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arXiv2026

PTIR-GS: Path-Traced Inverse Rendering with Global Illumination in 3D Gaussian Fields

Ray tracing enables 3D Gaussian fields to serve as a representation for physically based light transport. Faithful inverse rendering requires forward rendering and backward optimization to be defined within a consistent light-transport pipeline. Existing Gaussian inverse-rendering methods typically rely on splatting-derived G-buffers and screen-space optimization. The local affine approximation of perspective projection can introduce inconsistencies with path tracing, while simplified rendering formulations often neglect or approximate indirect illumination and visibility. Therefore, we propose a splatting-free path-traced inverse-rendering framework for 3D Gaussian fields that unifies forward rendering and backward optimization within the same recursive multi-bounce light-transport pipeline. We formulate light transport over overlapping Gaussian primitives directly in path space, enabling Monte Carlo path tracing and pathwise gradient replay over the same recursively sampled transport paths. The framework jointly optimizes materials and environment light under the full rendering equation, with ray-traced visibility and global illumination explicitly evaluated. Extensive experiments demonstrate competitive material estimation and improved path-traced rendering quality, producing more plausible shadows, reflections, and relighting under global illumination.

cs.GR↗
arXiv2026

TailorCoPilot: Enabling Agentic Pattern Making with Version-Controlled State Tracking

Experience-driven manufacturing, such as garment pattern making, faces a severe generational skills gap because its core expertise relies on undocumented tacit knowledge forged through day-to-day practice. To address this challenge, we present TailorCoPilot, an agentic pattern-making system built upon a specially designed version-control backend TailorTrace. TailorTrace models sewing patterns as structured, discrete states and records their transformations during the pattern-making process as explicit operation sequences defined upon the geometry primitives in the sewing pattern (panels, edges, vertices and stitches). Integrated into a conventional pattern-making GUI, TailorTrace enables seamless documentation of senior experts' tacit pattern-making knowledge without breaking their daily workflow. The documented knowledge further offers interactive, pedagogical scaffolding for novices, while providing a robust foundation to power TailorCoPilot and train future generative AI models. In a user study with novices and advanced novices, TailorCoPilot improved task completion rates, reduced time and perceived workload, and yielded higher-quality artifacts compared to skill-appropriate baselines. Ultimately, TailorCoPilot demonstrates a viable pathway to capture practice-based expertise, operationalizing it to support both generative AI advancements and human apprenticeship.

cs.HC↗
arXiv2026

Inverse Rendering for Modeling with Line Primitives

Faithfully capturing diverse real-world objects with fuzzy, anisotropic structures, such as hair, fur, fibers, and textiles, for efficient real-time visualization remains challenging. Recent radiance field reconstruction methods capture these structures from multi-view images using translucent volumetric primitives such as 3D Gaussians rather than opaque low-dimensional primitives (e.g., triangles, line segments, and polylines), thereby limiting compatibility with standard depth-tested rasterization, reflection modeling, and physical simulation. We present an inverse rendering method for reconstructing fuzzy geometry using explicit line segments, which are rasterized on a subpixel grid for anti-aliasing to reproduce a semi-transparent appearance. While straightforward to render, optimizing numerous line primitives to match target images poses a significant challenge. We address this by introducing a stochastic differentiable rasterizer for line segments that produces informative gradients with respect to vertex positions, attributes, and discrete connectivity. Experiments on synthetic and real-world datasets show that our method outperforms surface-based approaches in capturing fuzzy boundaries and achieves quality comparable to volumetric representations while relying entirely on explicit geometry. The resulting representation integrates seamlessly with standard graphics pipelines, enabling cross-platform rendering, various shading models, and physical simulation.

cs.GR↗
arXiv2026

Figures as Programs: Recursive Generation of Editable Scientific Figures

Scientific methodology figures are essential for communicating complex methods clearly, yet creating them remains labor-intensive and typically requires multiple rounds of refinement. Recent image-generation models can synthesize visually appealing raster figures, but producing a human-satisfactory result in a single generation step remains difficult. Moreover, precise edits to raster figures are challenging for both humans and models. We formulate scientific figure generation as recursive SVG program construction and propose \textsc{FigTree}, a \textit{multi-agent} system that automatically transforms a scientific paper into a structured vector figure. \textsc{FigTree} grounds figure content in the source paper, decomposes a figure into a hierarchy of local regions, generates each region as a short SVG program, and assembles the resulting fragments. A render-critic refinement loop jointly inspects the rendered figure and its underlying program, enabling visual defects to be traced to specific statements and accurately repaired. We conduct extensive evaluations of \textsc{FigTree} on figure quality and editability, showing that \textsc{FigTree} produces high-quality figures, while also enabling more effective editing than existing raster-based methods.

cs.AI↗
arXiv2026

Depth-1 expanders on the unitary group and applications

We construct a constant-degree and constant-gap quantum expander on $n$ qubits where each unitary can be implemented by a depth-$1$ and 1D circuit of Pauli or CNOT gates. We provide two applications of this expander. First, we use it to construct a family of frustration-free 1D Hamiltonians whose ground states obey the entanglement-gap relation $S = Θ(Δ^{-1/2})$; this is believed to be optimal, but achieving it had been open. Second, we use it to provide a streaming protocol that tests for closeness to a class of 1D volume-law entangled states. Moreover, we extend our quantum expander to a constant-degree and constant-gap expander on the unitary group where each unitary is a single $T$ gate, a single $T^{\dagger}$ gate, or a depth-$1$ Clifford circuit. This implies that a random sequence of unitaries from the expander yields a gapped walk on a dense subgroup of the unitary group. This improves upon previous work by Bourgain and Gamburd which did not control the dependence of the gap on the dimension.

quant-ph↗
arXiv2026

MeshSplatBench: A Unified Benchmark for Triangle-Based Neural Rendering

Triangle-based neural rendering bridges neural scene representations and conventional graphics pipelines by optimizing explicit geometric primitives compatible with standard rasterization hardware. However, existing approaches are evaluated almost exclusively within custom research renderers, obscuring their practical deployability in production engines. To bridge this gap, we introduce \textbf{MeshSplatBench}, a unified benchmark that systematically investigates triangle-based neural rendering across the complete pipeline from native optimization to game-engine deployment. MeshSplatBench establishes a standardized evaluation protocol while preserving each method's native optimization semantics, reproducing published results within $0.8\%$ PSNR deviation. Furthermore, we introduce a hierarchical Unity deployment protocol spanning three rendering tiers: native CUDA renderers, method-specific dedicated engine shaders, and standard opaque mesh pipelines, isolating the exact fidelity losses caused by engine adaptation \textit{vs.} representation reduction. Finally, we conduct a topological audit of reconstructed surfaces, demonstrating that explicit connectivity and shared indexing alone are insufficient to guarantee production-ready assets due to prevalent non-manifold structures, fragmented components, and boundary artifacts. Overall, MeshSplatBench demonstrates that rasterizability is merely a primitive-level attribute, whereas graphics readiness requires jthe holistic alignment of representation, topology, and engine compatibility. Source code will be released.

cs.GR↗
arXiv2026

Unifying Physics-Based Humanoid Interaction with a Context-Conditioned Interaction Prior

Developing unified physics-based humanoid controllers that can navigate complex 3D scenes and manipulate objects remains a longstanding challenge. Existing approaches are often specialized for either locomotion or object-centric manipulation, or rely on task-specific reward engineering that does not scale well across diverse behaviors. We present CHIP, a unified, physics-grounded framework for learning reusable humanoid interaction skills from heterogeneous motion data. Central to our approach is a conditional interaction prior that models a context-dependent distribution over these skills within a shared discrete space. Our method is trained in three stages. We first learn physics-based motion-imitation policies that acquire grounded teacher behaviors from heterogeneous interaction data. We then distill these behaviors into a context-conditioned interaction prior that captures reusable motion structure across locomotion and manipulation. Finally, we initialize downstream task policies from the pretrained prior and adapt them through prior-regularized online RL post-training. Experiments on a diverse suite of humanoid interaction tasks show that our approach supports scene-aware locomotion, contact-rich object manipulation, and compositional behaviors such as environment-aware object transport and long-horizon skill sequencing, while producing smooth transitions and physically plausible motion.

cs.RO↗
arXiv2026

Neural Centroidal Voronoi Tessellations

Centroidal Voronoi tessellation (CVT) is a fundamental primitive for high-quality surface sampling and isotropic remeshing in computer graphics. However, computing surface CVTs with classical solvers remains expensive: each optimization step repeatedly constructs restricted Voronoi diagrams (RVDs) and integrates quantities over their surface cells. We introduce Neural CVT, a learning-based surface-CVT solver that replaces these costly geometric computations with a recurrent neural optimizer, accelerating CVT optimization by one to two orders of magnitude in our benchmarks while preserving geometric fidelity. Given an input surface, we sample a dense point cloud and extract multi-scale geometric descriptors with a graph neural encoder. A lightweight recurrent optimizer then refines seed positions over a small number of iterations, aggregating interpolated surface features and optimization history to predict per-seed displacements. The framework is trained self-supervised using CVT objectives that promote uniform distributions and, when desired, feature alignment. Across diverse organic and CAD-like shapes, Neural CVT generalizes to unseen geometry, initialization strategies, and seed densities, producing isotropic, feature-preserving remeshes comparable to state-of-the-art offline optimization methods at a fraction of the computational cost. Code and trained models will be released.

cs.GR↗
arXiv2026

FrameTwin: Curve-Anchored Gaussian Alignment from Sparse Views for Adaptive Wireframe 3D Printing

We present FrameTwin, a curve-anchored Gaussian alignment framework that uses sparse-view images to close the control loop for adaptive wireframe 3D printing. Our key idea is to capture the deformation of thin wireframe structures from sparse-view images using Gaussian kernels anchored to parametric curves, yielding a compact and geometry-aware encoding that explicitly captures strut topology. Driven by a differentiable rendering pipeline, FrameTwin estimates a neural deformation field that aligns the partially printed target model with the deformed structure observed during fabrication, where the optimized curve-Gaussian representation serves as a digital twin of the evolving wireframe. Unlike general Gaussian-splatting approaches, our formulation constrains kernel placement along parametric curves, substantially reducing the ambiguity inherent in sparse-view observations of thin structures. The resultant deformation-field alignment enforces global consistency across all struts. By using the estimated deformation field to blend the distorted printed geometry with the remaining unprinted geometry, FrameTwin enables adaptive updates to future printing trajectories. We demonstrate that FrameTwin can robustly capture and compensate for deformation in wireframe models fabricated using a robotized 3D printing system.

cs.GR↗
arXiv2026

DesignAsCode: Bridging Structural Editability and Visual Fidelity in Graphic Design Generation

Graphic design generation demands a delicate balance between high visual fidelity and fine-grained structural editability. However, existing approaches typically bifurcate into either non-editable raster image synthesis or abstract layout generation devoid of visual content. Recent combinations of these two approaches attempt to bridge this gap but often suffer from rigid composition schemas and unresolvable visual dissonances (e.g., text-background conflicts) due to their inexpressive representation and open-loop nature. To address these challenges, we propose DesignAsCode, a novel framework that reimagines graphic design as a programmatic synthesis task using HTML/CSS. Specifically, we introduce a Plan-Implement-Reflect pipeline, incorporating a Semantic Planner to construct dynamic, variable-depth element hierarchies and a Visual-Aware Reflection mechanism that optimizes the code to rectify rendering artifacts. Extensive experiments demonstrate that DesignAsCode significantly outperforms baselines in both structural validity and aesthetic quality. Furthermore, our code-native representation unlocks advanced capabilities, including automatic layout retargeting, complex document generation (e.g., resumes), and CSS-based animation. Our project page is available at https://liuziyuan1109.github.io/design-as-code/.

cs.GR↗
arXiv2025

SplArt: Articulation Estimation and Part-Level Reconstruction with 3D Gaussian Splatting

Reconstructing articulated objects prevalent in daily environments is crucial for applications in augmented/virtual reality and robotics. However, existing methods face scalability limitations (requiring 3D supervision or costly annotations), robustness issues (being susceptible to local optima), and rendering shortcomings (lacking speed or photorealism). We introduce SplArt, a self-supervised, category-agnostic framework that leverages 3D Gaussian Splatting (3DGS) to reconstruct articulated objects and infer kinematics from two sets of posed RGB images captured at different articulation states, enabling real-time photorealistic rendering for novel viewpoints and articulations. SplArt augments 3DGS with a differentiable mobility parameter per Gaussian, achieving refined part segmentation. A multi-stage optimization strategy is employed to progressively handle reconstruction, part segmentation, and articulation estimation, significantly enhancing robustness and accuracy. SplArt exploits geometric self-supervision, effectively addressing challenging scenarios without requiring 3D annotations or category-specific priors. Evaluations on established and newly proposed benchmarks, along with applications to real-world scenarios using a handheld RGB camera, demonstrate SplArt's state-of-the-art performance and real-world practicality. Code is publicly available at https://github.com/ripl/splart.

cs.CV↗
arXiv2026

From Splats to Silicon: Rethinking Computational Efficiency of 3DGS

3D Gaussian splatting (3DGS) represents scenes with explicit primitives and supports real-time novel-view synthesis, yet its system efficiency varies substantially across scenes, viewpoints, rendering paths, and platform constraints. Existing studies pursue efficiency through representation and algorithm design, GPU runtime optimization, and architectural support, but their reported gains correspond to different points along the rendering and update paths. Connecting these indicators to end-to-end system benefit requires tracing how each optimization changes Gaussian selection, screen-space work, data movement, and stage or frame time. We therefore use a workload-centric framework to connect representation and algorithm research, GPU runtimes, and hardware architectures and to identify recurring workload patterns. We complement literature analysis with reproduced measurements and controlled GPU profiling of selected implementations, relating workload counts to stage time and memory traffic. Together, these comparisons show that system gains depend on workload reductions reaching downstream execution, granularity matching each stage, and the cost of data transfers, synchronization, and cached results, gradients, and optimizer data. Building on these findings, we discuss more consistent evaluation under rendering-quality constraints and identify key directions for future system design.

cs.AR↗
arXiv2026

Geodesic-informed Generative Diffusion Model For Topology-preserved Image Video Generation

Generative diffusion models have emerged as a class of powerful techniques for various imaging applications, including but not limited to synthesis, reconstruction, and segmentation. Despite their success, current generative models pose two key limitations. First, they primarily rely on image intensity and texture information, with limited attention to underlying object geometry. As a result, they do not guarantee geometric or topological consistency during the generation process, which is a crucial requirement for high-stakes domains such as computational anatomy, biology, and robotics, where preserving object structure is critical. Second, existing models fail to explicitly learn or represent shape changes in the generative process. Such deformation dynamics remain occluded within network parameters; hence leaving the transformation process uninterpretable and physically uninformed. To address these challenges, we introduce IGG (Image Generation informed by Geodesic dynamics), a novel framework that integrates topology-preserving geodesic principles into the diffusion-based generative process. In contrast to conventional methods that operate in image intensity space, IGG learns and synthesizes diverse samples within geodesic deformation spaces, where geometric object changes are learned as smooth and invertible smooth mappings from a given template/source image. Our code is publicly available at https://github.com/nellie689/IGG.

cs.LG↗
arXiv2026

The best approximation pair problem relative to two subsets in a normed space

In the classical best approximation pair (BAP) problem, one is given two nonempty, closed, convex and disjoint subsets in a finite- or an infinite-dimensional Hilbert space, and the goal is to find a pair of points, each from each subset, which realizes the distance between the subsets. Motivated by our recent algorithm for solving the BAP problem [Censor, Mansour, Reem, J. Approx. Theory (2024)], we discuss the problem in more general normed spaces and with possibly non-convex subsets, and focus our attention on the fundamental issues of uniqueness and existence of the solution to the problem. We present several sufficient geometric conditions for the (at most) uniqueness of a BAP. These conditions are related to the structure and the relative orientation of the boundaries of the subsets and to the norm. We also present many sufficient conditions for the existence of a BAP. In general, the paper re-examines several aspects related to the BAP problem, including the historical one, and shows, probably for the first time, how wide is the scope of the BAP problem in terms of the scientific communities which are involved in it (frequently independently) and in terms of its applications.

math.OC↗
arXiv2026

Learning Subgroup Relations Using Siamese Graph Neural Networks

Determining whether one finite group is isomorphic to a subgroup of another is a fundamental problem in computational group theory. In this work, we propose a Siamese Graph Neural Network (Siamese GNN) for subgroup prediction using Cayley graph representations of finite groups. Each input group is represented by its undirected Cayley graph and encoded by one branch of a Siamese GNN to produce a graph embedding. The resulting graph embeddings are combined with algebraic features derived directly from the input groups to construct a joint feature vector, which is processed by a fully connected classifier to predict subgroup relations between finite groups. By integrating graph-based structural representations with algebraic features, the proposed framework provides a unified approach for learning subgroup relations from finite groups. Experimental results on an expanded and more diverse dataset of 308 finite-group pairs drawn from 11 group families demonstrate the effectiveness of the proposed architecture, achieving a test BA of 91.67% on an independent test set. Additional experiments evaluate generalization to unseen groups, robustness to different Cayley graph generating sets, the contribution of GNN message passing, performance relative to non-neural baselines, and comparison with exact computational methods. These results illustrate the potential of geometric deep learning for subgroup prediction.

cs.LG↗
arXiv2026

ADELE - Adaptive Delaunay Grids for High-Fidelity Mesh-Native Reconstruction

Meshes remain the most practical representation for geometry reasoning and integration into graphics pipelines, yet existing reconstruction methods struggle to produce high-quality meshes. Most state-of-the-art approaches initially learn an intermediate representation (NeRF/3DGS) and treat mesh extraction as a post-processing step, which often leads to oversmoothed surfaces or poor quality meshes with excessive triangle counts.Existing mesh-native optimization methods alleviate some of these issues but suffer from fixed-resolution discretizations and unstable optimization behavior. In this paper, we introduce an adaptive mesh-based optimization framework and a practical mesh rendering technique to address these challenges. Our representation combines an optimizable Delaunay-triangulated tetrahedral grid with a multi-resolution hash grid. The former is refined through point pruning and insertion, while the latter provides latent features for SDF/appearance value predictions. We use volumetric rendering to bootstrap a coarse geometry while leveraging mesh-based rendering for recovering fine-grained details. Additionally, we propose a differentiable, rasterization-based depth-offset rendering formulation, reducing geometric artifacts and improving reconstruction quality. Our method significantly outperforms existing mesh optimization approaches across a variety of object-centric benchmarks while being competitive with state-of-the-art NeRF/3DGS methods.

cs.CV↗
arXiv2026

NanoGS: Training-Free Gaussian Splat Simplification

3D Gaussian Splat (3DGS) enables high-fidelity, real-time novel view synthesis by representing scenes with large sets of anisotropic primitives, but often requires millions of Splats, incurring significant storage and transmission costs. Most existing compression methods rely on GPU-intensive post-training optimization with calibrated images, limiting practical deployment. We introduce \textbf{NanoGS}, a training-free and lightweight framework for Gaussian Splat simplification. Instead of relying on image-based rendering supervision, NanoGS formulates simplification as local pairwise merging over a sparse spatial graph. The method approximates a pair of Gaussians with a single primitive using mass preserved moment matching and evaluates merge quality through a principled merge cost between the original mixture and its approximation. By restricting merge candidates to local neighborhoods and selecting compatible pairs efficiently, NanoGS produces compact Gaussian representations while preserving scene structure and appearance. NanoGS operates directly on existing Gaussian Splat models, runs efficiently on CPU, and preserves the standard 3DGS parameterization, enabling seamless integration with existing rendering pipelines. Experiments demonstrate that NanoGS substantially reduces primitive count while maintaining high rendering fidelity, providing an efficient and practical solution for Gaussian Splat simplification. Our project website is available at \href{https://saliteta.github.io/NanoGS/}{https://saliteta.github.io/NanoGS/}.

cs.CV↗
arXiv2026

Diff2DGS: Reliable Reconstruction of Occluded Surgical Scenes via 2D Gaussian Splatting

Real-time reconstruction of deformable surgical scenes is vital for advancing robotic surgery, improving intraoperative guidance, and enabling automation. Recent methods achieve dense reconstructions from da Vinci robotic surgery videos, with Gaussian Splatting (GS) offering real-time performance via graphics acceleration. However, reconstruction quality in occluded regions remains limited, and depth accuracy has not been fully assessed, as benchmarks like EndoNeRF and StereoMIS lack 3D ground truth. We propose Diff2DGS, a two-stage framework for reliable 3D reconstruction of occluded surgical scenes. First, a diffusion-based video module with temporal priors inpaints tissue occluded by instruments with high spatiotemporal consistency. Second, we adapt 2D Gaussian Splatting (2DGS) with a Learnable Deformation Model (LDM) to capture dynamic tissue deformation and anatomical geometry, and introduce adaptive depth weight to improve geometric fidelity. We further extend evaluation beyond image-quality metrics by performing quantitative depth analysis on the SCARED dataset. Diff2DGS outperforms state-of-the-art methods in both appearance and geometry, reaching 38.02 dB PSNR on EndoNeRF and 34.40 dB on StereoMIS. Our experiments also show that optimizing image quality alone does not necessarily ensure accurate 3D geometry.The code is available at https://diff2dgs.github.io/.

cs.CV↗