability of TetWeave to a broad range of challenging tasks in computer graphics and vision, such as multi-view 3D reconstruction, mesh compression and geometric texture generation. Our code is available at https://github.com/AlexandreBinninger/TetWeave.
Mesh reduction using quadric error metrics is the industry standard for producing level-of-detail (LOD) geometry for meshes. Although industry tools produce visually excellent LODs, mesh topology is often ruined during decimation. This is because tools focus on triangle simplification and preserving rendered appearance, whereas artists often produce quad dominant meshes with clean edge topology. Artist created manual LODs preserve both appearance and quad topology. Furthermore, most existing tools for quad decimation only accept pure quad meshes and cannot handle any triangles. The gap between quad and triangular mesh decimation is because they are built on fundamentally different operations, triangle simplification uses single edge collapses, whereas quad decimation requires that entire sets of edges be collapsed atomically. In this work, we demonstrate that single edge collapse can be used to preserve most input quads without degrading geometric quality. Single edge collapse quad preservation is made possible by introducing dihedral-angle weighted quadrics for every edge, allowing optimization to evenly space edges while preserving features. It is further enabled by explicitly ordering edge collapses with nearly equivalent quadric error in a way that preserves quad topology. In addition to quad preservation, we demonstrate that by introducing weights for quadrics on certain edges, our framework can be used to preserve symmetry and joint influences. To demonstrate our approach is suitable for skinned mesh decimation on triangle meshes, we show that QEM with attributes can preserve joint influences better than prior work. We implement and test our approach on 67 static and 19 animated meshes from Sketchfab. On both static and animated meshes, our approach consistently outperforms prior work with lower Chamfer and Hausdorff distance, while preserving more quad topology when present.