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.
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3D shapes from scanning, reconstruction, or AI-generated content often lack simple quad mesh layouts—critical for efficient editing and modeling. Existing quad-remeshing techniques typically produce complex layouts with irregular loops, leading to tedious manual cleanup and extensive algorithm tuning. We introduce SQUADGEN, a diffusion-based generative framework that leverages Chart Distance Fields (CDF) to synthesize simple quad layouts on 3D shapes. Our approach addresses two key challenges: (1) the discrete nature of mesh connectivity, which hinders learning, and (2) the scarcity of large-scale datasets with simple quad meshes. To overcome the first, we propose CDF, a continuous surface-based representation enabling effective learning and synthesis of quad layouts. To address the second, we define loop-aware simplicity metrics and construct a large-scale dataset of high-quality quad layouts recovered from public 3D repositories through a robust quad-recovery pipeline. Extensive evaluations across diverse 3D inputs show that SQUADGEN consistently outperforms existing methods, producing robust, artist-friendly simple quad layouts.
Constant mean curvature surfaces are æsthetically appealing geometric objects with applications in physics, differential geometry, and architecture. We present a straightforward discretization of constant mean curvature surfaces based on the classical observation that their Gauß maps are harmonic. Our construction is elementary—requiring only discrete Dirichlet energy minimization and a Poisson solve—yet it exactly mirrors this aspect of the smooth theory. A discrete analog of conjugation produces discrete constant Gauß curvature surfaces. Their unit offsets are discrete CMC surfaces with a conformal parameterization. Additionally, we introduce a novel Möbius-invariant discretization of the Dirichlet energy for sphere-valued maps on dual meshes that is derived from the discrete Willmore energy. It is more robust than standard formulations based on inverse cotangent weights. Our approach to the construction of constant mean curvature surfaces provides direct control over tangent planes along a boundary, if present, and naturally handles closed and periodic examples. We demonstrate the approach on a range of free-boundary, symmetric, and periodic CMC surfaces.
Incremental Potential Contact (IPC) has emerged as a robust and unifying formulation for contact-rich physical simulation by casting elasticity and collision handling as a single energy minimization problem. Achieving high performance, however, typically requires heavily specialized implementations that hard-code assumptions about energies, primitive types, and parameterizations, creating a major barrier to extensibility. Adding new energies or alternative parameterizations often requires re-deriving first and second-order derivatives, and implementing new assembly logic for the global Hessian and gradient. This challenge is further exacerbated by collision energies, where the same energy definition is often applied to mixed parameterizations, which can lead to a combinatorial explosion of parameterization-specific derivative and assembly cases. In this paper we introduce YASPS, a framework for physical simulation that resolves this limitation by making structural relationships explicit in a differentiable representation. YASPS introduces two relational operators, JOIN and UNION, which encode connectivity and heterogeneous parameterizations directly in the symbolic computation graph. Using symbolic differentiation over these operators, YASPS automatically derives local derivatives, and determines the induced sparsity and block structure of global gradients and Hessians from the same description while avoiding any code explosion induced by mixed-parameterizations. Targeting IPC workloads, YASPS compiles the resulting symbolic graphs into GPU kernels for local energy evaluation, derivative computation, and block-sparse matrix assembly, and solves the resulting Newton systems using a GPU-based iterative solver. This approach achieves performance competitive with state-of-the-art IPC implementations while enabling new energies and parameterizations to be added through localized symbolic definitions, without hand-written derivative or assembly code.
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/.
Fine-tuning-based adaptation is widely used to customize diffusion-based image generation, leading to large collections of community-created adapters that capture diverse subjects and styles. Adapters derived from the same base model can be merged linearly, enabling the synthesis of new visual results within a vast and continuous design space. To explore this space, current workflows rely on manual slider-based tuning, an approach that scales poorly and makes merging coefficient selection difficult, even when the candidate set is limited to 20–30 adapters. We propose GimmBO to support interactive exploration of adapter merging for image generation through Preferential Bayesian Optimization (PBO). Motivated by observations from real-world usage, including sparsity and constrained coefficient ranges, we introduce a two-stage BO backend that improves sampling efficiency and convergence in high-dimensional spaces. We evaluate our approach with simulated users and a user study, demonstrating improved convergence, high success rates, and consistent gains over BO and line-search baselines, and further show the flexibility of the framework through several extensions.
Many non-photorealistic rendering (NPR) styles, such as feature lines and hatching, are defined by image-space structure inherited from hand-drawn media. While recent path-space formulations like the stylized rendering equation (SRE) enable stylization to interact naturally with light transport, they provide no mechanism for enforcing image-space consistency. We present a conceptual framework for lifting image-space stylizations into path-space in a principled, SRE-compatible manner. Our key observation is that image-space consistency can be achieved by establishing geometrically-driven mappings from image-space to path-space. We demonstrate this through two complementary stylizations: feature lines and tone. For feature line rendering, we introduce a conditional lifting based on partial path-space variation, where a geometric path parametrization is combined with parallel transport to preserve image-space structure under distribution effects. This enables a curvature-aware, stochastic, geometry-driven formulation of line detection that generalizes prior ray-based methods. For tone-based styles, such as hatching and halftone, we propose a canonical lifting anchored to a material-independent mapping, motivated by stationary-phase arguments from wave optics. Its locally invertible approximation enables evaluation of image-space tone fields at arbitrary path vertices while preserving image-space structure under complex light transport. Both methods are implemented as ordinary style functions under the SRE and work with existing estimation and sampling strategies; demonstrating how image-space structure can be preserved within path-space rendering, enabling a broader class of expressive, physically-grounded NPR styles.
To enable differentiation with respect to object geometries, boundary path integrals—central to physics-based differentiable rendering—must be estimated numerically. Although their mathematical formulation is well established, designing efficient and robust numerical estimators remains challenging. Most state-of-the-art boundary sampling methods rely on primary-sample-space guiding, which tends to break down on finely tessellated geometries; reparameterization-based alternatives, meanwhile, often incur high variance and/or significant computational overhead. In this paper, we introduce a simple, robust, and consistent solution to this problem. At the core of our approach is a novel formulation of the boundary integral based on kernel-density estimation. Much like photon mapping, we slightly expand the measure-zero domain of integration with a kernel, sidestepping the need to sample directly on a delta-function region in path space. To our knowledge, this is the first such application of kernel-density methods for boundary integral evaluation. We validate our method by comparing its derivative estimates against finite differences (FD), and further demonstrate its practical utility by benchmarking against several state-of-the-art baselines in synthetic inverse-rendering scenarios.
Differentiable volume rendering enables gradient-based optimization of volumetric scenes, but unbiased estimators suffer from high gradient variance. We observe that the extinction gradients split into two components on structurally different integration domains: a scattering term evaluated at a single path vertex, and a transmittance term integrated along the ray segment. Because the domains are mismatched, existing estimators sample the two components at different locations, leaving the negative correlation between their opposite-signed contributions unexploited. We expose this overlooked correlation and exploit it through a principle we call sample matching: evaluate both components at shared sample locations. To enable this, we derive the first reformulation of the differential path integral that couples the two contributions within a single integrand, yielding an unbiased Monte Carlo estimator that ties them together by construction. For efficiency, the estimator reuses partially sampled light paths and amortizes in-scattering cost by evaluating gradients at multiple probe points per segment. On voxel-grid reconstruction, our estimator reduces gradient variance by up to 80% over differential ratio tracking (DRT), yielding faster convergence and higher reconstruction quality.
Differentiable path tracing offers a principled route to recovering physical material and lighting parameters, but the combination of high variance and poor numerical conditioning often makes it too brittle to use in practice. This is especially the case when lighting is altogether unknown, or when the scene contains complex light transport effects. Prior work recently showed that the variance reduction provided by a radiance cache can alleviate these challenges. We revisit the combination of inverse rendering and radiance caching with a twist, by introducing a spatial blending field that locally interpolates between the cache and standard unbiased estimators. Recursive application of this idea yields a rich design space of evaluation strategies and inter-estimator consistency losses; we map this space and identify effective components. A surprising property of the resulting algorithm is that it can accurately recover material parameters even when the lighting is not uniquely identifiable from the observations. Our experiments demonstrate significant improvements in speed and robustness over prior work, making a strong case for including radiance caching as a standard component of future physically based inverse rendering systems.
Discrete X-ray tomography reconstructs the internal structure of an object from X-ray projections, assuming that the volume is composed of a discrete set of known materials (e.g., steel, aluminum, and air). This is generally straightforward when many projections are available but becomes increasingly ill-posed as their number decreases. Discrete tomography has been extensively studied over the past five decades, resulting in a range of mature reconstruction algorithms. In this work, we introduce a new reconstruction method that draws inspiration from both classical computed tomography and recent advances in inverse rendering, demonstrating that a remarkably simple gradient-based inversion can significantly surpass the reconstruction quality of standard methods such as SIRT, DART, and TVR-DART. Our method represents each 3D location as a probability distribution over the set of known materials and minimizes a volumetric loss that encourages consistency with the measured projections. It supports nonlinear effects such as volumetric scattering and is simple to optimize and parallelize on compute accelerators. We evaluate our method on challenging 2D and 3D benchmarks, demonstrating superior performance particularly in sparse and limited-angle scenarios, where traditional techniques struggle with ambiguity.
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.
Elliptic partial differential equations are ubiquitous in graphics and engineering, but remain challenging to solve on complex or evolving geometries. Traditional discretization schemes (e.g., FEM/FDM) provide stable, globally coupled solutions but require heavy meshing or extreme refinement to accurately resolve geometric detail. In contrast, grid-free Monte Carlo methods (e.g., Walk on Spheres/Stars) adapt naturally to arbitrary geometry and offer massive parallelism, but rely on long random walks whose variance grows rapidly, particularly in the presence of Neumann boundaries, leading to slow convergence. We introduce a hybrid approach that combines the geometric flexibility of Monte Carlo estimation with deterministic global solves that do not introduce additional stochastic error. Our method decomposes the domain into simple, regular subdomains and uses Monte Carlo to estimate local first-passage solution operators (Poisson kernels), where walk lengths and variance are inherently controlled by the reduced spatial scale. These local operators are assembled into a sparse global system whose solution is obtained via a deterministic linear solve that exactly replaces simulating discrete random walks throughout the domain. This global solve trades stochastic variance for a fixed, resolution-dependent discretization bias, yielding stable and reusable solution operators. As a result, our method attains accurate, geometry-aware solutions even on coarse discretizations, and enables efficient solves and re-solves by computing and updating only the local operators affected by the geometry and its changes. We evaluate the approach on complex two-dimensional domains, benchmarking accuracy and convergence against standard grid-free and grid-based baselines, and demonstrate applications to microstructure simulation and flow-based path planning and streamline visualization.
Monte Carlo PDE solvers have become increasingly popular for solving heat-related partial differential equations in geometry processing and computer graphics due to their robustness in handling complex geometries. While existing methods can handle Dirichlet, Neumann, and linear Robin boundary conditions, nonlinear boundary conditions arising from thermal radiation remain largely unexplored. In this paper, we introduce a Picard-style fixed-point iteration framework that enables Monte Carlo PDE solvers to handle nonlinear radiative boundary conditions. While strict theoretical convergence is not generally guaranteed, our method remains stable and empirically convergent with a properly chosen relaxation coefficient. Even with imprecise initial boundary estimates, it progressively approaches the correct solution. Compared to standard linearization strategies, the proposed approach achieves significantly higher accuracy. To further address the high variance inherent in Monte Carlo estimators, we propose a heteroscedastic regression-based denoising technique specifically designed for on-boundary solution estimates, filling a gap left by prior variance reduction methods that focus solely on interior points. We validate our approach through extensive evaluations on synthetic benchmarks and demonstrate its effectiveness on practical heat radiation simulations with complex geometries.
Grid-free Monte Carlo methods are capable of solving Poisson equations on highly complex domains. However, existing methods operate solely in the primal domain and can converge slowly due to high variance. Inspired by gradient-domain rendering, we introduce a gradient-domain framework for Poisson problems. Specifically, we devise a new Monte Carlo estimator that directly targets differences of the solution between spatially varying query locations. Further, we adopt state-of-the-art reconstruction techniques originated in gradient-domain rendering to allow efficient reconstruction of the solutions without incurring additional bias. We demonstrate the effectiveness of our technique by comparing solutions obtained using our method and several state-of-the-art baselines.
The Walk on Spheres (WoS) algorithm is a mesh-free and highly flexible Monte Carlo method for solving partial differential equations, but its practical applicability is limited by slow O (N-1/2) convergence. While prior variance reduction techniques exploit spatial correlations through integral properties of the PDE, they do not fully utilize the intrinsic Markov structure of the WoS process. We introduce a new variance reduction framework based on reusing intermediate states along each random walk. Leveraging the Markov property, we show that every point visited by a WoS trajectory provides a valid unbiased estimator, but its direct use is hindered by the complex distribution induced by dynamically generated spheres. To resolve this, we propose the Walk on Probes (WoP) algorithm, which replaces dynamic spheres with a set of fixed, pre-distributed spherical probes inside the domain. This converts the intractable distribution of path points into samples on fixed boundaries, enabling efficient evaluation through the Poisson integral formula. We further develop a specialized method that combines control variates with self-normalization to further reduce variance. Together, these components substantially improve sample efficiency while preserving the flexibility of WoS. Code and data for this paper are at https://github.com/USTCGCL-WoS/Walk-on-Probes.
Providing haptic feedback in virtual reality (VR) remains challenging, with active haptic systems often being bulky and expensive, while passive haptics typically require pre-fabricated objects or extensive real-world setup. We present ProXeek, an LLM-based multi-agent system that opportunistically leverages real-world objects as haptic proxies for VR experiences. During VR development, the designers could annotate the virtual interactables with emphasized haptic characteristics using our node-based editing interface. On the user side, end users capture environmental snapshots via commodity VR headset, and the system employs LLM-based multimodal reasoning and multi-objective optimization to match virtual objects with viable physical proxies. Our technical evaluation demonstrates that ProXeek effectively identifies viable proxies, confirming the effectiveness of the algorithmic constraint design in our matching pipeline. Our user study further reveals that the ProXeek-selected physical objects could deliver significantly higher haptic fidelity and enhance presence compared to 3D-printed replicas and visual-only interaction.
Mixed Reality (MR) headsets promise a future of immersive telepresence where virtual humans blend indistinguishably into their real or virtual surroundings. Achieving this vision requires a method capable of capturing a user's motion, estimating their appearance under novel lighting, and understanding the surrounding environment - all from the constrained viewpoint of a head-mounted display (HMD). Existing approaches treat these as isolated problems: they either focus on driving avatars with baked-in lighting or rely on complex studio setups for relighting. In this paper, we present EgoRelight, a holistic framework for egocentric telepresence that simultaneously captures full-body human performance, synthesizes photorealistic and relightable appearance, and estimates high dynamic range (HDR) environment maps from a single HMD. First, to ensure accurate motion and surface reconstruction, we propose an egocentric perception module that leverages stereo down-facing cameras to extract dense depth maps, which serve as robust geometric control signals to drive a mesh-based avatar. Second, we introduce a novel neural appearance model that learns to synthesize view-dependent specular and view-independent diffuse shading separately. By employing a specialized ray-sampling strategy, our model generalizes to unseen illumination without relying on restrictive analytical BRDF priors. Third, we enable seamless avatar integration into the physical world via a test-time inverse rendering process, which recovers an HDR environment map by matching the pre-trained avatar's appearance to the live egocentric camera observations. We demonstrate the efficiency of our system through a social telepresence application, where remote users are coherently relit according to their local physical environment. Extensive experiments show that our individual components and the integrated system significantly outperform the best combinations of state-of-the-art baselines in both geometric accuracy and rendering as well as relighting fidelity. Further details can be found on our project page1.
We present a role-aware virtual agent navigational interaction that generates consistent, role-aligned movement behaviors. Our approach leverages Multimodal Large Language Models (MLLMs) to interpret multimodal inputs including scene information, user state, and high-level language role instruction, producing discrete navigation decisions and stylized planning path. Our approach enables virtual agents to behave consistently with narrative roles and respond to dynamic actions, such as playing a hide-and-seek taking into account the agent's role and the user's possible intention. Our approach demonstrates how MLLMs can go beyond language-based interaction to support embodied, spatial, and role-aware agent behaviors in immersive environments such as augmented reality.