Abstract In computer graphics and engineering, isotropic hyperelastic volumetric materials are commonly chosen from a small set of families (e.g., StVK, linear corotational, Neo‐Hookean, Ogden) and tuned by adjusting family‐specific parameters. This workflow obscures how different material families relate and provides no unified notion of “distance” or “amount and direction of nonlinearity” across families. Furthermore, for a general isotropic 3D hyperelastic energy density function ψ, the relationships between its parameter values, and visually intuitive properties such as an object's “stiffness”, volume preservation, or the “amount of nonlinearity”, are less clear and can be tedious to adjust. Starting with an arbitrary isotropic ψ, we define and compute Lamé parameters (capturing linear behavior: stiffness and volume preservation), using the Taylor expansion of ψ at the rest state. This makes it possible to quantitatively “equalize” the small‐deformation behavior of two materials, even if they come from different material families, or are defined by arbitrary isotropic energy densities ψ. We rigorously state and prove that Linear Corotational materials (arguably the most widely used materials in computer graphics) are the simplest possible nonlinear materials. To compare nonlinear behavior beyond the linearization, we define a distance metric between linearization‐matched materials, using third‐order terms of ψ (“weakly nonlinear behavior”). We further define SCIEN, a directional nonlinearity measure obtained by projecting a material onto the standard one‐parameter Seth‐Hill continuum (which includes Hencky, Linear Corotational, and StVK as special cases), thereby distinguishing stretch‐stiffening from compression‐stiffening and quantifying its strength. As a result, we can equalize and edit materials agnostically from any material family: two materials can be matched in small‐deformation response, in weakly nonlinear behavior, or in both, while keeping these properties decoupled. This provides a unified language and practical tools for comparing, organizing, and adjusting common nonlinear material models.
Music-driven character animation enables and enhances transformative applications in entertainment and interactive education. However, synthesizing realistic drumming motion from audio remains challenging due to the inherent tension between high-acceleration dynamics and the need for extreme spatial-temporal precision. Existing approaches, often reliant on motion matching or MIDI input, struggle with generalizing to diverse real-world audio. Moreover, the field lacks standardized evaluation metrics capable of distinguishing precise drumming from noisy motion. In this paper, we introduce a generative diffusion framework featuring a dual-objective loss function that decouples skeletal integrity from drumstick precision, thus enabling centimeter-level stick precision without sacrificing natural body dynamics. Additionally, leveraging our own dataset and data augmentation strategy, the model generalizes to non-curated, in-the-wild audio. To rigorously evaluate performance, we propose two novel metrics: an impact-to-target distance to quantify spatial precision and an audio-motion correlation score to assess temporal alignment. Our quantitative analysis and user studies demonstrate that our system generates high-quality motion that is often indistinguishable from ground-truth performances.
Abstract Garment animation systems are essential for high‐fidelity digital characters in various applications such as films and video games. We propose SSILK, a neural network‐based method that is explicitly designed to handle loose garments such as capes and robes, garment types that are notoriously hard to simulate via pose‐based garment neural simulators. We achieve this through three contributions. First, we formulate our method as a latent‐space time integration scheme inspired by Verlet integration, resulting in more temporally stable garment dynamics compared to prior methods. Second, we employ a hybrid proxy‐joint and blendshape decoder to represent full SO(3) transformations that can be too challenging to capture using blend‐shapes alone. Finally, we propose a data‐augmentation strategy to improve performance on out‐of‐distribution scenarios. We demonstrate the effectiveness of our method on various garment and character animations and compare it to the state of the art.
We present a fast, robust method for continuous collision detection (CCD) directly between pairs of complex signed distance fields (SDFs). By casting CCD as an alternating spatio-temporal optimization and driving a small set of smartly sampled surface points along SDF tangent spaces, our approach avoids dense sampling or triangle meshes entirely. The result is real-time SDF-SDF time-of-impact queries-often within 1 ms on a single CPU core-even for highly detailed, non-convex geometry undergoing fast spinning motion. This is, to our knowledge, the first practical CCD method operating directly on SDF pairs.
Recent advances in generative motion synthesis have enabled realtime autoregressive generation of diverse and realistic character animations conditioned on user inputs, as demonstrated by models such as the Conditional Autoregressive Motion Diffusion Model (CAMDM). However, real-world applications (e.g., computer games) often demand faster-than-realtime performance for large numbers of characters. We introduce F3AMD (Fast FiLM-conditioned Fourier Autoregressive Motion Diffusion), a framework that achieves an order of magnitude speedup over state-of-the-art systems for multi-character animation on both GPUs and CPUs while maintaining high motion quality. Our key insight is that autoregressive motion diffusion is primarily bottlenecked by architectural and sampling inefficiencies. To address this, F3AMD employs Fourier Neural Operators (FNOs) as encoder-decoder modules, substitutes Transformer backbones with FNO blocks, replaces condition concatenation with lightweight Feature-wise Linear Modulation (FiLM), and adopts a variance-exploding noise schedule with a deterministic sampler. This design enables a substantially lower-dimensional latent space, facilitates learning in both the spectral and temporal domains, and significantly improves sample efficiency. We conduct systematic ablations of key design factors, including latent dimension, backbone type, diffusion window length, and number of denoising steps. Our recommended configuration, F3AMD-FNO-96, achieves 20x speedup over the baseline CAMDM model, while maintaining comparable motion quality.
