We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable dynamics and predicts future states through efficient matrix evaluations instead of sequential time integration. This yields log-linear scaling in the number of time steps and allows large portions of the trajectory to be skipped while retaining accuracy. The resulting temporal efficiency is especially advantageous for optimization tasks such as control and initial-state estimation, where the objective often depends largely on the final configuration. To broaden the scope of Koopman-based reduced-order models in graphics, we introduce a discretization-agnostic extension that learns shared dynamic behavior across multiple shapes and mesh resolutions. Prior DMD-based approaches have been restricted to a single shape and discretization, which limits their usefulness for tasks involving geometry variation. Our formulation generalizes across both shape and discretization, which enables fast shape optimization that was previously impractical for DMD models. This expanded capability highlights the potential of Koopman operator learning as a practical tool for efficient deformable simulation and design.
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We present an algorithm for global knit structure planning that leverages a generalization of power diagrams to triangulated surfaces. This generalization is based on modified geodesic heat kernels and is used to quantize the curl measure of a normalized knitting time function gradient. Knit singularity positions are optimized jointly in a global fashion via an iterative Lloyd-type algorithm, leading to faster and more optimal placement of singularities than prior work, allowing for practical creation of denser knit graphs. In this denser setting, we present singularity ordering constraints that more robustly achieve helix-free knit graphs. The speed and robustness of the method is demonstrated via a diverse array of knits, and a virtual gallery of helix-free knit graphs. We also provide further demonstration of user constraints for knit singularity masking, level set alignment constraints, and apparent seam placement via curl boosting.
Continuous Collision Detection is essential in simulation and modeling for accurately identifying object collisions. While robust CCD techniques have matured for triangle meshes, ensuring floating-point robustness for parametric surfaces remains an open challenge due to their representational complexity and heightened algorithmic sensitivity. In this paper, we present the first floating-point-robust CCD framework for parametric surfaces. Built on the Time-Dependent Inclusion-Based Method (TDIBM), our approach introduces a novel error decomposition strategy that separates coefficient and arithmetic errors, enabling structured analysis and safety guarantees. To rigorously benchmark robustness, we develop a rational-arithmetic-based dataset by inverting the CCD process: we generate exact ground-truth datasets from prescribed collision outcomes. Our construction captures both typical scenarios and near-degenerate cases. We evaluate several CCD algorithms using this benchmark to provide an in-depth analysis. Together, our method and dataset establish a comprehensive foundation for analyzing, benchmarking, and improving floating-point robustness in parametric surface CCD. Code and dataset will be published upon acceptance.
Traditional statistical graphics are precise but often lack the visual appeal, memorability, and engagement of pictorial charts. We present a generative framework for the automated synthesis of pictorial charts that bridges the gap between semantic expression and structural faithfulness. Rather than treating charts merely as images to be stylized, we frame the problem as a dual-conditioned generation task guided by two parallel external control signals: a text prompt capturing the semantic context of the editing intent, and a context image providing the abstract statistical chart's global structure. To reinforce these controls within a Multi-Modal Diffusion Transformer, we introduce two complementary feature-level mechanisms: structural alignment to anchor spatial layouts to the input chart, and semantic alignment to transfer expressive textures from reference images. Generalizing across major visual channels (i.e., length, area, angle, and position) and diverse semantic domains, our method produces pictorial charts that are both artistically compelling and structurally consistent. Extensive quantitative evaluations and perceptual user studies demonstrate that our framework outperforms traditional controllable generation and image editing baselines, providing a foundation for high-fidelity, data-driven generative modeling in expressive visual storytelling. Project page: https://ssalign.github.io/.
Monte Carlo integration is widely used in computer graphics, especially in rendering, but we identify two key limitations. First, for each sample, we can often obtain rich auxiliary information, such as sample position, or geometric information. However, a classical Monte Carlo estimator cannot effectively use this information and only averages the function values. Second, the Monte Carlo formulation makes it difficult to adapt the sampling distribution toward truly informative regions, which can be critical for reconstructing the signal. To address these limitations, we argue that a sampler and integrator beyond the standard Monte Carlo methods is needed. We therefore propose an end-to-end sampling-integration approach that jointly learns both a sampler and an integrator using neural networks, enabling samples to be drawn and used in a more coupled and principled manner. By training on a dataset of integrands, the estimator can further use learned priors over integrand structure and specialize to a family of problems. We evaluate our method on diverse applications in lighting, transmittance, generalized winding number, and walk-on-spheres, spanning both linear and nonlinear cases, and a broad range of low- and high-dimensional settings. Even though the networks add computational overheads, in the equal-sample setting, our method achieves substantial improvements, providing a powerful alternative to traditional quadrature rules and sampling methods.
Lattice metamaterials enable lightweight, multifunctional structures, yet homogenization-based evaluation of their effective properties remains computationally expensive. Neural surrogates offer speed but often lack the accuracy and stability required for engineering-grade simulations. We introduce GMT, a Geometric Multigrid Transformer - a neural solver with high numerical fidelity for fast and reliable lattice homogenization. GMT achieves architectural alignment with Geometric Multigrid (GMG) by restructuring Point Transformer V3 to operate across sparse GMG hierarchies, capturing long-range dependencies and cross-level interactions essential for multigrid convergence. To enforce physical consistency, GMT incorporates physics-aware positional encoding for strict enforcement of periodicity and predicts both the finest-level solution and multi-level residual corrections. These predictions deliver a spectrally-aligned initialization, enabling end-to-end training under physics-informed and solver-aware losses and requiring only a single GMG V-cycle refinement to reach convergence. This fusion of neural prediction and numerical rigor achieves relative residual errors of 10-5 with a 160× speedup over state-of-the-art GPU-based solvers at equivalent accuracy - particularly at high resolutions (e.g., 5123), where traditional methods become most costly. We validate GMT across mechanical and thermal domains, demonstrate robust generalization to unseen geometries and non-periodic settings, and showcase scalability to high resolutions - enabling real-time design iteration, multi-scale simulations, high-throughput material discovery, and inverse design.
Shape deformation for morphing or editing purposes is a central challenge in Computer Graphics. While numerous methods exist, few allow for the explicit evaluation of the deformation at arbitrary times and locations directly, without resorting to intricate advection or interpolation schemes. In this paper, we propose a method that provides an explicit expression of the deformation parameterized as a flow, for continuously deforming shapes defined implicitly. Implicit surfaces are indeed particularly well suited for deformation tasks, since they inherently account for both the surface and the enclosed volume. Our approach leverages invertible neural networks to ensure theoretically that the deformation is a valid flow, while also providing differential quantities useful for geometric regularization. We demonstrate applications of this flow to shape morphing with and without landmarks, shape editing, and pairwise-to-any morphing where we compute pairwise morphings to a canonical shape allowing to deduce transformations between any pair through flow composition. The code for our method is available at https://github.com/camillebnm/explicit_flows_for_implicit_surfaces.
While yarn-level garments offer rich dynamic details and compelling visual realism compared to triangle-based models, their wide adoption is hindered by the immense computational cost due to the presence of a large number of degrees of freedom (DOFs). This paper proposes a novel simulation framework designed to enhance the performance and stability for numerical simulation of nonlinear, non-convex, and high-resolution knitwear. Our method generalizes the Douglas-Rachford Splitting (DRS) scheme to resolve the non-convex coupling between stretching, shearing, bending, twisting, and contacting at each yarn thread. A key contribution is a nested decomposition strategy that decouples the non-convex variational energy into independent and convex sub-problems. Such convexification improves solver robustness and removes the necessity for frequent line searches. We provide a theoretically grounded strategy for metric selection for each sub-problem, derived from an analysis of the convergence guarantee of DRS. Consequently, our method achieves close-to-optimal convergence along the nonlinear iterations rather than relying on ad-hoc parameter tuning. The paper also clarifies a formal connection between our generalized DRS and the ADMM (Alternating Direction Method of Multipliers) framework, extending the applicability of our analysis to a broader set of constrained dynamics problems. Experimental results demonstrate that our method robustly handles complex knitwear simulation scenes with superior efficiency, stability, and physical fidelity compared to existing methods. With a matrix-free GPU parallelization, our method allows an interactive simulation rate of knitwear of multi-million DOFs.
The Hong Kong University of Science and Technology (Guangzhou), China and The Hong Kong University of Science and Technology, China Establishing one-to-one stroke correspondences is fundamental to vector-based animation inbetweening. Animators may face great challenges when handling occlusion, as occluded strokes must be drawn explicitly in keyframes and manually hidden frame by frame after stroke interpolation. To reduce tedious effort, we present LayerInbetween, an occlusion-aware framework for vector stroke correspondence and automatic inbetweening. It performs automatic layering to guide stroke tracing and correspondence finding for occluded strokes, and to resolve occlusion with layers in the inbetween frames. To predict occluded strokes, we propose a Global-Local Layer Transformation (GLLT) module that progressively improves the spatial alignment of strokes across keyframes via layer guidance, thereby indicating their potential positions. Our framework is trained on a synthetic dataset comprising 17k+ pairs of keyframes with occlusion and their stroke correspondences. Extensive experiments demonstrate the effectiveness of LayerInbetween compared with existing methods and its generalization capabilities to various types of drawings. In addition to its superior performance, our vector-based inbetweening method enables more flexible editing of 2D animation than raster-based video generation. Code and data for this paper are available at https://github.com/MarkMoHR/LayerInbetween.
Retargeting motion across characters with varying body shapes while preserving interaction semantics, such as self-contact and near-body proximity, remains a challenging problem. While recent geometry-aware approaches address this by maintaining spatial relationships between predefined corresponding regions, their reliance on static correspondences often struggles when the target character exhibits exaggerated body proportions. In this paper, we present a geometry-aware motion retargeting framework that preserves interaction semantics by performing proximity matching over spatially adaptive anchors. Unlike prior methods with static anchor definitions, the proposed method dynamically repositions anchors to reachable regions on the target character. This is achieved via a Transformer-based anchor refinement strategy that predicts anchor displacements and constrains the translated anchors to remain on the target character geometry through differentiable soft projection. By incorporating pose-dependent spatial structures from the source character, the adapted anchors provide structurally coherent guidance for interaction-aware retargeting. Conditioned on these anchors, a graph-based autoencoder predicts target skeletal motion that preserves the spatial configuration of the source. To encourage task-aligned optimization between anchor adaptation and motion retargeting, we adopt an alternating training scheme in which each module is optimized in turn. Through extensive evaluations, we demonstrate that our method outperforms state-of-the-art approaches in preserving interaction fidelity across diverse character geometries. Code is available at Project Page.
Supporting a wide variety of motion styles is critical for creating diverse virtual characters, but current methods either require large stylized datasets or pre-trained models that cannot generalize beyond their training distribution. We present STyMo, a few-shot approach that learns motion style from only seconds of paired data and trains in one to two minutes. Our key insight is to decompose style into two components: a static component capturing time-invariant posture, and a temporal component capturing frame-wise dynamics. This decomposition yields an interpretable system where posture intensity, temporal exaggeration, and per-body-region style can be adjusted at runtime. Furthermore, the reduction in required training data and computation time structurally permits an iterative authoring workflow. To ensure robustness on arbitrary inputs, we further introduce a stylizability gate that automatically prevents artifacts on out-of-distribution motions. We demonstrate results across diverse motion styles, from subtle emotional variations to exaggerated character archetypes, and release our processed paired dataset to facilitate future research. The source code used in this paper can be found at: https://github.com/facebookresearch/STyMo
Hair is a rich medium of visual and cultural expression, yet its digital modeling remains challenging due to the duality of fluidity and structure. Many existing generative approaches rely primarily on continuous diffusion fields, which entangle global topology with local texture and obscure the semantic and structural organization of hairstyles. To address this, we propose HairGPT, a strand-centric framework that treats strands as generative primitives and formulates realistic 3D hairstyle synthesis as a dual-decoupled autoregressive sequence modeling problem. Our method applies spatial decoupling across semantic scalp regions and structural decoupling along a hierarchical strand representation, progressing from global layout to fine-grained style. We further introduce a geometric tokenizer and region-aware semantic annotations to guide strand-level generation, enabling compositional editing, synthesis of rare and complex hairstyles, and adaptation to stylized domains. By aligning generative modeling with the workflow of digital grooming, HairGPT turns hair generation from opaque texture synthesis into a structured and semantically controllable authoring process, supporting robust semantic conditioning and high-fidelity results across realistic and stylized domains.
We present Mixwell, a family of sharp 2D fluid brushes and GPU-accelerated analytical methods for progressive, resolution-independent physics-based mixing. Derived from idealized potential flow around a cylindrical tine, Mixwell includes a cusped, Kelvinlet-style regularized velocity brush that parsimoniously captures cylinder-fluid interactions. Building on Maxwell's 1869 drift formulation, we develop GPU-friendly evaluation strategies for particle drift in both infinite and finite strokes. For image-based workflows, we introduce cylindrical Reverse-Drift Functions (RDFs), displacement fields that encode tine insertion, motion, and removal. Like signed distance fields in geometric modeling, RDFs compose naturally and can be chained in shaders to model complex operations while avoiding intermediate texture blur. We also propose a periodicity-exploiting composition scheme for complex RDF patterns. All Mixwell operations are evaluated independently per sample, enabling truly progressive mixing and rendering without global solves, grids, or intermediate texture resampling. We demonstrate real-time GLSL and HLSL implementations and production integrations in Houdini (OpenCL, OSL), enabling progressive, arbitrary-resolution mixing and rendering with negligible numerical dissipation.
We present ST-FLIP, a spatiotemporal extension of the Fluid-Implicit Particle (FLIP) method for incompressible free-surface and two-phase liquid simulation. ST-FLIP enables time steps up to an order of magnitude larger than those typically used in CFL-constrained solvers, while preserving detailed flow structures and visual fidelity. It addresses a common failure mode of large time steps in hybrid particle-grid liquid solvers: temporal under-sampling of particle motion produces aliasing-driven free-surface artifacts after projection. Our key idea is to interpret particles as samples in four-dimensional space-time: in addition to standard spatial jittering, we randomize particle positions along the time axis as well and perform particle-to-grid deposition using a separable 4D kernel. This yields a Monte Carlo estimator of perstep time-slab-integrated particle quantities. Although particles are treated as samples in 4D space-time, our approach works as a lightweight plugin by collapsing to slab-integrated 3D grid fields for projection. Building on recent particle-based phase-field work, we reuse the particle-to-grid weight accumulators as a conceptual space-time phase field, providing variable-coefficient projection weights and eliminating the need for per-step surface reconstruction. The method can be easily integrated into existing FLIP/PIC or APIC solvers with negligible additional computational cost per time step. The effectiveness of our approach is demonstrated through a series of comparisons with state-of-the-art solvers, yielding several-fold speedups for multi-billion-particle simulations at high effective 3D resolutions on a single workstation.
Multi-axis fused filament fabrication (FFF) reduces staircase artifacts and support material by adapting nozzle orientation. However, reliable and highly customizable printing requires layers and toolpaths combining a number of challenging properties: following prescribed fields, preserving constant bead geometry, avoiding stops, retractions, and collisions. We present AtomSlicer, which takes a 3D tool-orientation field and perlayer 2-RoSy tangent direction fields, to generate field-aligned non-planar layers of near-constant thickness. It then computes collision-free deposition toolpaths that are continuous within each layer, and as continuous as possible across layers. AtomSlicer encodes geometry with three orthogonal phase fields sampled into oriented atoms, partitions them into fabricable layers, reconstructs layer meshes, and synthesizes 2-RoSy-aligned toolpaths. Unlike prior methods it treats user- or optimizer-defined fields as constraints, producing a feasible toolpath or reporting non-fabricability rather than modifying the specification. We validate on varied shapes, including a large Thingi10k study, and 13 printed models using constant extrusion per unit path length under a fixed bead profile. AtomSlicer reduces non-extruding travel to a few percent, cuts travel moves by one to two orders of magnitude versus planar and Atomizer baselines, and is 9×-60× faster than Atomizer.
We introduce the PhaseTree, a novel hierarchical construction-tree representation for compactly modeling volumetric objects composed of multiple phases or materials across scales. An object is defined as a single construction tree that combines phase-aware primitives through composition and warping operators, yielding a unified multiphase signed distance representation that naturally supports complex topologies and interfaces between phases. The PhaseTree is compatible with standard signed distance field workflows: single-phase algorithms can be directly promoted to a PhaseTree, and conversely reduced without loss of information. As a result, our model integrates seamlessly with existing algorithms and rendering pipelines. We extend classical Sphere Tracing to robustly handle multiphase configurations and show that, despite the additional expressiveness, our implementation preserves the compactness and resolution independence of signed distance fields and incurs less than a 25% runtime overhead compared to single-phase Sphere Tracing.
Selection is a core operation in interactive image editing, enabling tasks such as composition or manipulation. To be practically useful, a user should be able to specify and disambiguate the desired selection region through either text- or click-based interactions, and the system should support selecting not only objects but also other criteria, such as materials. Material-based selection can be particularly valuable for tasks like re-texturing surfaces or consistently editing all instances of a specific material in a scene. However, existing vision–language-model (VLM) based selection methods are largely object-centric and typically support only a single interaction modality, limiting their applicability in real editing workflows. In this work, we thus present Mask Any Object And Material (MAOAM), a unified selection framework that enables precise object- and material-level selection across both text- and click-based interactions. MAOAM leverages a VLM with a segmentation head to produce pixel-accurate masks from user prompts: the VLM interprets the user’s selection intent — object- or material-level — and encodes visual entities, attributes, and spatial relations, while the segmentation head decodes the VLM’s output token into a mask. A key challenge is that material selection datasets with text annotations are unavailable. We therefore propose a scalable data generation pipeline: we collect real and synthetic images with material masks, then leverage VLMs to generate material descriptions with rich visual-semantic information. Using the generated data, we train MAOAM with a multi-task objective over click- and text-based selection, along with an auxiliary VQA task derived from the material descriptions to facilitate deeper material understanding. Despite being trained with uni-modal prompts, our model exhibits an emergent improvement in selection quality when combining text and clicks at inference time, enabling more flexible image editing workflows. Experiments demonstrate accurate and coherent selections across diverse objects, materials, and interaction scenarios, highlighting robustness in practice.
As instruction-based editing models and multimodal large language models continue to advance, a wide range of image editing tasks have become feasible. However, achieving precise and consistent geometric image editing, such as translating, scaling and rotating in 3D space, remains a major challenge. In this work, we introduce BoxCtrl, a 3D-aware visual prompting framework to address this problem. Unlike text-only or coarse 2D-guided approaches, our method introduces informative RGB 3D bounding boxes projected onto 2D images as a visual prompting. Each box is outlined and its three orthogonal faces are individually painted with different RGB colors, which simultaneously encode its position, size and orientation, providing a compact and intuitive in-context visual example. The key to BoxCtrl’s success lies in its well-designed bounding boxes, which serve as visual prompting that decouple geometric control from appearance control. This design enables the model to learn consistent correspondences between faces with the same color in the latent space, leading to a more precise understanding of geometric intention and more accurate editing result. We introduce a two-stage training paradigm comprising Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL). To address the scarcity of paired training data, we first construct a large-scale synthetic dataset for the SFT stage, which equips the model with fundamental editing capabilities. However, the generalization of the SFT model is constrained by the synthetic-to-real domain gap. To bridge this, we incorporate an online RL stage leveraging unpaired real-world data. Guided by a comprehensive reward function evaluating both geometric accuracy and visual fidelity, our SFT-RL strategy significantly enhances geometric precision while maintaining photorealistic quality. Extensive experiments demonstrate that BoxCtrl achieves state-of-the-art performance across translation, rotation, scaling, and composite editing tasks. Our code is available at https://github.com/beaglew/BoxCtrl.
We present Diceplay, a modular physical display for abstract visual composition built from a grid of identical dice. Each die has six faces with distinct geometric primitives, and images emerge through the placement and orientation of the dice. While this medium enables reusable and reconfigurable physical imagery, it poses a challenging design problem: images must be expressed through discrete, extremely low-resolution abstractions, making manual authoring difficult. To address this challenge, we introduce a computational design system that automatically generates Diceplay configurations from text prompts. Our key technical contribution is a grammar-based formulation that relaxes this discrete design space into a smooth optimization landscape, enabling gradient-based optimization using score distillation sampling. We show that our approach consistently produces meaningful abstractions for this medium, whereas state-of-the-art smoothing techniques fail in this extremely challenging regime. We demonstrate our method across a range of prompts and fabricated examples, showing how computationally generated abstractions can be realized as physical visual artifacts.
Photorealistic volume rendering suffers from slow convergence with traditional path tracing algorithms and poses significant challenges for real-time applications. In this paper, we present Multi-feature Radiance Baking Neural Networks (MRBNN), a neural volumetric rendering method that achieves real-time performance by leveraging analytic decomposition of scattering with an efficient learned representation. Our method reformulates in-scattering integral in Volumetric Radiance Transfer Equation to diagonal scaling operator in spherical harmonics spectrum. Building on this formulation, we propose a compact factorized representation with low-rank compression in latent space that replaces costly integration. We then introduce efficient dual-pattern feature sampling and a lightweight neural decoder for fast radiance prediction. With these dedicated designs, MRBNN achieves 4 ∼ 5 × speedup over the state-of-the-art while maintaining high visual fidelity. Moreover, our method addresses key limitations of prior work, including over-illumination artifacts and inability to handle volumes with spatially varying albedo or heterogeneous phase parameters. Extensive experiments demonstrate that our neural baking method can synthesize photorealistic images for complex volumes in a few milliseconds.