The explosion of generative 3D assets has created a massive demand for animation, yet current motion capture methods remain brittle, restricted to species-specific templates (e.g., SMPL) or requiring labor-intensive manual rigging. We introduce TopoCap, the first unified framework capable of extracting motion from monocular video and retargeting it onto characters with arbitrary, unseen skeletal topologies, i.e., from bipeds to hexapods and inanimate objects, without test-time optimization. Our key insight is that while skeletal structures are combinatorial and discrete, the underlying physics of motion occupy a continuous, low-dimensional manifold. We materialize this insight via a two-stage generative pipeline. First, we learn a Universal Motion Manifold using a Graph CVAE that compresses heterogeneous kinematic chains into a shared, fixed-length latent code. By explicitly conditioning the decoder on a structural embedding of the target rig, we disentangle motion dynamics from skeletal topology. Second, we treat video-to-animation as a conditional flow matching problem, predicting these topology-agnostic codes from visual features. To learn this generalized prior, we introduce Mobjaverse, a massive-scale dataset curated from Objaverse-XL. Comprising over 5,000 unique skeletal topologies and 2 million frames, it exceeds the structural diversity of existing datasets by two orders of magnitude. Extensive experiments demonstrate that TopoCapoutperforms specialist models on human and quadruped benchmarks while enabling zero-shot retargeting for the long tail of 3D creatures. Dataset is publicly available at https://huggingface.co/datasets/duckduckplz/Mobjaverse
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Reconstructing realistic, physically plausible garments from a single image remains a fundamental challenge. Template-free methods capture surface geometry but lack explicit sewing structure for simulation; while programmatic systems are simulation-ready but constrained by predefined templates. This reveals a fundamental representation gap between geometric reconstruction and structured garment construction. We present PatternGSL, a structured garment representation in the form of a template-free and learnable specification language that encodes complete sewing patterns, including panel boundaries, parameterized seams, and explicit stitch topology, in a compact and standardized form. PatternGSL preserves the physical rigor of pattern-based models while removing template dependence, elevating sewing structure as a first-class target for generative modeling. We further propose a vision-language framework that predicts PatternGSL specifications directly from a single image and decodes them into garments using lightweight deterministic validity handling, without optimization-based refinement or manual cleanup. In addition, we introduce PatternGSLData, the first large-scale image-to-GSL paired dataset comprising 300K samples with complete sewing pattern annotations, enabling supervised VLM training for structured garment reconstruction. Experiments demonstrate improved pattern accuracy over prior baselines, explicit sewing-structure recovery, reliable cloth simulation, and pattern-level editing through the same deterministic decoding pipeline. Code and data-processing scripts will be released at https://github.com/PatternGSL/PatternGSL.
Adaptive densification is the engine of 3D Gaussian Splatting (3DGS). However, when transposed to the optimization-based Generative Distillation paradigm, this reconstruction-native mechanism reveals fundamental limitations, resulting in inefficient representations cluttered with redundant primitives. We diagnose this failure as a Densification Dilemma stemming from the stochastic nature of generative guidance: the standard magnitude-based accumulation indiscriminately aggregates transient noise alongside geometric signals, making it difficult to strike a balance between over-densification and under-fitting. To resolve this, we introduce Context-Adaptive Moment Estimation (CAdam), a novel framework that reinterprets densification as a statistically grounded signal verification problem. CAdam leverages the first moment of gradients to exploit the interference principle—where stochastic fluctuations cancel out via destructive interference while consistent geometric drifts accumulate via constructive interference—effectively disentangling the underlying signal from the generative noise floor. This is further augmented by a quantile-based context awareness and an intrinsic Signal-to-Noise Ratio (SNR) gating mechanism, which ensure robust adaptation across optimization stages and enable the soft termination of densification. Extensive experiments across diverse objectives (SDS, ISM, VFDS) and strong generative 3DGS backbones show that CAdam reduces Gaussian count by 85%–97% relative to standard densification while preserving overall comparable perceptual quality. These results highlight signal-aware density control as a practical way to improve memory efficiency in optimization-based generative distillation.
We propose a new framework to systematically incorporate data uncertainty in Gaussian Splatting. Being the new paradigm of neural rendering, Gaussian Splatting has been investigated in many applications, with the main effort in extending its representation, improving its optimization process, and accelerating its speed. However, one orthogonal, much needed, but under-explored area is data uncertainty. In standard 4D Gaussian Splatting, data uncertainty can manifest as view sparsity, missing frames, camera asynchronization, etc. So far, there has been little research to holistically incorporating various types of data uncertainty under a single framework. To this end, we propose Graphical X Splatting, or GraphiXS, a new probabilistic framework that considers multiple types of data uncertainty, aiming for a fundamental augmentation of the current 4D Gaussian Splatting paradigm into a probabilistic setting. GraphiXS is general and can be instantiated with a range of primitives, e.g. Gaussians, Student’s-t. Furthermore, GraphiXS can be used to ‘upgrade’ existing methods to accommodate data uncertainty. Through exhaustive evaluation and comparison, we demonstrate that GraphiXS can systematically model various uncertainties in data, outperform existing methods in many settings where data are missing or polluted in space and time, and therefore is a major generalization of the current 4D Gaussian Splatting research.
Anisotropic friction is a critical source of propulsion for efficient locomotion of many terrestrial animals. The interplay between animal morphology, control, and anisotropically frictional contact makes designing optimal anisotropic friction for terrestrial locomotion intriguing and challenging. We propose a computational pipeline for co-designing anisotropic friction and controllers of terrestrial robots with diverse morphologies. Our pipeline presents a co-design algorithm that alternates between optimizing direction of anisotropic friction and training a neural network controller to improve the locomotion performance of a given robot morphology. Based on the intuition that controller’s performance does not change significantly when the frictional force differs slightly, we introduce the concept of trust-region into robot co-design, allowing the controller network to continue training from the previous iteration. Our evaluation on various morphologies show that anisotropic friction is critical for terrestrial robot locomotion, and our pipeline is statistically better than current state-of-the-art methods. Furthermore, we reveal that large language models (LLM) constitute a strong baseline for this kind of co-design problems, worth receiving more attention. We demonstrate that co-designing anisotropic friction and control unlocks effective locomotion in various downstream tasks, including locomotion on uneven terrain, navigation in a maze, and object manipulation. To validate our pipeline in the real world, we design and 3D print a variety of scales and systematically measure their anisotropic friction coefficients. Then we construct a multi-link robot with anisotropic scales designed by our pipeline and compare its performance with isotropic scales. Our real-world experiments confirm that isotropic scales are insufficient to support terrestrial robots’ locomotion abilities, and computationally co-designing friction and control enables robots to perform tasks including turning, slithering, and other non-trivial locomotion tasks.
Coordinate-motion assemblies can only be disassembled by the simultaneous motion of multiple parts along distinct paths, providing high structural stability and enabling efficient robotic assembly. Existing examples are largely limited to architectural structures using joint-based connections, or puzzles created through trial-and-error, as the relationship between part geometry and coordinate motion remains poorly understood. Computationally designing such assemblies is challenging because it requires jointly achieving distributed contacts across the entire assembly and a unique coordinate motion for disassembly that rules out other feasible motions. We address this challenge by establishing a theoretical connection between part geometry and unique coordinate motion, enabling us to rigorously verify whether a given assembly admits a unique coordinate motion. Building on this theory, we introduce a two-stage algorithm that optimizes contact interfaces for a target motion and constructs physically feasible part geometries that conform to a user-specified global shape. We demonstrate our approach on models with complex geometries and topologies, including assemblies with large part counts, and validate it through physical fabrication and experiments.
We introduce Kinematic Kitbashing, an optimization framework that synthesizes articulated 3D objects by assembling reusable parts conditioned on an abstract kinematic graph. Given the graph and a library of articulated parts, our method optimizes per-part similarity transformations that place, orient, and scale each component into a coherent articulated object; optional graph edits further enable novel assemblies beyond the prescribed connectivity. Central to our method is an exemplar-based analogy for part placement: each reused component is paired with a single source asset that exemplifies how it attaches to its parent. We capture this attachment context using vector distance fields and measure consistency by integrating the matching error over the joint’s full motion range. This yields a kinematics-aware attachment energy that favors placements that preserve the exemplar’s local attachment neighborhood throughout articulation. To incorporate task-level functionality, we use this attachment energy as a prior in an annealed Langevin sampling framework, enabling gradient-free optimization of black-box functionality objectives. We demonstrate the versatility of kinematic kitbashing across diverse applications, including instantiating kinematic graphs from user-selected or automatically retrieved parts, synthesizing assemblies with user-defined functionality, and re-targeting articulations via graph edits.
Gears transmit rotary motion via meshing teeth, with circular gears commonly used to produce constant-speed rotation and non-circular gears enabling variable-speed rotation. In order to generate complex motion, gears are typically combined with other mechanical parts such as linkages, cam-followers, and belts, which often leads to complex structures and reduced transmission efficiency. To address these limitations, recent research has been investigating non-conventional gears that can transfer complex motion while preserving key properties of gears, such as compactness, high transmission efficiency, and load-bearing capability. In this paper, we present a new gear mechanism called the multi-point conjugation gear mechanism for exactly generating a user-specified 3D motion under external loads. The mechanism contains a single pair of gears modeled by a pair of conjugate surfaces with multiple conjugation points. We introduce an optimization-based approach that designs this new gear mechanism by modeling multiple sub-gear pairs that satisfy multi-point conjugation and fabricability requirements, whose load-bearing performance is quantified using a measure of dynamic form closure. We demonstrate the effectiveness of our approach by modeling various multi-point conjugation gear mechanisms that generate different kinds of motions, evaluating their kinematic performance and load-bearing performance using 3D printed prototypes, and presenting two application examples.
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.
We present a global, discrete optimization framework for quad-dominant mesh reduction that formulates simplification as an edge selection problem under coupled topological and geometric constraints. Unlike greedy edge-collapse heuristics, which make irreversible local decisions, and rigid poly-chord removal schemes, which over-constrain global structure, our method casts quad-dominant reduction as an Integer Linear Programming (ILP) problem that jointly optimizes edge flow continuity and geometric fidelity in a single global optimization. To make this formulation both tractable and adaptive, we segment poly-chords at geometrically meaningful breakpoints to relax otherwise rigid topological constraints, and introduce geometry-aware soft constraints that steer the optimization toward preserving high-curvature and deformation-critical regions. Extensive experiments demonstrate that our approach consistently outperforms state-of-the-art methods in preserving quad structure and edge flow, while achieving competitive geometric accuracy and significantly benefiting downstream editing applications.
The low-poly style is a popular genre of vector graphics that depicts objects and scenes as flat-shaded meshes of low polygon count, often with a limited palette. In this paper, we propose a method to generate 2D low-poly meshes to abstract images. While it has been possible to achieve this look with general-purpose image generators and vector-based diffusion models, the resulting images are not guaranteed to be valid polygonal meshes. A key problem is that polygons overlap or intersect and, in the case of pixel-based image generators, the shapes are often not polygons. Moreover, the colors are not guaranteed to be constrained to a fixed palette. Aside from aesthetic considerations, this has practical consequences: it complicates editing and fabricating the results. We solve this problem by representing an image as a 2D polygonal mesh and optimizing the topology, geometry and coloring of the mesh using score distillation sampling, while enforcing geometric constraints, such as manifoldness and bijectivity. This presents unique challenges due to the discrete nature of the topology, which we handle using a fine-to-coarse strategy based on mesh simplification. By also constraining the colors to a fixed palette, we are able to produce various fabrications such as mosaics, embroidery, crocheting, patchwork and stencils from the resulting vector images. Code is at https://github.com/rubenwiersma/alps.
Recent radiance-field-based reconstruction methods, such as NeRF and 3DGS, achieve high visual fidelity for indoor scenes, but often break down under scene editing due to baked illumination and the lack of explicit light transport. In contrast, inverse path tracing methods based on mesh representations enforce correct light transport but require highly accurate geometry, making them difficult to apply robustly to real indoor scenes. We present Emission-Aware Gaussians and Path Tracing (EAG-PT), a method for physically based reconstruction and rendering of indoor scenes using a unified 2D Gaussian representation, targeting editable diffuse global illumination. Our approach consists of three key ideas: (1) representing indoor scenes with 2D Gaussians as a transport-friendly geometric proxy that avoids explicit mesh reconstruction; (2) explicitly separating emissive and non-emissive components during reconstruction to support editing; and (3) decoupling reconstruction from final rendering by using efficient single-bounce optimization and high-quality multi-bounce path tracing, respectively. Experiments on synthetic and real indoor scenes show that EAG-PT produces more natural and physically consistent edited renderings than radiance-field reconstructions, while preserving finer geometric detail and avoiding mesh-induced artifacts compared with mesh-based inverse path tracing. These results highlight the potential of our approach for applications such as interior design, XR content creation, and embodied AI.
Augmenting the surface of 3D objects with capacitive sensing is particularly challenging when their volumes cannot be modified. In this paper, we present a computational fabrication pipeline that retrofits surface-only sensor layouts to 3D geometries for multi-touch interaction. Our system scans real-world objects to obtain their 3D mesh, generates and optimizes a 3D sensor design of drive and sense lines for mutual-capacitance sensing that complies with physical and hardware sensing constraints, and unfolds them into individual 2D stencils that can be cut from conductive material. Our fabrication pipeline cuts these from thin copper foil with a vinyl cutter and then assists manual sensor attachment by projecting the sensor design onto the dynamically registered real-world object. We connect the resulting electrode mesh to a mutual-capacitance scanning controller and resolve touch interaction in real time. We demonstrate our approach with four 3D geometries and evaluate our method and fabrication pipeline on them.
Computing injective, flip-free embeddings of simplicial meshes is a fundamental challenge in geometry processing. While the Total Lifted Content (TLC) energy provides a smooth functional with theoretically guaranteed injective global minima, its non-convex nature presents significant optimization hurdles. In this work, we propose a Nonlinear Multigrid (MG/Opt) framework specifically tailored for efficient TLC energy minimization. Our approach leverages a topology-preserving mesh hierarchy to rapidly eliminate low-frequency errors on coarse scales while maintaining rigorous gradient consistency between hierarchical levels through linear correction terms. To address the persistent challenge of local inversions, we introduce a targeted smoothing strategy and an adaptive parameter scheduling mechanism that balances global convergence speed with local injectivity precision. Experimental evaluations across extensive 2D and 3D benchmark datasets demonstrate the robustness of our approach. Our method achieves a 100% convergence success rate across all tested 2D cases and all but one 3D dataset (the VOLMAP benchmark). Furthermore, our MG/Opt framework delivers substantial performance gains, achieving up to 63 × speedup on high-resolution subdivided datasets compared to traditional solvers. These results confirm that our multigrid strategy provides a scalable and reliable solution for large-scale injective mapping problems. Code and data for this paper are at https://github.com/distmeshM/MGOpt_TLC
Geometry optimization often encounters sparse gradients from limited observations, which can cause optimization to drift toward unnatural shapes. Prior work stabilizes this process by exploiting spatial structure encoded by the Laplacian operator within a single shape, enforcing spatial smoothness on gradients. However, such smoothness alone propagates gradients to unobserved regions without any prior knowledge of how shapes typically deform in a given domain. We introduce statistical gradient filtering, which leverages statistical structure across a shape collection by learning shape variations via principal component analysis (PCA) and guiding geometry updates along directions consistent with this learned prior. Unlike previous PCA-based methods that constrain solutions to a linear subspace or modify the objective with regularization terms, we filter gradients at each iteration to steer the optimization path toward plausible shapes, without restricting the solution space or altering the original objective. We validate our approach across a range of shape optimization tasks, demonstrating robust convergence even under challenging conditions.
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction. Our method decomposes permutation into patch-level local orderings and a compact quotient-graph ordering of separators, preserving the essential structure required by sparse Cholesky factorization while avoiding its most expensive components. We integrate our algorithm into vendor-maintained sparse Cholesky solvers on both CPUs and GPUs. Across a range of graphics applications, including single factorizations and repeated factorizations, our method reduces permutation time and improves the sparse Cholesky solve performance by up to 6.27 ×. Our code is available at https://github.com/BehroozZare/fast-permute.
We present a training algorithm to mitigate optimization instabilities in small neural networks, like those used in real-time neural shading applications. While large, overparameterized models exhibit predictable convergence, smaller architectures often suffer from high optimization variance: differently initialized models converge to disparate local minima. To reduce these training instabilities, we introduce an optimization approach that utilizes an ensemble of network instances during training. We prune underperforming instances and dynamically resize training batches to maintain wall-clock timings comparable to—or faster than—single-instance training. This strategy allows efficiently exploring the weight space yielding a well-performing model with significantly higher likelihood than optimizing a single instance only. We develop and analyze the algorithm in the context of learning reflectance functions for neural shading. This is a challenging task for small neural models due to the high dynamic range of the target function. In addition to our multi-instance training method, we also revisit the choices of loss functions, activation functions, and input parameterization to further improve quality and training robustness.
Vectorization of line art and sketches is an important problem in computer graphics and remains an active area of research. In this paper, we leverage several recent advances in the field to introduce a new state-of-the-art method for line art vectorization. First, we show that it is possible to go beyond heuristics to extract a meaningful set of strokes from a raster image. We leverage both depth prediction and semantic feature extraction models to propose a more principled approach to split the skeleton graph of the sketch into subgraphs to initialize a set of strokes, producing results that better align with artistic intent. Second, we model strokes as Bézier curves with both geometric and appearance components, and employ 2D Gaussian splatting for fast, differentiable rendering. This formulation enables efficient fitting of strokes to the input while jointly optimizing control points and brush texture. We further demonstrate promising results on video by incorporating temporal tracking and adaptive keyframe introduction. Our evaluation shows that we achieve state-of-the-art results for image reconstruction, while being fast and producing strokes of high quality. More importantly, the fitting is highly compatible with user input, through the correction of the splines and the selection of optimization parameters.
Low-discrepancy points have proven to be a useful source of samples for numerical integration via quasi-Monte Carlo integration. Low-discrepancy points are typically uniformly distributed in the unit hypercube. It is thus common to transform the input uniform points into target non-uniform samples via mapping, just like how uniform random numbers are used for generating non-uniform samples. Unfortunately, this common approach does not guarantee to carry over the low-discrepancy nature of the input points into the output non-uniform samples, giving the resulting non-uniform samples suboptimal discrepancy. The existing methods for generating low-discrepancy points focus only on uniform points, thus generating non-uniform and low-discrepancy samples has been an open problem. We introduce an optimization framework to approximate non-uniform low-discrepancy samples by numerically minimizing the discrepancy metric for non-uniform samples. We propose a differentiable numerical estimator of the generalized non-uniform discrepancy to enable gradient-based optimization. Our differentiable discrepancy estimator turns a challenging problem of generating non-uniform low-discrepancy samples into a simple numerical optimization problem. Since optimization can generate only one set of samples, we further propose a neural network architecture to encode the sample generation process, allowing us to generate multiple sets of samples from conditional targets without runtime optimization. We experimentally validate that our method reduces discrepancy below prior methods at least up to a certain sample size and consequently achieves lower integration error on numerical integration problems.
The fundamental limitation of traditional strand-based modeling is not simply data scarcity, but the ill-posedness of inferring complex 3D fields from 2D imagery without structural constraints. This unconstrained regression leads to catastrophic failures in resolving both global occlusion (e.g., in ponytails) and local directionality (e.g., in curls), resulting in over-smoothed, plausible-but-incorrect geometries. To resolve this, we integrate the strong geometric priors of Large Reconstruction Models (LRMs) into the strand generation pipeline. Using the LRM mesh as a structural anchor, we employ a novel Dual Orientation AutoEncoder to lift coarse geometry into high-fidelity strands. By resolving vector field singularities through latent-space optimization and surface-guided refinement, our method effectively disentangles complex topological structures, setting a new benchmark for robustness and accuracy in hair reconstruction.