Daily Papers

Shape assembly aims to reassemble parts (or fragments) into a complete object, which is a common task in our daily life. Different from the semantic part assembly (e.g., assembling a chair's semantic parts like legs into a whole chair), geometric part assembly (e.g., assembling bowl fragments into a complete bowl) is an emerging task in computer vision and robotics. Instead of semantic information, this task focuses on geometric information of parts. As the both geometric and pose space of fractured parts are exceptionally large, shape pose disentanglement of part representations is beneficial to geometric shape assembly. In our paper, we propose to leverage SE(3) equivariance for such shape pose disentanglement. Moreover, while previous works in vision and robotics only consider SE(3) equivariance for the representations of single objects, we move a step forward and propose leveraging SE(3) equivariance for representations considering multi-part correlations, which further boosts the performance of the multi-part assembly. Experiments demonstrate the significance of SE(3) equivariance and our proposed method for geometric shape assembly. Project page: https://crtie.github.io/SE-3-part-assembly/

Multimodal models for text-to-image generation have achieved strong visual fidelity, yet they remain brittle under compositional structural constraints-notably generative numeracy, attribute binding, and part-level relations. To address these challenges, we propose Shape-of-Thought (SoT), a visual CoT framework that enables progressive shape assembly via coherent 2D projections without external engines at inference time. SoT trains a unified multimodal autoregressive model to generate interleaved textual plans and rendered intermediate states, helping the model capture shape-assembly logic without producing explicit geometric representations. To support this paradigm, we introduce SoT-26K, a large-scale dataset of grounded assembly traces derived from part-based CAD hierarchies, and T2S-CompBench, a benchmark for evaluating structural integrity and trace faithfulness. Fine-tuning on SoT-26K achieves 88.4% on component numeracy and 84.8% on structural topology, outperforming text-only baselines by around 20%. SoT establishes a new paradigm for transparent, process-supervised compositional generation. The code is available at https://anonymous.4open.science/r/16FE/. The SoT-26K dataset will be released upon acceptance.

Human-designed visual manuals are crucial components in shape assembly activities. They provide step-by-step guidance on how we should move and connect different parts in a convenient and physically-realizable way. While there has been an ongoing effort in building agents that perform assembly tasks, the information in human-design manuals has been largely overlooked. We identify that this is due to 1) a lack of realistic 3D assembly objects that have paired manuals and 2) the difficulty of extracting structured information from purely image-based manuals. Motivated by this observation, we present IKEA-Manual, a dataset consisting of 102 IKEA objects paired with assembly manuals. We provide fine-grained annotations on the IKEA objects and assembly manuals, including decomposed assembly parts, assembly plans, manual segmentation, and 2D-3D correspondence between 3D parts and visual manuals. We illustrate the broad application of our dataset on four tasks related to shape assembly: assembly plan generation, part segmentation, pose estimation, and 3D part assembly.

Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead while yielding two consistent benefits: faster convergence (up to 6.9times) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.

Shape assembly is a ubiquitous task in daily life, integral for constructing complex 3D structures like IKEA furniture. While significant progress has been made in developing autonomous agents for shape assembly, existing datasets have not yet tackled the 4D grounding of assembly instructions in videos, essential for a holistic understanding of assembly in 3D space over time. We introduce IKEA Video Manuals, a dataset that features 3D models of furniture parts, instructional manuals, assembly videos from the Internet, and most importantly, annotations of dense spatio-temporal alignments between these data modalities. To demonstrate the utility of IKEA Video Manuals, we present five applications essential for shape assembly: assembly plan generation, part-conditioned segmentation, part-conditioned pose estimation, video object segmentation, and furniture assembly based on instructional video manuals. For each application, we provide evaluation metrics and baseline methods. Through experiments on our annotated data, we highlight many challenges in grounding assembly instructions in videos to improve shape assembly, including handling occlusions, varying viewpoints, and extended assembly sequences.

Shape assembly, the process of combining parts into a complete whole, is a crucial robotic skill with broad real-world applications. Among various assembly tasks, geometric assembly--where broken parts are reassembled into their original form (e.g., reconstructing a shattered bowl)--is particularly challenging. This requires the robot to recognize geometric cues for grasping, assembly, and subsequent bimanual collaborative manipulation on varied fragments. In this paper, we exploit the geometric generalization of point-level affordance, learning affordance aware of bimanual collaboration in geometric assembly with long-horizon action sequences. To address the evaluation ambiguity caused by geometry diversity of broken parts, we introduce a real-world benchmark featuring geometric variety and global reproducibility. Extensive experiments demonstrate the superiority of our approach over both previous affordance-based and imitation-based methods. Project page: https://sites.google.com/view/biassembly/.

3D assembly tasks, such as furniture assembly and component fitting, play a crucial role in daily life and represent essential capabilities for future home robots. Existing benchmarks and datasets predominantly focus on assembling geometric fragments or factory parts, which fall short in addressing the complexities of everyday object interactions and assemblies. To bridge this gap, we present 2BY2, a large-scale annotated dataset for daily pairwise objects assembly, covering 18 fine-grained tasks that reflect real-life scenarios, such as plugging into sockets, arranging flowers in vases, and inserting bread into toasters. 2BY2 dataset includes 1,034 instances and 517 pairwise objects with pose and symmetry annotations, requiring approaches that align geometric shapes while accounting for functional and spatial relationships between objects. Leveraging the 2BY2 dataset, we propose a two-step SE(3) pose estimation method with equivariant features for assembly constraints. Compared to previous shape assembly methods, our approach achieves state-of-the-art performance across all 18 tasks in the 2BY2 dataset. Additionally, robot experiments further validate the reliability and generalization ability of our method for complex 3D assembly tasks.

We introduce Breaking Bad, a large-scale dataset of fractured objects. Our dataset consists of over one million fractured objects simulated from ten thousand base models. The fracture simulation is powered by a recent physically based algorithm that efficiently generates a variety of fracture modes of an object. Existing shape assembly datasets decompose objects according to semantically meaningful parts, effectively modeling the construction process. In contrast, Breaking Bad models the destruction process of how a geometric object naturally breaks into fragments. Our dataset serves as a benchmark that enables the study of fractured object reassembly and presents new challenges for geometric shape understanding. We analyze our dataset with several geometry measurements and benchmark three state-of-the-art shape assembly deep learning methods under various settings. Extensive experimental results demonstrate the difficulty of our dataset, calling on future research in model designs specifically for the geometric shape assembly task. We host our dataset at https://breaking-bad-dataset.github.io/.

We introduce Rectified Point Flow, a unified parameterization that formulates pairwise point cloud registration and multi-part shape assembly as a single conditional generative problem. Given unposed point clouds, our method learns a continuous point-wise velocity field that transports noisy points toward their target positions, from which part poses are recovered. In contrast to prior work that regresses part-wise poses with ad-hoc symmetry handling, our method intrinsically learns assembly symmetries without symmetry labels. Together with a self-supervised encoder focused on overlapping points, our method achieves a new state-of-the-art performance on six benchmarks spanning pairwise registration and shape assembly. Notably, our unified formulation enables effective joint training on diverse datasets, facilitating the learning of shared geometric priors and consequently boosting accuracy. Project page: https://rectified-pointflow.github.io/.

Assembling objects from parts requires understanding multimodal instructions, linking them to 3D components, and predicting physically plausible 6-DoF motions for each assembly step. Existing datasets focus on simplified scenarios, overlooking shape complexities and assembly trajectories in industrial assemblies. We introduce AssemblyBench, a synthetic dataset of 2,789 industrial objects with multimodal instruction manuals, corresponding 3D part models, and part assembly trajectories. We also propose a transformer-based model, AssemblyDyno, which uses the instructional manual and the 3D shape of each part to jointly predict assembly order and part assembly trajectories. AssemblyDyno outperforms prior works in both assembly pose estimation and trajectory feasibility, where the latter is evaluated by our physics-based simulations.

We present Assembler, a scalable and generalizable framework for 3D part assembly that reconstructs complete objects from input part meshes and a reference image. Unlike prior approaches that mostly rely on deterministic part pose prediction and category-specific training, Assembler is designed to handle diverse, in-the-wild objects with varying part counts, geometries, and structures. It addresses the core challenges of scaling to general 3D part assembly through innovations in task formulation, representation, and data. First, Assembler casts part assembly as a generative problem and employs diffusion models to sample plausible configurations, effectively capturing ambiguities arising from symmetry, repeated parts, and multiple valid assemblies. Second, we introduce a novel shape-centric representation based on sparse anchor point clouds, enabling scalable generation in Euclidean space rather than SE(3) pose prediction. Third, we construct a large-scale dataset of over 320K diverse part-object assemblies using a synthesis and filtering pipeline built on existing 3D shape repositories. Assembler achieves state-of-the-art performance on PartNet and is the first to demonstrate high-quality assembly for complex, real-world objects. Based on Assembler, we further introduce an interesting part-aware 3D modeling system that generates high-resolution, editable objects from images, demonstrating potential for interactive and compositional design. Project page: https://assembler3d.github.io

Physical products are often complex assemblies combining a multitude of 3D parts modeled in computer-aided design (CAD) software. CAD designers build up these assemblies by aligning individual parts to one another using constraints called joints. In this paper we introduce JoinABLe, a learning-based method that assembles parts together to form joints. JoinABLe uses the weak supervision available in standard parametric CAD files without the help of object class labels or human guidance. Our results show that by making network predictions over a graph representation of solid models we can outperform multiple baseline methods with an accuracy (79.53%) that approaches human performance (80%). Finally, to support future research we release the Fusion 360 Gallery assembly dataset, containing assemblies with rich information on joints, contact surfaces, holes, and the underlying assembly graph structure.

Shape primitive abstraction, which decomposes complex 3D shapes into simple geometric elements, plays a crucial role in human visual cognition and has broad applications in computer vision and graphics. While recent advances in 3D content generation have shown remarkable progress, existing primitive abstraction methods either rely on geometric optimization with limited semantic understanding or learn from small-scale, category-specific datasets, struggling to generalize across diverse shape categories. We present PrimitiveAnything, a novel framework that reformulates shape primitive abstraction as a primitive assembly generation task. PrimitiveAnything includes a shape-conditioned primitive transformer for auto-regressive generation and an ambiguity-free parameterization scheme to represent multiple types of primitives in a unified manner. The proposed framework directly learns the process of primitive assembly from large-scale human-crafted abstractions, enabling it to capture how humans decompose complex shapes into primitive elements. Through extensive experiments, we demonstrate that PrimitiveAnything can generate high-quality primitive assemblies that better align with human perception while maintaining geometric fidelity across diverse shape categories. It benefits various 3D applications and shows potential for enabling primitive-based user-generated content (UGC) in games. Project page: https://primitiveanything.github.io

Structured shape completion recovers missing geometry as primitives rather than as unstructured points, which enables primitive-based surface reconstruction. Instead of following the prevailing cascade, we rethink how primitives and points should interact, and find it more effective to decode primitives in a dedicated pathway that attends to shared shape features. Following this principle, we present UniCo, which in a single feed-forward pass predicts a set of primitives with complete geometry, semantics, and inlier membership. To drive this unified representation, we introduce primitive proxies, learnable queries that are contextualized to produce assembly-ready outputs. To ensure consistent optimization, our training strategy couples primitives and points with online target updates. Across synthetic and real-world benchmarks with four independent assembly solvers, UniCo consistently outperforms recent baselines, lowering Chamfer distance by up to 50% and improving normal consistency by up to 7%. These results establish an attractive recipe for structured 3D understanding from incomplete data. Project page: https://unico-completion.github.io.

3D assembly is fundamental to modern manufacturing and digital content creation. In this paper, we present PART, a unified transformer-based framework for 3D part retrieval and assembly: given a target shape and a part library, PART automatically selects the appropriate parts and predicts their 6-DoF poses to reconstruct the target. While prior work has achieved impressive progress on assembling a pre-defined set of parts, this more practical retrieval-based setting remains largely unexplored. The task faces three key challenges: (i) a combinatorially explosive search space that grows exponentially with library size; (ii) variable-length outputs, as different targets require different numbers of parts; and (iii) continuous 6-DoF pose estimation for part assembly. To address these, we formulate retrieval and assembly as a set prediction problem and design a novel transformer-based framework that retrieves parts and regresses their poses with variable-length output. Additionally, we exploit the duality between part pose estimation and target segmentation through joint training and a novel segmentation-enhanced optimization module. Finally, We curate a large-scale dataset of 80K+ shapes, and the results show that PART generalizes to scene layouts, image targets, and real-world scans. Project Page: https://iambrc.github.io/PART-project-page/.

3D part assembly aims to understand part relationships and predict their 6-DoF poses to construct realistic 3D shapes, addressing the growing demand for autonomous assembly, which is crucial for robots. Existing methods mainly estimate the transformation of each part by training neural networks under supervision, which requires a substantial quantity of manually labeled data. However, the high cost of data collection and the immense variability of real-world shapes and parts make traditional methods impractical for large-scale applications. In this paper, we propose first a zero-shot part assembly method that utilizes pre-trained point cloud diffusion models as discriminators in the assembly process, guiding the manipulation of parts to form realistic shapes. Specifically, we theoretically demonstrate that utilizing a diffusion model for zero-shot part assembly can be transformed into an Iterative Closest Point (ICP) process. Then, we propose a novel pushing-away strategy to address the overlap parts, thereby further enhancing the robustness of the method. To verify our work, we conduct extensive experiments and quantitative comparisons to several strong baseline methods, demonstrating the effectiveness of the proposed approach, which even surpasses the supervised learning method. The code has been released on https://github.com/Ruiyuan-Zhang/Zero-Shot-Assembly.

While text-3D editing has made significant strides in leveraging score distillation sampling, emerging approaches still fall short in delivering separable, precise and consistent outcomes that are vital to content creation. In response, we introduce FocalDreamer, a framework that merges base shape with editable parts according to text prompts for fine-grained editing within desired regions. Specifically, equipped with geometry union and dual-path rendering, FocalDreamer assembles independent 3D parts into a complete object, tailored for convenient instance reuse and part-wise control. We propose geometric focal loss and style consistency regularization, which encourage focal fusion and congruent overall appearance. Furthermore, FocalDreamer generates high-fidelity geometry and PBR textures which are compatible with widely-used graphics engines. Extensive experiments have highlighted the superior editing capabilities of FocalDreamer in both quantitative and qualitative evaluations.

3D part assembly aims to reconstruct a complete shape from a set of unassembled parts by predicting a rigid SE(3) transformation for each part. Because the placement of a part is rarely determined by its own geometry, the task demands reasoning over the entire part set, and existing methods, which rely on pairwise relations or iterative generation and verification, scale poorly to objects with many parts. We present LLM2R, which casts part assembly as sequence modeling with a pretrained decoder-only large language model (LLM): a Point-BERT encoder and a Q-Former compress each part into a block of geometric tokens, the blocks of all parts are concatenated, and a causal LLM adapted with Low-Rank Adaptation (LoRA) processes the sequence in one forward pass. Causal attention, however, lets the hidden states of a part observe only the parts that precede it. LLM2R therefore appends a block of learnable summary tokens after the last part: these tokens follow every part, so their states aggregate the whole assembly at a constant token cost, and a part-aware pose head fuses each part's states with them before predicting its rotation and translation. One architecture thus handles semantic and geometric assembly and predicts all poses in a single non-autoregressive pass. LLM2R achieves the highest part accuracy and success rate on all three PartNet categories, the best rotation error, translation error, and part accuracy on PartNeXt, and the lowest translation error and fastest inference on Breaking Bad, where only a fracture-specialized method is more accurate. Its advantage grows with the number of parts: at 100 parts it exceeds GARF by 33.5 points in part accuracy on Breaking Bad and Assembler by 29.1 points on PartNet, and it transfers zero-shot to unseen categories with more than 16 points higher part accuracy than the strongest of three baselines.

We introduce SPAFormer, an innovative model designed to overcome the combinatorial explosion challenge in the 3D Part Assembly (3D-PA) task. This task requires accurate prediction of each part's poses in sequential steps. As the number of parts increases, the possible assembly combinations increase exponentially, leading to a combinatorial explosion that severely hinders the efficacy of 3D-PA. SPAFormer addresses this problem by leveraging weak constraints from assembly sequences, effectively reducing the solution space's complexity. Since the sequence of parts conveys construction rules similar to sentences structured through words, our model explores both parallel and autoregressive generation. We further strengthen SPAFormer through knowledge enhancement strategies that utilize the attributes of parts and their sequence information, enabling it to capture the inherent assembly pattern and relationships among sequentially ordered parts. We also construct a more challenging benchmark named PartNet-Assembly covering 21 varied categories to more comprehensively validate the effectiveness of SPAFormer. Extensive experiments demonstrate the superior generalization capabilities of SPAFormer, particularly with multi-tasking and in scenarios requiring long-horizon assembly. Code is available at https://github.com/xuboshen/SPAFormer.

Multimodal large language models can write code to produce complex programs as well as use programs to do 3D modeling, which opens up a new avenue for 3D generation powered by their priors, world knowledge and reasoning. Yet existing benchmarks rarely evaluate 3D modeling through code. Such modeling demands more than runnable code: from a text or visual specification, a model must generate a parametric 3D program that is geometrically precise, semantically aligned and assembly-consistent. We introduce P3D-Bench, a benchmark for parametric 3D generation. Unlike a 3D mesh, a parametric 3D program exposes explicit dimensions, construction operations and part relations, revealing whether a model recovers a design's structure, not just its appearance. Under a unified protocol, P3D-Bench covers three task families (Text-to-3D, Image-to-3D and Assembly-3D) and scores each output for executability, geometric fidelity, topology, text-grounded constraints, multiview semantic alignment and part-level structure. We evaluate frontier MLLMs and text-only LLMs on 400 text cases, 400 image cases and 203 annotated assemblies, with domain-specific models as reference points. Our extensive evaluation yields three findings. First, assemblies are the hardest setting, where models still fail to compose multiple parts into a coherent structure. Second, models can often recover the global shape and semantic identity of the target object, yet fail to reproduce the precise parametric geometry specified by the input. Third, part-level modeling remains weak on assemblies, where models recover neither the geometry of each part nor the right number of parts. These results position P3D-Bench as a benchmark for evaluating precise parametric geometry and part-level structure in parametric 3D generation.

We propose an approach for generating crochet instructions (patterns) from an input 3D model. We focus on Amigurumi, which are knitted stuffed toys. Given a closed triangle mesh, and a single point specified by the user, we generate crochet instructions, which when knitted and stuffed result in a toy similar to the input geometry. Our approach relies on constructing the geometry and connectivity of a Crochet Graph, which is then translated into a crochet pattern. We segment the shape automatically into chrochetable components, which are connected using the join-as-you-go method, requiring no additional sewing. We demonstrate that our method is applicable to a large variety of shapes and geometries, and yields easily crochetable patterns.

Multi-part assembly poses significant challenges for robots to execute long-horizon, contact-rich manipulation with generalization across complex geometries. We present Fabrica, a dual-arm robotic system capable of end-to-end planning and control for autonomous assembly of general multi-part objects. For planning over long horizons, we develop hierarchies of precedence, sequence, grasp, and motion planning with automated fixture generation, enabling general multi-step assembly on any dual-arm robots. The planner is made efficient through a parallelizable design and is optimized for downstream control stability. For contact-rich assembly steps, we propose a lightweight reinforcement learning framework that trains generalist policies across object geometries, assembly directions, and grasp poses, guided by equivariance and residual actions obtained from the plan. These policies transfer zero-shot to the real world and achieve 80% successful steps. For systematic evaluation, we propose a benchmark suite of multi-part assemblies resembling industrial and daily objects across diverse categories and geometries. By integrating efficient global planning and robust local control, we showcase the first system to achieve complete and generalizable real-world multi-part assembly without domain knowledge or human demonstrations. Project website: http://fabrica.csail.mit.edu/

The advent of large language models, enabling flexibility through instruction-driven approaches, has revolutionized many traditional generative tasks, but large models for 3D data, particularly in comprehensively handling 3D shapes with other modalities, are still under-explored. By achieving instruction-based shape generations, versatile multimodal generative shape models can significantly benefit various fields like 3D virtual construction and network-aided design. In this work, we present ShapeGPT, a shape-included multi-modal framework to leverage strong pre-trained language models to address multiple shape-relevant tasks. Specifically, ShapeGPT employs a word-sentence-paragraph framework to discretize continuous shapes into shape words, further assembles these words for shape sentences, as well as integrates shape with instructional text for multi-modal paragraphs. To learn this shape-language model, we use a three-stage training scheme, including shape representation, multimodal alignment, and instruction-based generation, to align shape-language codebooks and learn the intricate correlations among these modalities. Extensive experiments demonstrate that ShapeGPT achieves comparable performance across shape-relevant tasks, including text-to-shape, shape-to-text, shape completion, and shape editing.

Part-aware 3D asset generation enables applications such as editing, articulation, simulation, and fabrication, yet existing methods can generate visually complete individual parts without ensuring that they form a valid physical assembly. Consequently, generated neighboring parts may interpenetrate, lack valid connections, or collapse under gravity. We propose a physics-guided framework for improving single-image part-aware 3D generation with physically compatible geometry and stable connections. Our method resolves inter-part penetration, recovers a contact graph between neighboring parts, and introduces parameterized connectors at their contact surfaces. Using feedback from physical simulation, we refine connector placement, orientation, and dimensions to improve assembly stability while preserving the generated geometry. We further introduce a physics-based evaluation protocol that complements conventional geometric metrics by directly testing assembly validity and stability under gravity. Experiments comparing against multiple part-aware 3D generators show substantial improvements in physical realizability and stability while maintaining geometric quality. We additionally validate the resulting parts through 3D printing and real-world assembly.

The CAD design process includes a number of repetitive steps when creating assemblies. This issue is compounded when engineering whole product lines or design families, as steps like inserting parts common to all variations, such as fasteners and product-integral base parts, get repeated numerous times. This makes creating designs time-, and as a result, cost-intensive. While many CAD software packages have APIs, the effort of creating use-case specific plugins to automate creation of assemblies usually outweighs the benefit. We developed a plugin for the CAD software package "Fusion 360" which tackles this issue. The plugin adds several graphical interfaces to Fusion 360 that allow parts to be annotated with types, subtype hierarchies to be managed, and requests to synthesize assembly programs for assemblies to be posed. The plugin is use-case agnostic and is able to generate arbitrary open kinematic chain structures. We envision engineers working with CAD software being able to make designed parts reusable and automate the generation of different design alternatives as well as whole product lines.

We present Muses, the first training-free method for fantastic 3D creature generation in a feed-forward paradigm. Previous methods, which rely on part-aware optimization, manual assembly, or 2D image generation, often produce unrealistic or incoherent 3D assets due to the challenges of intricate part-level manipulation and limited out-of-domain generation. In contrast, Muses leverages the 3D skeleton, a fundamental representation of biological forms, to explicitly and rationally compose diverse elements. This skeletal foundation formalizes 3D content creation as a structure-aware pipeline of design, composition, and generation. Muses begins by constructing a creatively composed 3D skeleton with coherent layout and scale through graph-constrained reasoning. This skeleton then guides a voxel-based assembly process within a structured latent space, integrating regions from different objects. Finally, image-guided appearance modeling under skeletal conditions is applied to generate a style-consistent and harmonious texture for the assembled shape. Extensive experiments establish Muses' state-of-the-art performance in terms of visual fidelity and alignment with textual descriptions, and potential on flexible 3D object editing. Project page: https://luhexiao.github.io/Muses.github.io/.

Native 3D generators now recover impressive mesh geometry from a single image. However, a dense mesh stays soft where a machined object should be sharp, it carries no part decomposition, and it exposes no parameter a user could edit. To address this, we explore the paradigm of 3D shape as code, leveraging and scaling the coding ability of an LLM for 3D modeling. We introduce Procedura, a novel 3D modeling agent framework that writes an object as a procedural assembly, a parametric program whose named parts are joined by typed, machine-checkable mates. From a text prompt, the agent plans the object as an assembly graph and writes the program part by part, solving each placement from the mated frames rather than guessing it, and admitting a part only once compile, mate, and connectivity checks pass. A decoupled vision critic then refines the assembly one diagnosed fix at a time. Moreover, the same graph carries per-part materials and a simulator-validated articulation. We evaluate on P3D-Bench under its assembly judge, and with the same judge on MechBench-36, our hard-surface benchmark. On both, Procedura outperforms state-of-the-art native 3D generators and every prior 3D-code agent on judged quality, produces the sharpest edges of any method we evaluate, and is the only one whose output is an editable, part-structured program.

3D shape generation aims to produce innovative 3D content adhering to specific conditions and constraints. Existing methods often decompose 3D shapes into a sequence of localized components, treating each element in isolation without considering spatial consistency. As a result, these approaches exhibit limited versatility in 3D data representation and shape generation, hindering their ability to generate highly diverse 3D shapes that comply with the specified constraints. In this paper, we introduce a novel spatial-aware 3D shape generation framework that leverages 2D plane representations for enhanced 3D shape modeling. To ensure spatial coherence and reduce memory usage, we incorporate a hybrid shape representation technique that directly learns a continuous signed distance field representation of the 3D shape using orthogonal 2D planes. Additionally, we meticulously enforce spatial correspondences across distinct planes using a transformer-based autoencoder structure, promoting the preservation of spatial relationships in the generated 3D shapes. This yields an algorithm that consistently outperforms state-of-the-art 3D shape generation methods on various tasks, including unconditional shape generation, multi-modal shape completion, single-view reconstruction, and text-to-shape synthesis.

In geometrically frustrated assemblies local inter-subunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here, we use theory and coarse-grained simulation to study a recently developed class of ``curvamer'' particles, flexible shell-like particles that exhibit self-limiting assembly due to the build up of curvature deformation in cohesive stacks. To address a generic, yet poorly understood aspect of frustrated assembly, we introduce a model of curvamer assembly that incorporates both {\it intra-particle} shape deformation as well as compliance of {\it inter-particle} cohesive gaps, an effect we can attribute to a {\it finite range of attraction} between particles. We show that the ratio of intra-particle (bending elasticity) to inter-particle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation through curvamer stacks. We find a transition from uniformly-bound, curvature-focusing stacks at small size to gap-opened, uniformly curved stacks at large size is controlled by a dimensionless measure of inter- versus intra-curvamer stiffness. The finite range of inter-particle attraction determines range of cohesion in stacks are self-limiting, a prediction which is in strong agreement with numerical studies of our coarse-grained colloidal model. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multi-particle scales.

3D fragment reassembly aims to recover the rigid poses of unordered fragment point clouds or meshes in a common object coordinate system to reconstruct the complete shape. The problem becomes particularly challenging as the number of fragments grows, since the target shape is unknown and fragments provide weak semantic cues. Existing end-to-end approaches are prone to cascading failures due to unreliable contact reasoning, most notably inaccurate fragment adjacencies. To address this, we propose Structure-Aware Reassembly (SARe), a generative framework with SARe-Gen for Euclidean-space assembly generation and SARe-Refine for inference-time refinement, with explicit contact modeling. SARe-Gen jointly predicts fracture-surface token probabilities and an inter-fragment contact graph to localize contact regions and infer candidate adjacencies. It adopts a query-point-based conditioning scheme and extracts aligned local geometric tokens at query locations from a frozen geometry encoder, yielding queryable structural representations without additional structural pretraining. We further introduce an inference-time refinement stage, SARe-Refine. By verifying candidate contact edges with geometric-consistency checks, it selects reliable substructures and resamples the remaining uncertain regions while keeping verified parts fixed, leading to more stable and consistent assemblies in the many-fragment regime. We evaluate SARe across three settings, including synthetic fractures, simulated fractures from scanned real objects, and real physically fractured scans. The results demonstrate state-of-the-art performance, with more graceful degradation and higher success rates as the fragment count increases in challenging large-scale reassembly.

Assembling furniture amounts to solving the discrete-continuous optimization task of selecting the furniture parts to assemble and estimating their connecting poses in a physically realistic manner. The problem is hampered by its combinatorially large yet sparse solution space thus making learning to assemble a challenging task for current machine learning models. In this paper, we attempt to solve this task by leveraging the assembly instructions provided in diagrammatic manuals that typically accompany the furniture parts. Our key insight is to use the cues in these diagrams to split the problem into discrete and continuous phases. Specifically, we present Manual-PA, a transformer-based instruction Manual-guided 3D Part Assembly framework that learns to semantically align 3D parts with their illustrations in the manuals using a contrastive learning backbone towards predicting the assembly order and infers the 6D pose of each part via relating it to the final furniture depicted in the manual. To validate the efficacy of our method, we conduct experiments on the benchmark PartNet dataset. Our results show that using the diagrams and the order of the parts lead to significant improvements in assembly performance against the state of the art. Further, Manual-PA demonstrates strong generalization to real-world IKEA furniture assembly on the IKEA-Manual dataset.

Posing 3D characters is a fundamental task in computer graphics and vision. However, existing methods like auto-rigging and pose-conditioned generation often struggle with challenges such as inaccurate skinning weight prediction, topological imperfections, and poor pose conformance, limiting their robustness and generalizability. To overcome these limitations, we introduce Make-It-Poseable, a novel feed-forward framework that reformulates character posing as a latent-space transformation problem. Instead of deforming mesh vertices as in traditional pipelines, our method reconstructs the character in new poses by directly manipulating its latent representation. At the core of our method is a latent posing transformer that manipulates shape tokens based on skeletal motion. This process is facilitated by a dense pose representation for precise control. To ensure high-fidelity geometry and accommodate topological changes, we also introduce a latent-space supervision strategy and an adaptive completion module. Our method demonstrates superior performance in posing quality. It also naturally extends to 3D editing applications like part replacement and refinement.

Industrial CAD workflows require robust, generalizable 3D geometric representations supporting accuracy and explainability. We introduce Shape, a self-supervised foundation model converting surface meshes into dense per-token embeddings. Shape combines a structured 3D latent grid, a multi-scale geometry-aware tokenizer (MAGNO) with cross-attention, and a transformer processor using grouped-query attention and RMSNorm. A learned reconstruction prior enables per-region attribution for explainable predictions. Pretraining uses masked-token reconstruction of normalized geometry statistics and multi-resolution contrastive consistency. The 10.9M-parameter backbone is pretrained on 61,052 CAD meshes from Thingi10K, MFCAD, and Fusion360. On a held-out split of 2,983 meshes, Shape achieves reconstruction R2 = 0.729 and 98.1% top-1 retrieval under the Wang-Isola protocol, with near-zero reconstruction train/val gap (contrastive scores use a larger evaluation pool). A 2x2 ablation on loss type and target-space normalization shows per-dimension normalization is critical: without it, performance collapses (R2 < 0.14, top-1 < 88%); with it, both losses succeed (R2 > 0.70, top-1 > 96%). Smooth-L1 offers secondary stability. Code, embeddings, and an interactive demo are released at https://github.com/simd-ai/shape.

Furniture assembly is a crucial yet challenging task for robots, requiring precise dual-arm coordination where one arm manipulates parts while the other provides collaborative support and stabilization. To accomplish this task more effectively, robots need to actively adapt support strategies throughout the long-horizon assembly process, while also generalizing across diverse part geometries. We propose A3D, a framework which learns adaptive affordances to identify optimal support and stabilization locations on furniture parts. The method employs dense point-level geometric representations to model part interaction patterns, enabling generalization across varied geometries. To handle evolving assembly states, we introduce an adaptive module that uses interaction feedback to dynamically adjust support strategies during assembly based on previous interactions. We establish a simulation environment featuring 50 diverse parts across 8 furniture types, designed for dual-arm collaboration evaluation. Experiments demonstrate that our framework generalizes effectively to diverse part geometries and furniture categories in both simulation and real-world settings.

3D shape modeling is labor-intensive, time-consuming, and requires years of expertise. To facilitate 3D shape modeling, we propose a 3D shape generation network that takes a 3D VR sketch as a condition. We assume that sketches are created by novices without art training and aim to reconstruct geometrically realistic 3D shapes of a given category. To handle potential sketch ambiguity, our method creates multiple 3D shapes that align with the original sketch's structure. We carefully design our method, training the model step-by-step and leveraging multi-modal 3D shape representation to support training with limited training data. To guarantee the realism of generated 3D shapes we leverage the normalizing flow that models the distribution of the latent space of 3D shapes. To encourage the fidelity of the generated 3D shapes to an input sketch, we propose a dedicated loss that we deploy at different stages of the training process. The code is available at https://github.com/Rowl1ng/3Dsketch2shape.

A CAD model is not engineering-grade merely because it looks correct. It must satisfy design requirements, respond predictably to parameter changes, support controlled edits, match a reference structural response under a declared analysis, and connect to other parts through valid joints. We present CADEngBench, a two-track benchmark for these capabilities. CADEngBench-P evaluates 300 parametric parts, each used for one zero-to-CAD task and one functional-editing task (600 tasks in total), through boundary-representation (B-Rep) validity, engineering and DFM checks, parameter-family perturbations, functional editing, and matched linear-static FEA in CalculiX. CADEngBench-A evaluates 150 body pairs through ranked joint retrieval, exact face-and-edge grounding, joint-frame prediction, and kinematic verification. Across eight multimodal, code-capable models, editing supplied CAD is substantially easier than generating it, while complex edits and matched FEA remain difficult. Assembly predictions often locate the relevant region but fail to recover the recorded joint or mating entities. These results show that CAD evaluation must test engineering behavior rather than appearance alone.

Assembly101 is a new procedural activity dataset featuring 4321 videos of people assembling and disassembling 101 "take-apart" toy vehicles. Participants work without fixed instructions, and the sequences feature rich and natural variations in action ordering, mistakes, and corrections. Assembly101 is the first multi-view action dataset, with simultaneous static (8) and egocentric (4) recordings. Sequences are annotated with more than 100K coarse and 1M fine-grained action segments, and 18M 3D hand poses. We benchmark on three action understanding tasks: recognition, anticipation and temporal segmentation. Additionally, we propose a novel task of detecting mistakes. The unique recording format and rich set of annotations allow us to investigate generalization to new toys, cross-view transfer, long-tailed distributions, and pose vs. appearance. We envision that Assembly101 will serve as a new challenge to investigate various activity understanding problems.

Spatial reasoning is a fundamental capability for embodied intelligence, especially for fine-grained manipulation tasks such as robotic assembly. Recent methods based on vision-language models (VLMs) largely rely on coarse 2D perception and struggle to perform accurate reasoning over complex 3D geometry. To address this limitation, we propose AssemLM, a spatial multimodal large language model for robotic assembly that integrates assembly manuals, point clouds, and textual instructions to predict task-critical 6D assembly poses with explicit geometric understanding. To bridge raw 3D perception and high-level linguistic reasoning, AssemLM employs a specialized point cloud encoder to extract fine-grained geometric and rotational features for accurate 3D spatial reasoning in assembly tasks. In addition, we introduce AssemBench, a large-scale benchmark for assembly-oriented spatial reasoning with over 900K multimodal samples and precise 6D pose annotations, extending evaluation from 2D grounding to full 3D geometric inference. Extensive experiments and real-robot evaluations demonstrate that AssemLM achieves state-of-the-art 6D pose reasoning performance and effectively supports fine-grained, multi-step assembly tasks in real-world settings. Code, models, and the AssemBench dataset will be made publicly available.

Parametric computer-aided design (CAD) is a standard paradigm used to design manufactured objects, where a 3D shape is represented as a program supported by the CAD software. Despite the pervasiveness of parametric CAD and a growing interest from the research community, currently there does not exist a dataset of realistic CAD models in a concise programmatic form. In this paper we present the Fusion 360 Gallery, consisting of a simple language with just the sketch and extrude modeling operations, and a dataset of 8,625 human design sequences expressed in this language. We also present an interactive environment called the Fusion 360 Gym, which exposes the sequential construction of a CAD program as a Markov decision process, making it amendable to machine learning approaches. As a use case for our dataset and environment, we define the CAD reconstruction task of recovering a CAD program from a target geometry. We report results of applying state-of-the-art methods of program synthesis with neurally guided search on this task.

Automated assembly of 3D fractures is essential in orthopedics, archaeology, and our daily life. This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces. Our approach leverages hierarchical features of global and local geometry to match and align the fracture surfaces. Our framework consists of four components: (1) front-end point feature extractor with attention layers, (2) surface segmentation to separate fracture and original parts, (3) multi-parts matching to find correspondences among fracture surface points, and (4) robust global alignment to recover the global poses of the pieces. We show how to jointly learn segmentation and matching and seamlessly integrate feature matching and rigidity constraints. We evaluate Jigsaw on the Breaking Bad dataset and achieve superior performance compared to state-of-the-art methods. Our method also generalizes well to diverse fracture modes, objects, and unseen instances. To the best of our knowledge, this is the first learning-based method designed specifically for 3D fracture assembly over multiple pieces. Our code is available at https://jiaxin-lu.github.io/Jigsaw/.

Computer-aided design (CAD) tools are utilized in the manufacturing industry for modeling everything from cups to spacecraft. These programs are complex to use and typically require years of training and experience to master. Structured and well-constrained 2D sketches and 3D constructions are crucial components of CAD modeling. A well-executed CAD model can be seamlessly integrated into the manufacturing process, thereby enhancing production efficiency. Deep generative models of 3D shapes and 3D object reconstruction models have garnered significant research interest. However, most of these models produce discrete forms of 3D objects that are not editable. Moreover, the few models based on CAD operations often have substantial input restrictions. In this work, we fine-tuned pre-trained models to create OpenECAD models (0.55B, 0.89B, 2.4B and 3.1B), leveraging the visual, logical, coding, and general capabilities of visual language models. OpenECAD models can process images of 3D designs as input and generate highly structured 2D sketches and 3D construction commands, ensuring that the designs are editable. These outputs can be directly used with existing CAD tools' APIs to generate project files. To train our network, we created a series of OpenECAD datasets. These datasets are derived from existing public CAD datasets, adjusted and augmented to meet the specific requirements of vision language model (VLM) training. Additionally, we have introduced an approach that utilizes dependency relationships to define and generate sketches, further enriching the content and functionality of the datasets.

Computer-aided design (CAD) defines 3D models as compact, precise, and editable representations, making it directly useful for several fields. Recently, CAD generation has been gaining more attention in both the research community and industry. Crafting CAD models has long been a painstaking and time-intensive task, demanding both precision and expertise from designers. Prior works have achieved early success in single-part CAD generation, which is not well-suited for real-world applications, as multiple parts need to be assembled under semantic constraints and geometric compatibility. In this paper, we propose CADKnitter, a compositional CAD generation framework with geometric-guiding cues to steer diffusion sampling. CADKnitter is able to generate a complementary CAD part that follows both the geometric constraints of the given CAD model and the semantic constraints of the desired design text prompt. We also curate a dataset, so-called KnitCAD, containing over 310,000 samples of CAD models, along with textual prompts and assembly metadata that provide semantic and geometric constraints. Intensive experiments demonstrate that our proposed method outperforms other state-of-the-art baselines by a clear margin. Our project page is available at https://cadknitter.github.io/.

Large Language Models (LLMs) have demonstrated impressive capabilities in a wide range of code generation tasks. However, generating code for certain domains remains challenging. One such domain is Computer-Aided Design (CAD) program, where the goal is to produce scripted parametric models that define object geometry for precise design and manufacturing applications. A key challenge in LLM-based CAD program generation is the limited geometric complexity of generated shapes compared to those found in real-world industrial designs. This shortfall is in part due to the lack of diversity in the available CAD program training data. To address this, we propose a novel data augmentation paradigm that prompts an LLM to generate CAD programs conditioned on a reference surface program and a modeling procedure - an idea inspired by practices in industrial design. By varying the reference surface using a collection of organic shapes, our method enriches the geometric distribution of generated CAD models. In particular, it introduces edges and faces defined by spline-based curvature, which are typically missing or underrepresented in existing open-source CAD program datasets. Experiments show that our method produces CAD samples with significantly greater geometric diversity and a higher resemblance to industry-grade CAD designs in terms of the proportion of organic shape primitives. This enhancement makes our CAD data augmentation approach a useful tool for training LLMs and other deep learning models in CAD generation.

Mechanical design and manufacturing workflows conventionally begin with conceptual design, followed by the creation of a computer-aided design (CAD) model and fabrication through material-extrusion (MEX) printing. This process requires converting CAD geometry into machine-readable G-code through slicing and path planning. While each step is well established, dependence on CAD modeling remains a major bottleneck: constructing object-specific 3D geometry is slow and poorly suited to rapid prototyping. Even minor design variations typically necessitate manual updates in CAD software, making iteration time-consuming and difficult to scale. To address this limitation, we introduce Image2Gcode, an end-to-end data-driven framework that bypasses the CAD stage and generates printer-ready G-code directly from images and part drawings. Instead of relying on an explicit 3D model, a hand-drawn or captured 2D image serves as the sole input. The framework first extracts slice-wise structural cues from the image and then employs a denoising diffusion probabilistic model (DDPM) over G-code sequences. Through iterative denoising, the model transforms Gaussian noise into executable print-move trajectories with corresponding extrusion parameters, establishing a direct mapping from visual input to native toolpaths. By producing structured G-code directly from 2D imagery, Image2Gcode eliminates the need for CAD or STL intermediates, lowering the entry barrier for additive manufacturing and accelerating the design-to-fabrication cycle. This approach supports on-demand prototyping from simple sketches or visual references and integrates with upstream 2D-to-3D reconstruction modules to enable an automated pipeline from concept to physical artifact. The result is a flexible, computationally efficient framework that advances accessibility in design iteration, repair workflows, and distributed manufacturing.

The 3D CAD shapes in current 3D benchmarks are mostly collected from online model repositories. Thus, they typically have insufficient geometric details and less informative textures, making them less attractive for comprehensive and subtle research in areas such as high-quality 3D mesh and texture recovery. This paper presents 3D Furniture shape with TextURE (3D-FUTURE): a richly-annotated and large-scale repository of 3D furniture shapes in the household scenario. At the time of this technical report, 3D-FUTURE contains 20,240 clean and realistic synthetic images of 5,000 different rooms. There are 9,992 unique detailed 3D instances of furniture with high-resolution textures. Experienced designers developed the room scenes, and the 3D CAD shapes in the scene are used for industrial production. Given the well-organized 3D-FUTURE, we provide baseline experiments on several widely studied tasks, such as joint 2D instance segmentation and 3D object pose estimation, image-based 3D shape retrieval, 3D object reconstruction from a single image, and texture recovery for 3D shapes, to facilitate related future researches on our database.

Ropes, cables, and other deformable linear objects appear in tasks from untangling to cable routing and suturing, yet controlling their shape remains a challenge in robot manipulation. We study model-based shape control in a general setting: the object lies unfixated on a support surface and two arms may grasp and move it anywhere along its length. Because each arm chooses a grasp point, direction, and magnitude, the joint action space is combinatorially large, and the dynamics model's per-prediction cost bounds how much of it a planner can search. We present ForwardDLO, a recurrent latent dynamics model for this unfixated bimanual setting that predicts per-segment displacements grounded in the observed rope state at every step. Our model reaches accuracy comparable to more expensive baselines while containing no explicit segment-to-segment operations, which makes batched evaluation of candidate actions cheap. On open-loop prediction of real rope motion it reaches the lowest error of the learned models we evaluate, 13% below the strongest baseline. Within a fixed time budget it scores 8 to 22 times more candidate actions than models of comparable accuracy while matching them in real-world shape matching; and on a simulated routing task at a 30Hz control rate, this throughput converts into 98% task success versus at most 30% for the baselines at their own budgets. We release the model, code, and a dataset of 2.42 million simulated and 14,107 real rope transitions at https://anonymous.4open.science/r/ForwardDLO/

In medical and industrial domains, providing guidance for assembly processes can be critical to ensure efficiency and safety. Errors in assembly can lead to significant consequences such as extended surgery times and prolonged manufacturing or maintenance times in industry. Assembly scenarios can benefit from in-situ augmented reality visualization, i.e., augmentations in close proximity to the target object, to provide guidance, reduce assembly times, and minimize errors. In order to enable in-situ visualization, 6D pose estimation can be leveraged to identify the correct location for an augmentation. Existing 6D pose estimation techniques primarily focus on individual objects and static captures. However, assembly scenarios have various dynamics, including occlusion during assembly and dynamics in the appearance of assembly objects. Existing work focus either on object detection combined with state detection, or focus purely on the pose estimation. To address the challenges of 6D pose estimation in combination with assembly state detection, our approach ASDF builds upon the strengths of YOLOv8, a real-time capable object detection framework. We extend this framework, refine the object pose, and fuse pose knowledge with network-detected pose information. Utilizing our late fusion in our Pose2State module results in refined 6D pose estimation and assembly state detection. By combining both pose and state information, our Pose2State module predicts the final assembly state with precision. The evaluation of our ASDF dataset shows that our Pose2State module leads to an improved assembly state detection and that the improvement of the assembly state further leads to a more robust 6D pose estimation. Moreover, on the GBOT dataset, we outperform the pure deep learning-based network and even outperform the hybrid and pure tracking-based approaches.

3D shape is a crucial but heavily underutilized cue in today's computer vision systems, mostly due to the lack of a good generic shape representation. With the recent availability of inexpensive 2.5D depth sensors (e.g. Microsoft Kinect), it is becoming increasingly important to have a powerful 3D shape representation in the loop. Apart from category recognition, recovering full 3D shapes from view-based 2.5D depth maps is also a critical part of visual understanding. To this end, we propose to represent a geometric 3D shape as a probability distribution of binary variables on a 3D voxel grid, using a Convolutional Deep Belief Network. Our model, 3D ShapeNets, learns the distribution of complex 3D shapes across different object categories and arbitrary poses from raw CAD data, and discovers hierarchical compositional part representations automatically. It naturally supports joint object recognition and shape completion from 2.5D depth maps, and it enables active object recognition through view planning. To train our 3D deep learning model, we construct ModelNet -- a large-scale 3D CAD model dataset. Extensive experiments show that our 3D deep representation enables significant performance improvement over the-state-of-the-arts in a variety of tasks.

We present ShapeNet: a richly-annotated, large-scale repository of shapes represented by 3D CAD models of objects. ShapeNet contains 3D models from a multitude of semantic categories and organizes them under the WordNet taxonomy. It is a collection of datasets providing many semantic annotations for each 3D model such as consistent rigid alignments, parts and bilateral symmetry planes, physical sizes, keywords, as well as other planned annotations. Annotations are made available through a public web-based interface to enable data visualization of object attributes, promote data-driven geometric analysis, and provide a large-scale quantitative benchmark for research in computer graphics and vision. At the time of this technical report, ShapeNet has indexed more than 3,000,000 models, 220,000 models out of which are classified into 3,135 categories (WordNet synsets). In this report we describe the ShapeNet effort as a whole, provide details for all currently available datasets, and summarize future plans.

Computer-aided design (CAD) significantly enhances the efficiency, accuracy, and innovation of design processes by enabling precise 2D and 3D modeling, extensive analysis, and optimization. Existing methods for creating CAD models rely on latent vectors or point clouds, which are difficult to obtain and costly to store. Recent advances in Multimodal Large Language Models (MLLMs) have inspired researchers to use natural language instructions and images for CAD model construction. However, these models still struggle with inferring accurate 3D spatial location and orientation, leading to inaccuracies in determining the spatial 3D starting points and extrusion directions for constructing geometries. This work introduces CAD-GPT, a CAD synthesis method with spatial reasoning-enhanced MLLM that takes either a single image or a textual description as input. To achieve precise spatial inference, our approach introduces a 3D Modeling Spatial Mechanism. This method maps 3D spatial positions and 3D sketch plane rotation angles into a 1D linguistic feature space using a specialized spatial unfolding mechanism, while discretizing 2D sketch coordinates into an appropriate planar space to enable precise determination of spatial starting position, sketch orientation, and 2D sketch coordinate translations. Extensive experiments demonstrate that CAD-GPT consistently outperforms existing state-of-the-art methods in CAD model synthesis, both quantitatively and qualitatively.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Parametric computer-aided design (CAD) is the dominant paradigm in mechanical engineering for physical design. Distinguished by relational geometry, parametric CAD models begin as two-dimensional sketches consisting of geometric primitives (e.g., line segments, arcs) and explicit constraints between them (e.g., coincidence, perpendicularity) that form the basis for three-dimensional construction operations. Training machine learning models to reason about and synthesize parametric CAD designs has the potential to reduce design time and enable new design workflows. Additionally, parametric CAD designs can be viewed as instances of constraint programming and they offer a well-scoped test bed for exploring ideas in program synthesis and induction. To facilitate this research, we introduce SketchGraphs, a collection of 15 million sketches extracted from real-world CAD models coupled with an open-source data processing pipeline. Each sketch is represented as a geometric constraint graph where edges denote designer-imposed geometric relationships between primitives, the nodes of the graph. We demonstrate and establish benchmarks for two use cases of the dataset: generative modeling of sketches and conditional generation of likely constraints given unconstrained geometry.

We introduce a method for learning to generate the surface of 3D shapes. Our approach represents a 3D shape as a collection of parametric surface elements and, in contrast to methods generating voxel grids or point clouds, naturally infers a surface representation of the shape. Beyond its novelty, our new shape generation framework, AtlasNet, comes with significant advantages, such as improved precision and generalization capabilities, and the possibility to generate a shape of arbitrary resolution without memory issues. We demonstrate these benefits and compare to strong baselines on the ShapeNet benchmark for two applications: (i) auto-encoding shapes, and (ii) single-view reconstruction from a still image. We also provide results showing its potential for other applications, such as morphing, parametrization, super-resolution, matching, and co-segmentation.

In daily life, humans utilize hands to manipulate objects. Modeling the shape of objects that are manipulated by the hand is essential for AI to comprehend daily tasks and to learn manipulation skills. However, previous approaches have encountered difficulties in reconstructing the precise shapes of hand-held objects, primarily owing to a deficiency in prior shape knowledge and inadequate data for training. As illustrated, given a particular type of tool, such as a mug, despite its infinite variations in shape and appearance, humans have a limited number of 'effective' modes and poses for its manipulation. This can be attributed to the fact that humans have mastered the shape prior of the 'mug' category, and can quickly establish the corresponding relations between different mug instances and the prior, such as where the rim and handle are located. In light of this, we propose a new method, CHORD, for Category-level Hand-held Object Reconstruction via shape Deformation. CHORD deforms a categorical shape prior for reconstructing the intra-class objects. To ensure accurate reconstruction, we empower CHORD with three types of awareness: appearance, shape, and interacting pose. In addition, we have constructed a new dataset, COMIC, of category-level hand-object interaction. COMIC contains a rich array of object instances, materials, hand interactions, and viewing directions. Extensive evaluation shows that CHORD outperforms state-of-the-art approaches in both quantitative and qualitative measures. Code, model, and datasets are available at https://kailinli.github.io/CHORD.

In this paper, we develop a new method to automatically convert 2D line drawings from three orthographic views into 3D CAD models. Existing methods for this problem reconstruct 3D models by back-projecting the 2D observations into 3D space while maintaining explicit correspondence between the input and output. Such methods are sensitive to errors and noises in the input, thus often fail in practice where the input drawings created by human designers are imperfect. To overcome this difficulty, we leverage the attention mechanism in a Transformer-based sequence generation model to learn flexible mappings between the input and output. Further, we design shape programs which are suitable for generating the objects of interest to boost the reconstruction accuracy and facilitate CAD modeling applications. Experiments on a new benchmark dataset show that our method significantly outperforms existing ones when the inputs are noisy or incomplete.

Computer-aided design (CAD) is vital to modern manufacturing, yet model creation remains labor-intensive and expertise-heavy. To enable non-experts to translate intuitive design intent into manufacturable artifacts, recent large language models-based text-to-CAD efforts focus on command sequences or script-based formats like CadQuery. However, these formats are kernel-dependent and lack universality for manufacturing. In contrast, the Standard for the Exchange of Product Data (STEP, ISO 10303) file is a widely adopted, neutral boundary representation (B-rep) format directly compatible with manufacturing, but its graph-structured, cross-referenced nature poses unique challenges for auto-regressive LLMs. To address this, we curate a dataset of ~40K STEP-caption pairs and introduce novel preprocessing tailored for the graph-structured format of STEP, including a depth-first search-based reserialization that linearizes cross-references while preserving locality and chain-of-thought(CoT)-style structural annotations that guide global coherence. We integrate retrieval-augmented generation to ground predictions in relevant examples for supervised fine-tuning, and refine generation quality through reinforcement learning with a specific Chamfer Distance-based geometric reward. Experiments demonstrate consistent gains of our STEP-LLM in geometric fidelity over the Text2CAD baseline, with improvements arising from multiple stages of our framework: the RAG module substantially enhances completeness and renderability, the DFS-based reserialization strengthens overall accuracy, and the RL further reduces geometric discrepancy. Both metrics and visual comparisons confirm that STEP-LLM generates shapes with higher fidelity than Text2CAD. These results show the feasibility of LLM-driven STEP model generation from natural language, showing its potential to democratize CAD design for manufacturing.

This paper proposes a novel "auto-agglomerative" 3D fracture assembly method, PuzzleFusion++, resembling how humans solve challenging spatial puzzles. Starting from individual fragments, the approach 1) aligns and merges fragments into larger groups akin to agglomerative clustering and 2) repeats the process iteratively in completing the assembly akin to auto-regressive methods. Concretely, a diffusion model denoises the 6-DoF alignment parameters of the fragments simultaneously, and a transformer model verifies and merges pairwise alignments into larger ones, whose process repeats iteratively. Extensive experiments on the Breaking Bad dataset show that PuzzleFusion++ outperforms all other state-of-the-art techniques by significant margins across all metrics, in particular by over 10% in part accuracy and 50% in Chamfer distance. The code will be available on our project page: https://puzzlefusion-plusplus.github.io.

Robotic manipulation remains a core challenge in robotics, particularly for contact-rich tasks such as industrial assembly and disassembly. Existing datasets have significantly advanced learning in manipulation but are primarily focused on simpler tasks like object rearrangement, falling short of capturing the complexity and physical dynamics involved in assembly and disassembly. To bridge this gap, we present REASSEMBLE (Robotic assEmbly disASSEMBLy datasEt), a new dataset designed specifically for contact-rich manipulation tasks. Built around the NIST Assembly Task Board 1 benchmark, REASSEMBLE includes four actions (pick, insert, remove, and place) involving 17 objects. The dataset contains 4,551 demonstrations, of which 4,035 were successful, spanning a total of 781 minutes. Our dataset features multi-modal sensor data, including event cameras, force-torque sensors, microphones, and multi-view RGB cameras. This diverse dataset supports research in areas such as learning contact-rich manipulation, task condition identification, action segmentation, and task inversion learning. The REASSEMBLE will be a valuable resource for advancing robotic manipulation in complex, real-world scenarios. The dataset is publicly available on our project website: https://tuwien-asl.github.io/REASSEMBLE_page/.

Generating 3D shapes at part level is pivotal for downstream applications such as mesh retopology, UV mapping, and 3D printing. However, existing part-based generation methods often lack sufficient controllability and suffer from poor semantically meaningful decomposition. To this end, we introduce X-Part, a controllable generative model designed to decompose a holistic 3D object into semantically meaningful and structurally coherent parts with high geometric fidelity. X-Part exploits the bounding box as prompts for the part generation and injects point-wise semantic features for meaningful decomposition. Furthermore, we design an editable pipeline for interactive part generation. Extensive experimental results show that X-Part achieves state-of-the-art performance in part-level shape generation. This work establishes a new paradigm for creating production-ready, editable, and structurally sound 3D assets. Codes will be released for public research.

We introduce AutoPartGen, a model that generates objects composed of 3D parts in an autoregressive manner. This model can take as input an image of an object, 2D masks of the object's parts, or an existing 3D object, and generate a corresponding compositional 3D reconstruction. Our approach builds upon 3DShape2VecSet, a recent latent 3D representation with powerful geometric expressiveness. We observe that this latent space exhibits strong compositional properties, making it particularly well-suited for part-based generation tasks. Specifically, AutoPartGen generates object parts autoregressively, predicting one part at a time while conditioning on previously generated parts and additional inputs, such as 2D images, masks, or 3D objects. This process continues until the model decides that all parts have been generated, thus determining automatically the type and number of parts. The resulting parts can be seamlessly assembled into coherent objects or scenes without requiring additional optimization. We evaluate both the overall 3D generation capabilities and the part-level generation quality of AutoPartGen, demonstrating that it achieves state-of-the-art performance in 3D part generation.

Recent advancements in implicit 3D representations and generative models have markedly propelled the field of 3D object generation forward. However, it remains a significant challenge to accurately model geometries with defined sharp features under parametric controls, which is crucial in fields like industrial design and manufacturing. To bridge this gap, we introduce a framework that employs Large Language Models (LLMs) to generate text-driven 3D shapes, manipulating 3D software via program synthesis. We present 3D-PreMise, a dataset specifically tailored for 3D parametric modeling of industrial shapes, designed to explore state-of-the-art LLMs within our proposed pipeline. Our work reveals effective generation strategies and delves into the self-correction capabilities of LLMs using a visual interface. Our work highlights both the potential and limitations of LLMs in 3D parametric modeling for industrial applications.

We present a novel alignment-before-generation approach to tackle the challenging task of generating general 3D shapes based on 2D images or texts. Directly learning a conditional generative model from images or texts to 3D shapes is prone to producing inconsistent results with the conditions because 3D shapes have an additional dimension whose distribution significantly differs from that of 2D images and texts. To bridge the domain gap among the three modalities and facilitate multi-modal-conditioned 3D shape generation, we explore representing 3D shapes in a shape-image-text-aligned space. Our framework comprises two models: a Shape-Image-Text-Aligned Variational Auto-Encoder (SITA-VAE) and a conditional Aligned Shape Latent Diffusion Model (ASLDM). The former model encodes the 3D shapes into the shape latent space aligned to the image and text and reconstructs the fine-grained 3D neural fields corresponding to given shape embeddings via the transformer-based decoder. The latter model learns a probabilistic mapping function from the image or text space to the latent shape space. Our extensive experiments demonstrate that our proposed approach can generate higher-quality and more diverse 3D shapes that better semantically conform to the visual or textural conditional inputs, validating the effectiveness of the shape-image-text-aligned space for cross-modality 3D shape generation.

Shape-Text matching is an important task of high-level shape understanding. Current methods mainly represent a 3D shape as multiple 2D rendered views, which obviously can not be understood well due to the structural ambiguity caused by self-occlusion in the limited number of views. To resolve this issue, we directly represent 3D shapes as point clouds, and propose to learn joint embedding of point clouds and texts by bidirectional matching between parts from shapes and words from texts. Specifically, we first segment the point clouds into parts, and then leverage optimal transport method to match parts and words in an optimized feature space, where each part is represented by aggregating features of all points within it and each word is abstracted by its contextual information. We optimize the feature space in order to enlarge the similarities between the paired training samples, while simultaneously maximizing the margin between the unpaired ones. Experiments demonstrate that our method achieves a significant improvement in accuracy over the SOTAs on multi-modal retrieval tasks under the Text2Shape dataset. Codes are available at https://github.com/JLUtangchuan/Parts2Words.

Industrial Computer-Aided Design (CAD) code generation requires models to produce executable parametric programs from visual or textual inputs. Beyond recognizing the outer shape of a part, this task involves understanding its 3D structure, inferring engineering parameters, and choosing CAD operations that reflect how the part would be designed and manufactured. Despite the promise of Multimodal large language models (MLLMs) for this task, they are rarely evaluated on whether these capabilities jointly hold in realistic industrial CAD settings. We present BenchCAD, a unified benchmark for industrial CAD reasoning. BenchCAD contains 17,900 execution-verified CadQuery programs across 106 industrial part families, including bevel gears, compression springs, twist drills, and other reusable engineering designs. It evaluates models through visual question answering, code question answering, image-to-code generation, and instruction-guided code editing, enabling fine-grained analysis across perception, parametric abstraction, and executable program synthesis. Across 10+ frontier models, BenchCAD shows that current systems often recover coarse outer geometry but fail to produce faithful parametric CAD programs. Common failures include missing fine 3D structure, misinterpreting industrial design parameters, and replacing essential operations such as sweeps, lofts, and twist-extrudes with simpler sketch-and-extrude patterns. Fine-tuning and reinforcement learning improve in-distribution performance, but generalization to unseen part families remains limited. These results position BenchCAD as a benchmark for measuring and improving the industrial readiness of multimodal CAD automation.

2D assembly diagrams are often abstract and hard to follow, creating a need for intelligent assistants that can monitor progress, detect errors, and provide step-by-step guidance. In mixed reality settings, such systems must recognize completed and ongoing steps from the camera feed and align them with the diagram instructions. Vision Language Models (VLMs) show promise for this task, but face a depiction gap because assembly diagrams and video frames share few visual features. To systematically assess this gap, we construct IKEA-Bench, a benchmark of 1,623 questions across 6 task types on 29 IKEA furniture products, and evaluate 19 VLMs (2B-38B) under three alignment strategies. Our key findings: (1) assembly instruction understanding is recoverable via text, but text simultaneously degrades diagram-to-video alignment; (2) architecture family predicts alignment accuracy more strongly than parameter count; (3) video understanding remains a hard bottleneck unaffected by strategy. A three-level mechanistic analysis further reveals that diagrams and video occupy disjoint ViT subspaces, and that adding text shifts models from visual to text-driven reasoning. These results identify visual encoding as the primary target for improving cross-depiction robustness. Project page: https://ryenhails.github.io/IKEA-Bench/

We explore the effects of various plasticity functions on assemblies of neurons. To bridge the gap between experimental and computational theories we make use of a conceptual framework, the Assembly Calculus, which is a formal system for the description of brain function based on assemblies of neurons. The Assembly Calculus includes operations for projecting, associating, and merging assemblies of neurons. Our research is focused on simulating different plasticity functions with Assembly Calculus. Our main contribution is the modification and evaluation of the projection operation. We experiment with Oja's and Spike Time-Dependent Plasticity (STDP) rules and test the effect of various hyper-parameters.

Prior to the deep learning era, shape was commonly used to describe the objects. Nowadays, state-of-the-art (SOTA) algorithms in medical imaging are predominantly diverging from computer vision, where voxel grids, meshes, point clouds, and implicit surface models are used. This is seen from numerous shape-related publications in premier vision conferences as well as the growing popularity of ShapeNet (about 51,300 models) and Princeton ModelNet (127,915 models). For the medical domain, we present a large collection of anatomical shapes (e.g., bones, organs, vessels) and 3D models of surgical instrument, called MedShapeNet, created to facilitate the translation of data-driven vision algorithms to medical applications and to adapt SOTA vision algorithms to medical problems. As a unique feature, we directly model the majority of shapes on the imaging data of real patients. As of today, MedShapeNet includes 23 dataset with more than 100,000 shapes that are paired with annotations (ground truth). Our data is freely accessible via a web interface and a Python application programming interface (API) and can be used for discriminative, reconstructive, and variational benchmarks as well as various applications in virtual, augmented, or mixed reality, and 3D printing. Exemplary, we present use cases in the fields of classification of brain tumors, facial and skull reconstructions, multi-class anatomy completion, education, and 3D printing. In future, we will extend the data and improve the interfaces. The project pages are: https://medshapenet.ikim.nrw/ and https://github.com/Jianningli/medshapenet-feedback

In this paper, we democratise 3D content creation, enabling precise generation of 3D shapes from abstract sketches while overcoming limitations tied to drawing skills. We introduce a novel part-level modelling and alignment framework that facilitates abstraction modelling and cross-modal correspondence. Leveraging the same part-level decoder, our approach seamlessly extends to sketch modelling by establishing correspondence between CLIPasso edgemaps and projected 3D part regions, eliminating the need for a dataset pairing human sketches and 3D shapes. Additionally, our method introduces a seamless in-position editing process as a byproduct of cross-modal part-aligned modelling. Operating in a low-dimensional implicit space, our approach significantly reduces computational demands and processing time.

We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual instructions, leading to ambiguity and limited control. Image Sculpting converts 2D objects into 3D, enabling direct interaction with their 3D geometry. Post-editing, these objects are re-rendered into 2D, merging into the original image to produce high-fidelity results through a coarse-to-fine enhancement process. The framework supports precise, quantifiable, and physically-plausible editing options such as pose editing, rotation, translation, 3D composition, carving, and serial addition. It marks an initial step towards combining the creative freedom of generative models with the precision of graphics pipelines.

Recent progress in 3D object generation has greatly improved both the quality and efficiency. However, most existing methods generate a single mesh with all parts fused together, which limits the ability to edit or manipulate individual parts. A key challenge is that different objects may have a varying number of parts. To address this, we propose a new end-to-end framework for part-level 3D object generation. Given a single input image, our method generates high-quality 3D objects with an arbitrary number of complete and semantically meaningful parts. We introduce a dual volume packing strategy that organizes all parts into two complementary volumes, allowing for the creation of complete and interleaved parts that assemble into the final object. Experiments show that our model achieves better quality, diversity, and generalization than previous image-based part-level generation methods.

Recent advances in 3D shape generation have achieved impressive results, but most existing methods rely on clean, unoccluded, and well-segmented inputs. Such conditions are rarely met in real-world scenarios. We present ShapeR, a novel approach for conditional 3D object shape generation from casually captured sequences. Given an image sequence, we leverage off-the-shelf visual-inertial SLAM, 3D detection algorithms, and vision-language models to extract, for each object, a set of sparse SLAM points, posed multi-view images, and machine-generated captions. A rectified flow transformer trained to effectively condition on these modalities then generates high-fidelity metric 3D shapes. To ensure robustness to the challenges of casually captured data, we employ a range of techniques including on-the-fly compositional augmentations, a curriculum training scheme spanning object- and scene-level datasets, and strategies to handle background clutter. Additionally, we introduce a new evaluation benchmark comprising 178 in-the-wild objects across 7 real-world scenes with geometry annotations. Experiments show that ShapeR significantly outperforms existing approaches in this challenging setting, achieving an improvement of 2.7x in Chamfer distance compared to state of the art.

Reverse engineering 3D computer-aided design (CAD) models from images is an important task for many downstream applications including interactive editing, manufacturing, architecture, robotics, etc. The difficulty of the task lies in vast representational disparities between the CAD output and the image input. CAD models are precise, programmatic constructs that involve sequential operations combining discrete command structure with continuous attributes, making it challenging to learn and optimize in an end-to-end fashion. Concurrently, input images introduce inherent challenges such as photometric variability and sensor noise, complicating the reverse engineering process. In this work, we introduce a novel approach that conditionally factorizes the task into two sub-problems. First, we leverage vision-language foundation models (VLMs), a finetuned Llama3.2, to predict the global discrete base structure with semantic information. Second, we propose TrAssembler that, conditioned on the discrete structure with semantics, predicts the continuous attribute values. To support the training of our TrAssembler, we further constructed an annotated CAD dataset of common objects from ShapeNet. Putting all together, our approach and data demonstrate significant first steps towards CAD-ifying images in the wild. Code and data can be found in https://github.com/qq456cvb/Img2CAD.

Text- and image-conditioned video generation models have achieved strong visual fidelity and temporal coherence, but they often fail to generate motion governed by kinematic and geometric constraints. In these settings, object parts must remain rigid, maintain contact or coupling with neighboring components, and transfer motion consistently across connected parts. These requirements are especially explicit in articulated mechanical assemblies, where motion is constrained by rigid-link geometry, contact/coupling relations, and transmission through kinematic chains. A generated video may therefore appear plausible while violating the intended mechanism, such as rotating a part that should translate, deforming a rigid component, breaking coupling between parts, or failing to move downstream components. To evaluate this gap, We introduce MechVerse, a benchmark for mechanically consistent image-to-video generation. MechVerse contains 21,156 synthetic clips from 1,357 mechanical assemblies across 141 categories, organized into three tiers of increasing kinematic complexity: independent articulation, pairwise coupling, and densely coupled multi-part mechanisms. Each clip is paired with a structured prompt describing part identities, stationary supports, moving components, motion primitives, direction, speed/extent, and inter-part dependencies. We evaluate proprietary, open-source, and fine-tuned image-to-video models using standard video metrics, instruction-following scores, and human judgments of motion correctness and kinematic coupling. Results show that current models can preserve appearance and smoothness while failing to generate mechanically admissible motion, with errors increasing as coupling complexity grows. MechVerse provides a benchmark for measuring and improving mechanism-aware video generation from image and language inputs.

Constructing computer-aided design (CAD) models is labor-intensive but essential for engineering and manufacturing. Recent advances in Large Language Models (LLMs) have inspired the LLM-based CAD generation by representing CAD as command sequences. But these methods struggle in practical scenarios because command sequence representation does not support entity selection (e.g. faces or edges), limiting its ability to support complex editing operations such as chamfer or fillet. Further, the discretization of a continuous variable during sketch and extrude operations may result in topological errors. To address these limitations, we present Pointer-CAD, a novel LLM-based CAD generation framework that leverages a pointer-based command sequence representation to explicitly incorporate the geometric information of B-rep models into sequential modeling. In particular, Pointer-CAD decomposes CAD model generation into steps, conditioning the generation of each subsequent step on both the textual description and the B-rep generated from previous steps. Whenever an operation requires the selection of a specific geometric entity, the LLM predicts a Pointer that selects the most feature-consistent candidate from the available set. Such a selection operation also reduces the quantization error in the command sequence-based representation. To support the training of Pointer-CAD, we develop a data annotation pipeline that produces expert-level natural language descriptions and apply it to build a dataset of approximately 575K CAD models. Extensive experimental results demonstrate that Pointer-CAD effectively supports the generation of complex geometric structures and reduces segmentation error to an extremely low level, achieving a significant improvement over prior command sequence methods, thereby significantly mitigating the topological inaccuracies introduced by quantization error.

We propose a training-free approach to 3D editing that enables the editing of a single shape within a few minutes. The edited 3D mesh aligns well with the prompts, and remains identical for regions that are not intended to be altered. To this end, we first project the 3D object onto 4-view images and perform synchronized multi-view image editing along with user-guided text prompts and user-provided rough masks. However, the targeted regions to be edited are ambiguous due to projection from 3D to 2D. To ensure precise editing only in intended regions, we develop a 3D segmentation pipeline that detects edited areas in 3D space, followed by a merging algorithm to seamlessly integrate edited 3D regions with the original input. Extensive experiments demonstrate the superiority of our method over previous approaches, enabling fast, high-quality editing while preserving unintended regions.

Large language models (LLMs) have recently advanced text-driven 3D generation, yet Text-to-CAD remains far from supporting industrial product design. Existing benchmarks focus primarily on generating single-part CAD models and evaluate them using geometric similarity metrics that fail to capture functionality, manufacturability, and assemblability. To address this gap, we introduce MUSE, a Text-to-CAD benchmark focused on complex, editable boundary representation (B-Rep) assemblies. MUSE pairs practical design instances with structured Design Specifications and evaluates generated models through a three-stage protocol: code check, geometric check, and design-intent alignment. The final stage uses design-specific rubrics to assess functionality, manufacturability, and assemblability, moving beyond shape matching toward practical design quality. To enable scalable evaluation, we use a rubric-based visual language model (VLM) judge and validate its reliability through human annotation. Experiments on closed-source and open-source LLMs reveal a clear failure cascade from executable code to valid geometry and finally to engineering-ready design, with even the strongest models achieving limited success on fine-grained engineering criteria. Together, MUSE provides a realistic benchmark and evaluation framework for advancing Text-to-CAD from geometric generation toward true engineering design. Our project website, including the leaderboard, dataset, and code, is available at https://dong7313.github.io/muse-benchmark/.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.

Deep implicit functions (DIFs) have emerged as a powerful paradigm for many computer vision tasks such as 3D shape reconstruction, generation, registration, completion, editing, and understanding. However, given a set of 3D shapes with associated covariates there is at present no shape representation method which allows to precisely represent the shapes while capturing the individual dependencies on each covariate. Such a method would be of high utility to researchers to discover knowledge hidden in a population of shapes. For scientific shape discovery, we propose a 3D Neural Additive Model for Interpretable Shape Representation (NAISR) which describes individual shapes by deforming a shape atlas in accordance to the effect of disentangled covariates. Our approach captures shape population trends and allows for patient-specific predictions through shape transfer. NAISR is the first approach to combine the benefits of deep implicit shape representations with an atlas deforming according to specified covariates. We evaluate NAISR with respect to shape reconstruction, shape disentanglement, shape evolution, and shape transfer on three datasets: 1) Starman, a simulated 2D shape dataset; 2) the ADNI hippocampus 3D shape dataset; and 3) a pediatric airway 3D shape dataset. Our experiments demonstrate that Starman achieves excellent shape reconstruction performance while retaining interpretability. Our code is available at https://github.com/uncbiag/NAISR{https://github.com/uncbiag/NAISR}.

Computer-aided design (CAD) is the backbone of modern industrial design, yet learned CAD generators still fall short of real engineering pipelines: they neither iterate like engineers nor evaluate what engineering requires. Prior work has treated CAD generation as two disjoint steps, part synthesis and assembly, where the former is graded by proximity to a gold reference and the latter, when handled at all, is reduced to a separate constraint solving step. In this work, we introduce a more industry-native task formulation that requires a model to produce a fully assembled multi-part STEP file from a free-form engineering brief, which is then validated via finite element analysis (FEA). FEA validation reveals that Codex (GPT-5.5) and Claude Code (Opus-4.7) agents do not produce a single strict-passing artifact in the main first-attempt sweep, with the best configuration meeting only about 20% of typed requirements on average. Moreover, we introduce two additional supervision signals, a novel text-only blueprint schema and a 21-view image renderer that aids the agent's visual inspection, that better align the generation loop with how engineers iterate in practice. On S2O and Fusion360, the same feedback tools improve geometric reconstruction, with GPT-5.5/xhigh rising from 0.444 to 0.592 Box-IoU on S2O and from 0.397 to 0.505 on Fusion360. Together these signals move CAD programs toward artifacts that are not only visually plausible but also checked against physical and structural requirements.

Reconstructing articulated objects with multiple movable parts is essential for understanding object structure and enabling physical interaction. However, this reconstruction task poses significant challenges due to the entanglement of geometry, appearance, and motion parameters during optimization. Existing methods rely primarily on photometric supervision, which commonly fails to disentangle these interdependent components, resulting in poor part decomposition with blurred boundaries and geometric artifacts. To address this limitation, we introduce StructureGS, a reconstruction framework for articulated objects that integrates structure-aware guidance into 3D Gaussian Splatting. Our approach leverages oriented bounding boxes of object parts to enforce two key structural properties: spatial coherence, which constrains each part's geometry to remain compact and spatially coherent within its designated region, and structural connectivity, which enforces physically plausible contact relationships between adjacent parts. These properties are realized through structure-aware losses that inject explicit structural constraints into the optimization process. Extensive experiments demonstrate that our method achieves state-of-the-art performance in articulated object reconstruction, producing high-quality results with well-defined part geometries.

We introduce a new generative model that combines latent diffusion with persistent homology to create 3D shapes with high diversity, with a special emphasis on their topological characteristics. Our method involves representing 3D shapes as implicit fields, then employing persistent homology to extract topological features, including Betti numbers and persistence diagrams. The shape generation process consists of two steps. Initially, we employ a transformer-based autoencoding module to embed the implicit representation of each 3D shape into a set of latent vectors. Subsequently, we navigate through the learned latent space via a diffusion model. By strategically incorporating topological features into the diffusion process, our generative module is able to produce a richer variety of 3D shapes with different topological structures. Furthermore, our framework is flexible, supporting generation tasks constrained by a variety of inputs, including sparse and partial point clouds, as well as sketches. By modifying the persistence diagrams, we can alter the topology of the shapes generated from these input modalities.

Human perception of 3D shapes goes beyond reconstructing them as a set of points or a composition of geometric primitives: we also effortlessly understand higher-level shape structure such as the repetition and reflective symmetry of object parts. In contrast, recent advances in 3D shape sensing focus more on low-level geometry but less on these higher-level relationships. In this paper, we propose 3D shape programs, integrating bottom-up recognition systems with top-down, symbolic program structure to capture both low-level geometry and high-level structural priors for 3D shapes. Because there are no annotations of shape programs for real shapes, we develop neural modules that not only learn to infer 3D shape programs from raw, unannotated shapes, but also to execute these programs for shape reconstruction. After initial bootstrapping, our end-to-end differentiable model learns 3D shape programs by reconstructing shapes in a self-supervised manner. Experiments demonstrate that our model accurately infers and executes 3D shape programs for highly complex shapes from various categories. It can also be integrated with an image-to-shape module to infer 3D shape programs directly from an RGB image, leading to 3D shape reconstructions that are both more accurate and more physically plausible.

Current 3D generative models mostly produce a final surface: a visually strong but largely opaque mesh. Interactive 3D worlds need more than a surface. They need named parts, an assembly hierarchy, measurable constraints, local edit handles, and joints for articulation. We present Nova3D, a system that generates 3D assets as executable Blender source code; the compiled mesh, a binary glTF (GLB), is treated as the artifact, not the asset. Because the output is a program, semantic handles exist at generation time rather than being recovered afterward by segmentation or rigging. We evaluate on Nova3D-Bench, a frozen, spec-grounded benchmark of 54 items across six domains and three difficulty levels with text and image inputs, against eleven baselines in four families (mesh-native, part-structured, code-native, and CAD) plus a same-LLM ablation. Nova3D produces an executable program and a valid artifact for 54/54 items. Every asset exposes named parts organized in a parent-child assembly tree; no mesh-native, CAD, or segmentation baseline exposes either. It satisfies 51/52 prompt-stated numeric and count constraints (best baseline: 11/52), passes 14/18 blinded local edits with locality preserved in 18/18, and articulates 59 joints across 12 assets at 98.3% geometric validity, where every baseline exposes zero native joints. Its geometry is competitive: it wins the structured domains in a pairwise shape-quality tournament and is second only to the strongest mesh-native model, while conceding texture realism to baked-PBR systems. The central result is representational: code-native generation turns a generated 3D object from an opaque surface into a programmable asset that downstream systems can inspect, measure, edit, and animate.

3D creation has always been a unique human strength, driven by our ability to deconstruct and reassemble objects using our eyes, mind and hand. However, current 3D design tools struggle to replicate this natural process, requiring considerable artistic expertise and manual labor. This paper introduces BANG, a novel generative approach that bridges 3D generation and reasoning, allowing for intuitive and flexible part-level decomposition of 3D objects. At the heart of BANG is "Generative Exploded Dynamics", which creates a smooth sequence of exploded states for an input geometry, progressively separating parts while preserving their geometric and semantic coherence. BANG utilizes a pre-trained large-scale latent diffusion model, fine-tuned for exploded dynamics with a lightweight exploded view adapter, allowing precise control over the decomposition process. It also incorporates a temporal attention module to ensure smooth transitions and consistency across time. BANG enhances control with spatial prompts, such as bounding boxes and surface regions, enabling users to specify which parts to decompose and how. This interaction can be extended with multimodal models like GPT-4, enabling 2D-to-3D manipulations for more intuitive and creative workflows. The capabilities of BANG extend to generating detailed part-level geometry, associating parts with functional descriptions, and facilitating component-aware 3D creation and manufacturing workflows. Additionally, BANG offers applications in 3D printing, where separable parts are generated for easy printing and reassembly. In essence, BANG enables seamless transformation from imaginative concepts to detailed 3D assets, offering a new perspective on creation that resonates with human intuition.

Recognizing specific objects onboarded without a labeled training set recurs across manufacturing and service robotics, yet the conventional renderable prior, a computer-aided-design (CAD) model, is often unavailable. Two-dimensional capture supplies no shape prior, and frozen foundation features fail on geometrically similar, low-texture industrial parts. We ask what a short object-centric scan buys for recognition beyond the captured images themselves: each object is reconstructed with 3D Gaussian Splatting (3DGS), summarized into a per-class shape prototype, and fused with frozen DINOv2 image features. First, the scan recovers the recognition value of CAD without CAD: geometry from RGB-D depth (on T-LESS), 3DGS, and CAD gives comparable recognition (tied on HOPE, within 1.6 points on T-LESS); 3DGS is only a convenient route to a point cloud. Second, the payoff is governed by how recognizable the shape is: on shape-distinctive household objects (HOPE) geometry alone reaches 0.920 versus image-only 0.832, a ceiling below which fixed-weight fusion (0.872) sits. On shape-confusable textureless industrial parts (T-LESS) the gain is modest but consistent (0.560 to 0.591 fused, above both single signals). Third, the prior is complementary, not uniformly additive: it rescues far more image failures than it breaks successes, and its benefit grows under partial occlusion. Finally, the worth lies in geometry, not rendered pixels: 3DGS renderings do not help the image side, and frozen-feature recognition is nearly lighting-invariant (within 2.5 points). The study is scoped to recognition, not the BOP pose benchmark.

Inspired by generative paradigms in image and video, 3D shape generation has made notable progress, enabling the rapid synthesis of high-fidelity 3D assets from a single image. However, current methods still face challenges, including the lack of intricate details, overly smoothed surfaces, and fragmented thin-shell structures. These limitations leave the generated 3D assets still one step short of meeting the standards favored by artists. In this paper, we present ShapeGen, which achieves high-quality image-to-3D shape generation through 3D representation and supervision improvements, resolution scaling up, and the advantages of linear transformers. These advancements allow the generated assets to be seamlessly integrated into 3D pipelines, facilitating their widespread adoption across various applications. Through extensive experiments, we validate the impact of these improvements on overall performance. Ultimately, thanks to the synergistic effects of these enhancements, ShapeGen achieves a significant leap in image-to-3D generation, establishing a new state-of-the-art performance.

The ability to design a tool for a task marks a level of intelligence beyond merely understanding, selecting, or using one. Existing methods for robotic tool design typically optimize a tool's continuous shape and action within a structure that is prescribed or generated beforehand, so the structure itself stays outside the physical optimization loop. We study task-driven tool design from scratch, where tool structure, shape, and action are all derived from the desired physical outcome. Here we show that the three elements can be designed jointly by HOT, a hierarchical optimization whose upper level searches over discrete tool structures with BASS, while lower-level physical optimization evaluates their task behavior and returns milestone progress as behavioral evidence for the search, ultimately providing jointly optimized shape and action. On four tool-use tasks with distinct physical functions, HOT discovers functional structures after evaluating only a small fraction of search spaces containing up to 56 million structures, and the subsequent refinement of their geometry lowers the task loss on all tasks while preserving success, through deformations that are functionally interpretable. Once 3D printed, the tools accomplish all tasks on a real robot with the actions found in simulation. Designing tools from required physical effects, rather than a catalog of known tools, is a step toward the open-ended tool making seen in humans and animals.

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on shape primitives defined recursively. Bottom-up techniques for this shape parsing task rely on primitive detection and are inherently slow since the search space over possible primitive combinations is large. In contrast, our model uses a recurrent neural network that parses the input shape in a top-down manner, which is significantly faster and yields a compact and easy-to-interpret sequence of modeling instructions. Our model is also more effective as a shape detector compared to existing state-of-the-art detection techniques. We finally demonstrate that our network can be trained on novel datasets without ground-truth program annotations through policy gradient techniques.

Current diffusion or flow-based generative models for 3D shapes divide to two: distilling pre-trained 2D image diffusion models, and training directly on 3D shapes. When training a diffusion or flow models on 3D shapes a crucial design choice is the shape representation. An effective shape representation needs to adhere three design principles: it should allow an efficient conversion of large 3D datasets to the representation form; it should provide a good tradeoff of approximation power versus number of parameters; and it should have a simple tensorial form that is compatible with existing powerful neural architectures. While standard 3D shape representations such as volumetric grids and point clouds do not adhere to all these principles simultaneously, we advocate in this paper a new representation that does. We introduce Mosaic-SDF (M-SDF): a simple 3D shape representation that approximates the Signed Distance Function (SDF) of a given shape by using a set of local grids spread near the shape's boundary. The M-SDF representation is fast to compute for each shape individually making it readily parallelizable; it is parameter efficient as it only covers the space around the shape's boundary; and it has a simple matrix form, compatible with Transformer-based architectures. We demonstrate the efficacy of the M-SDF representation by using it to train a 3D generative flow model including class-conditioned generation with the 3D Warehouse dataset, and text-to-3D generation using a dataset of about 600k caption-shape pairs.

We introduce ShapeWords, an approach for synthesizing images based on 3D shape guidance and text prompts. ShapeWords incorporates target 3D shape information within specialized tokens embedded together with the input text, effectively blending 3D shape awareness with textual context to guide the image synthesis process. Unlike conventional shape guidance methods that rely on depth maps restricted to fixed viewpoints and often overlook full 3D structure or textual context, ShapeWords generates diverse yet consistent images that reflect both the target shape's geometry and the textual description. Experimental results show that ShapeWords produces images that are more text-compliant, aesthetically plausible, while also maintaining 3D shape awareness.

Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are largely restricted to difficult-to-edit formats like meshes or Breps or editable simple sketch-and-extrude pipelines and low-complexity datasets. We introduce CADFit, a hybrid optimization-based CAD reconstruction framework that recovers complex, editable CAD construction sequences from meshes by incrementally fitting and validating parametric operations using geometric feedback. Our approach is distinguished by formulating reconstruction as an IoU-driven optimization over structured CAD programs and supporting a rich set of operations, including extrusions, revolutions, fillets, and chamfers. Experiments on multiple CAD benchmarks show that CADFit outperforms state-of-the-art mesh-to-CAD methods in volumetric Intersection-over-Union and Chamfer Distance, while substantially reducing the Invalid Ratio of reconstructed CAD programs, particularly for complex designs. We further present a multimodal pipeline that enables end-to-end reconstruction of CAD construction sequences from images by combining image-based geometry reconstruction with CADFit. By enabling accurate reconstruction of higher-complexity CAD models, CADFit provides a practical foundation for generating richer datasets and advancing future learning-based approaches to CAD reverse engineering. The code is available at: https://github.com/ghadinehme/CADFit.

A hallmark of human dexterity is the cooperative use of fingers, where different fingers take on distinct yet coordinated roles to accomplish fine manipu- lation, such as capping a pen with the hand that holds it. We study this finger-level coordination through in-hand assembly: mating two rigid objects within a single dexterous hand, with no second arm and no fixture. We present a reinforcement learning formulation to solve this problem in a unified framework, which is driven by a goal relative pose between the two parts. Finger coordination is shaped by a function-based auxiliary reward and regularized toward a single human reference pose, while domain randomization and a fusion of historical proprioception and object observation confer robustness to occlusion-induced estimation noise. The same recipe solves three different assembly tasks (Bottle, Syringe, and Marker). Trained purely in simulation, the policies transfer zero-shot to hardware with a single camera, demonstrating robustness to state-estimation errors caused by oc- clusion. Our experiments also reveal that in-hand assembly places demands on hand morphology and can serve as a benchmark for modern robotic hand systems. Videos and code are available at https://ltbgbird.github.io/in-hand-assembly-page/.

Recent years have seen an explosion of work and interest in text-to-3D shape generation. Much of the progress is driven by advances in 3D representations, large-scale pretraining and representation learning for text and image data enabling generative AI models, and differentiable rendering. Computational systems that can perform text-to-3D shape generation have captivated the popular imagination as they enable non-expert users to easily create 3D content directly from text. However, there are still many limitations and challenges remaining in this problem space. In this state-of-the-art report, we provide a survey of the underlying technology and methods enabling text-to-3D shape generation to summarize the background literature. We then derive a systematic categorization of recent work on text-to-3D shape generation based on the type of supervision data required. Finally, we discuss limitations of the existing categories of methods, and delineate promising directions for future work.

Recently, Large Language Models (LLMs) have achieved significant success, prompting increased interest in expanding their generative capabilities beyond general text into domain-specific areas. This study investigates the generation of parametric sequences for computer-aided design (CAD) models using LLMs. This endeavor represents an initial step towards creating parametric 3D shapes with LLMs, as CAD model parameters directly correlate with shapes in three-dimensional space. Despite the formidable generative capacities of LLMs, this task remains challenging, as these models neither encounter parametric sequences during their pretraining phase nor possess direct awareness of 3D structures. To address this, we present CAD-Llama, a framework designed to enhance pretrained LLMs for generating parametric 3D CAD models. Specifically, we develop a hierarchical annotation pipeline and a code-like format to translate parametric 3D CAD command sequences into Structured Parametric CAD Code (SPCC), incorporating hierarchical semantic descriptions. Furthermore, we propose an adaptive pretraining approach utilizing SPCC, followed by an instruction tuning process aligned with CAD-specific guidelines. This methodology aims to equip LLMs with the spatial knowledge inherent in parametric sequences. Experimental results demonstrate that our framework significantly outperforms prior autoregressive methods and existing LLM baselines.

Significant progress has been made in training large generative models for natural language and images. Yet, the advancement of 3D generative models is hindered by their substantial resource demands for training, along with inefficient, non-compact, and less expressive representations. This paper introduces Make-A-Shape, a new 3D generative model designed for efficient training on a vast scale, capable of utilizing 10 millions publicly-available shapes. Technical-wise, we first innovate a wavelet-tree representation to compactly encode shapes by formulating the subband coefficient filtering scheme to efficiently exploit coefficient relations. We then make the representation generatable by a diffusion model by devising the subband coefficients packing scheme to layout the representation in a low-resolution grid. Further, we derive the subband adaptive training strategy to train our model to effectively learn to generate coarse and detail wavelet coefficients. Last, we extend our framework to be controlled by additional input conditions to enable it to generate shapes from assorted modalities, e.g., single/multi-view images, point clouds, and low-resolution voxels. In our extensive set of experiments, we demonstrate various applications, such as unconditional generation, shape completion, and conditional generation on a wide range of modalities. Our approach not only surpasses the state of the art in delivering high-quality results but also efficiently generates shapes within a few seconds, often achieving this in just 2 seconds for most conditions.

We address semantic 3D part segmentation: decomposing objects into parts with meaningful names. While datasets exist with part annotations, their definitions are inconsistent across datasets, limiting robust training. Previous methods produce unlabeled decompositions or retrieve single parts without complete shape annotations. We propose ALIGN-Parts, which formulates part naming as a direct set alignment task. Our method decomposes shapes into partlets - implicit 3D part representations - matched to part descriptions via bipartite assignment. We combine geometric cues from 3D part fields, appearance from multi-view vision features, and semantic knowledge from language-model-generated affordance descriptions. Text-alignment loss ensures partlets share embedding space with text, enabling a theoretically open-vocabulary matching setup, given sufficient data. Our efficient and novel, one-shot, 3D part segmentation and naming method finds applications in several downstream tasks, including serving as a scalable annotation engine. As our model supports zero-shot matching to arbitrary descriptions and confidence-calibrated predictions for known categories, with human verification, we create a unified ontology that aligns PartNet, 3DCoMPaT++, and Find3D, consisting of 1,794 unique 3D parts. We also show examples from our newly created Tex-Parts dataset. We also introduce 2 novel metrics appropriate for the named 3D part segmentation task.

Current 3D generation methods lack explicit local control: geometric adherence is often defined by a global control strength, and appearance cannot be specified locally. We present SpaceFlow, a training-free pipeline for locally controllable 3D generation from text descriptions and a collection of geometric primitives. Each primitive serves as a proxy for an object part and is assigned a local control level, enabling users to specify whether regions should strictly follow the input shape or allow generative completion. During structure generation, we enforce these spatial constraints within the generative flow process. For appearance synthesis, the generated structure is segmented and matched to the primitives. Each generated part is conditioned only on its assigned text or image cue, thereby limiting cross-part leakage. Regional geometry metrics demonstrate that SpaceFlow preserves the specified geometry in high-control regions and enables plausible shape variation in low-control areas. A user study further indicates that the resulting balance between geometric fidelity and generative freedom remains competitive in overall quality. When evaluating appearance on fixed geometry, text-conditioned routing achieves state-of-the-art prompt faithfulness and color/material accuracy. Qualitative results additionally show localized routing of image cues. The project page is available at SpaceFlow3D.github.io.

Autonomous wire harness assembly requires robots to manipulate complex branched cables with high precision and reliability. A key challenge in automating this process is predicting how these flexible and branched structures behave under manipulation. Without accurate predictions, it is difficult for robots to reliably plan or execute assembly operations. While existing research has made progress in modeling single-threaded Deformable Linear Objects (DLOs), extending these approaches to Branched Deformable Linear Objects (BDLOs) presents fundamental challenges. The junction points in BDLOs create complex force interactions and strain propagation patterns that cannot be adequately captured by simply connecting multiple single-DLO models. To address these challenges, this paper presents Differentiable discrete branched Elastic rods for modeling Furcated DLOs in real-Time (DEFT), a novel framework that combines a differentiable physics-based model with a learning framework to: 1) accurately model BDLO dynamics, including dynamic propagation at junction points and grasping in the middle of a BDLO, 2) achieve efficient computation for real-time inference, and 3) enable planning to demonstrate dexterous BDLO manipulation. A comprehensive series of real-world experiments demonstrates DEFT's efficacy in terms of accuracy, computational speed, and generalizability compared to state-of-the-art alternatives. Project page:https://roahmlab.github.io/DEFT/.

Deep generative models of 3D shapes have received a great deal of research interest. Yet, almost all of them generate discrete shape representations, such as voxels, point clouds, and polygon meshes. We present the first 3D generative model for a drastically different shape representation --- describing a shape as a sequence of computer-aided design (CAD) operations. Unlike meshes and point clouds, CAD models encode the user creation process of 3D shapes, widely used in numerous industrial and engineering design tasks. However, the sequential and irregular structure of CAD operations poses significant challenges for existing 3D generative models. Drawing an analogy between CAD operations and natural language, we propose a CAD generative network based on the Transformer. We demonstrate the performance of our model for both shape autoencoding and random shape generation. To train our network, we create a new CAD dataset consisting of 178,238 models and their CAD construction sequences. We have made this dataset publicly available to promote future research on this topic.

Building AI systems that can plan, act, and create in the physical world requires more than pattern recognition. Such systems must understand the causal mechanisms and constraints governing physical processes in order to guide sequential decisions. This capability relies on internal representations, analogous to an internal language model, that relate observations, actions, and resulting environmental changes. However, many existing benchmarks treat visual perception and programmatic reasoning as separate problems, focusing either on visual recognition or on symbolic tasks. The domain of origami provides a natural testbed that integrates these modalities. Constructing shapes through folding operations requires visual perception, reasoning about geometric and physical constraints, and sequential planning, while remaining sufficiently structured for systematic evaluation. We introduce OrigamiBench, an interactive benchmark in which models iteratively propose folds and receive feedback on physical validity and similarity to a target configuration. Experiments with modern vision-language models show that scaling model size alone does not reliably produce causal reasoning about physical transformations. Models fail to generate coherent multi-step folding strategies, suggesting that visual and language representations remain weakly integrated.

Recent advances in synthetic methods enable designing subunits that self-assemble into structures with well-defined sizes and architectures, but yields are frequently suppressed by the formation of off-target metastable structures. Increasing the complexity (number of distinct inter-subunit interaction types) can inhibit off-target structures, but leads to slower kinetics and higher synthesis costs. Here, we use icosahedral shells formed of programmable triangular subunits as a model system, and identify design principles that produce the highest target yield at the lowest complexity. We use a symmetry-based construction to create a range of design complexities, starting from the maximal symmetry Caspar-Klug assembly up to the fully addressable, zero-symmetry assembly. Kinetic Monte Carlo simulations reveal that the most prominent defects leading to off-target assemblies are a class of disclinations. We derive symmetry-based rules for identifying the optimal (lowest-complexity, highest-symmetry) design that inhibits these disclinations, leading to robust, high-fidelity assembly of targets with arbitrarily large sizes. Optimal complexity varies non-monotonically with target size, with `magic' sizes appearing for high-symmetry designs in which symmetry axes do not intersect vertices of the triangular net. The optimal designs at magic sizes require 12 times fewer inequivalent interaction-types than the (minimal symmetry) fully addressable construction.

Computer-Aided Design (CAD) is a foundational component of industrial prototyping, where models are defined not by raw coordinates but by construction sequences such as sketches and extrusions. This sequential structure enables both efficient prototype initialization and subsequent editing. Text-guided CAD prototyping, which unifies Text-to-CAD generation and CAD editing, has the potential to streamline the entire design pipeline. However, prior work has not explored this setting, largely because standard large language model (LLM) tokenizers decompose CAD sequences into natural-language word pieces, failing to capture primitive-level CAD semantics and hindering attention modules from modeling geometric structure. We conjecture that a multimodal tokenization strategy, aligned with CAD's primitive and structural nature, can provide more effective representations. To this end, we propose CAD-Tokenizer, a framework that represents CAD data with modality-specific tokens using a sequence-based VQ-VAE with primitive-level pooling and constrained decoding. This design produces compact, primitive-aware representations that align with CAD's structural nature. Applied to unified text-guided CAD prototyping, CAD-Tokenizer significantly improves instruction following and generation quality, achieving better quantitative and qualitative performance over both general-purpose LLMs and task-specific baselines.

Articulated object recognition -- the task of identifying both the geometry and kinematic joints of objects with movable parts -- is essential for enabling robots to interact with everyday objects such as doors and laptops. However, existing approaches often rely on strong assumptions, such as a known number of articulated parts; require additional inputs, such as depth images; or involve complex intermediate steps that can introduce potential errors -- limiting their practicality in real-world settings. In this paper, we introduce ScrewSplat, a simple end-to-end method that operates solely on RGB observations. Our approach begins by randomly initializing screw axes, which are then iteratively optimized to recover the object's underlying kinematic structure. By integrating with Gaussian Splatting, we simultaneously reconstruct the 3D geometry and segment the object into rigid, movable parts. We demonstrate that our method achieves state-of-the-art recognition accuracy across a diverse set of articulated objects, and further enables zero-shot, text-guided manipulation using the recovered kinematic model. See the project website at: https://screwsplat.github.io.

Text-to-3D synthesis has recently seen intriguing advances by combining the text-to-image models with 3D representation methods, e.g., Gaussian Splatting (GS), via Score Distillation Sampling (SDS). However, a hurdle of existing methods is the low efficiency, per-prompt optimization for a single 3D object. Therefore, it is imperative for a paradigm shift from per-prompt optimization to one-stage generation for any unseen text prompts, which yet remains challenging. A hurdle is how to directly generate a set of millions of 3D Gaussians to represent a 3D object. This paper presents BrightDreamer, an end-to-end single-stage approach that can achieve generalizable and fast (77 ms) text-to-3D generation. Our key idea is to formulate the generation process as estimating the 3D deformation from an anchor shape with predefined positions. For this, we first propose a Text-guided Shape Deformation (TSD) network to predict the deformed shape and its new positions, used as the centers (one attribute) of 3D Gaussians. To estimate the other four attributes (i.e., scaling, rotation, opacity, and SH coefficient), we then design a novel Text-guided Triplane Generator (TTG) to generate a triplane representation for a 3D object. The center of each Gaussian enables us to transform the triplane feature into the four attributes. The generated 3D Gaussians can be finally rendered at 705 frames per second. Extensive experiments demonstrate the superiority of our method over existing methods. Also, BrightDreamer possesses a strong semantic understanding capability even for complex text prompts. The project code is available at https://vlislab22.github.io/BrightDreamer.

We introduce a new method of generating Computer Aided Design (CAD) profiles via a sequence of simple geometric constructions including curve offsetting, rotations and intersections. These sequences start with geometry provided by a designer and build up the points and curves of the final profile step by step. We demonstrate that adding construction steps between the designer's input geometry and the final profile improves generation quality in a similar way to the introduction of a chain of thought in language models. Similar to the constraints in a parametric CAD model, the construction sequences reduce the degrees of freedom in the modeled shape to a small set of parameter values which can be adjusted by the designer, allowing parametric editing with the constructed geometry evaluated to floating point precision. In addition we show that applying reinforcement learning to the construction sequences gives further improvements over a wide range of metrics, including some which were not explicitly optimized.

Multimodal alignment facilitates the retrieval of instances from one modality when queried using another. In this paper, we consider a novel setting where such an alignment is between (i) instruction steps that are depicted as assembly diagrams (commonly seen in Ikea assembly manuals) and (ii) video segments from in-the-wild videos; these videos comprising an enactment of the assembly actions in the real world. To learn this alignment, we introduce a novel supervised contrastive learning method that learns to align videos with the subtle details in the assembly diagrams, guided by a set of novel losses. To study this problem and demonstrate the effectiveness of our method, we introduce a novel dataset: IAW for Ikea assembly in the wild consisting of 183 hours of videos from diverse furniture assembly collections and nearly 8,300 illustrations from their associated instruction manuals and annotated for their ground truth alignments. We define two tasks on this dataset: First, nearest neighbor retrieval between video segments and illustrations, and, second, alignment of instruction steps and the segments for each video. Extensive experiments on IAW demonstrate superior performances of our approach against alternatives.

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. This morphing is obtained by deforming a reference shape, through the resolution of a sequence of linear elasticity equations, onto the target shape. In particular, our approach does not assume any knowledge of a boundary parametrization. Furthermore, we demonstrate how constraints can be imposed on specific points, lines and surfaces in the reference domain to ensure alignment with their counterparts in the target domain after morphing. Additionally, we show how the proposed methodology can be integrated in an offline and online paradigm, which is useful in reduced-order modeling scenarii involving variable shapes. This framework facilitates the efficient computation of the morphings in various geometric configurations, thus improving the versatility and applicability of the approach. The methodology is illustrated on the regression problem of the drag and lift coefficients of airfoils of non-parameterized variable shapes.

Existing methods for text-to-CAD generation either operate in a single pass with no geometric verification or rely on lossy visual feedback that cannot resolve dimensional errors. We present CADSmith, a multi-agent pipeline that generates CadQuery code from natural language. It then undergoes an iterative refinement process through two nested correction loops: an inner loop that resolves execution errors and an outer loop grounded in programmatic geometric validation. The outer loop combines exact measurements from the OpenCASCADE kernel (bounding box dimensions, volume, solid validity) with holistic visual assessment from an independent vision-language model Judge. This provides both the numerical precision and the high-level shape awareness needed to converge on the correct geometry. The system uses retrieval-augmented generation over API documentation rather than fine-tuning, maintaining a current database as the underlying CAD library evolves. We evaluate on a custom benchmark of 100 prompts in three difficulty tiers (T1 through T3) with three ablation configurations. Against a zero-shot baseline, CADSmith achieves a 100% execution rate (up from 95%), improves the median F1 score from 0.9707 to 0.9846, the median IoU from 0.8085 to 0.9629, and reduces the mean Chamfer Distance from 28.37 to 0.74, demonstrating that closed-loop refinement with programmatic geometric feedback substantially improves the quality and reliability of LLM-generated CAD models.

In this work we target a learnable output representation that allows continuous, high resolution outputs of arbitrary shape. Recent works represent 3D surfaces implicitly with a Neural Network, thereby breaking previous barriers in resolution, and ability to represent diverse topologies. However, neural implicit representations are limited to closed surfaces, which divide the space into inside and outside. Many real world objects such as walls of a scene scanned by a sensor, clothing, or a car with inner structures are not closed. This constitutes a significant barrier, in terms of data pre-processing (objects need to be artificially closed creating artifacts), and the ability to output open surfaces. In this work, we propose Neural Distance Fields (NDF), a neural network based model which predicts the unsigned distance field for arbitrary 3D shapes given sparse point clouds. NDF represent surfaces at high resolutions as prior implicit models, but do not require closed surface data, and significantly broaden the class of representable shapes in the output. NDF allow to extract the surface as very dense point clouds and as meshes. We also show that NDF allow for surface normal calculation and can be rendered using a slight modification of sphere tracing. We find NDF can be used for multi-target regression (multiple outputs for one input) with techniques that have been exclusively used for rendering in graphics. Experiments on ShapeNet show that NDF, while simple, is the state-of-the art, and allows to reconstruct shapes with inner structures, such as the chairs inside a bus. Notably, we show that NDF are not restricted to 3D shapes, and can approximate more general open surfaces such as curves, manifolds, and functions. Code is available for research at https://virtualhumans.mpi-inf.mpg.de/ndf/.

We propose Segment Any Mesh, a novel zero-shot mesh part segmentation method that overcomes the limitations of shape analysis-based, learning-based, and contemporary approaches. Our approach operates in two phases: multimodal rendering and 2D-to-3D lifting. In the first phase, multiview renders of the mesh are individually processed through Segment Anything to generate 2D masks. These masks are then lifted into a mesh part segmentation by associating masks that refer to the same mesh part across the multiview renders. We find that applying Segment Anything to multimodal feature renders of normals and shape diameter scalars achieves better results than using only untextured renders of meshes. By building our method on top of Segment Anything, we seamlessly inherit any future improvements made to 2D segmentation. We compare our method with a robust, well-evaluated shape analysis method, Shape Diameter Function, and show that our method is comparable to or exceeds its performance. Since current benchmarks contain limited object diversity, we also curate and release a dataset of generated meshes and use it to demonstrate our method's improved generalization over Shape Diameter Function via human evaluation. We release the code and dataset at https://github.com/gtangg12/samesh

We propose a remeshing-enhanced method for generatively deforming shapes with visual losses. It is intuitive that sufficiently drastic deformations of a mesh without changing its triangulation can easily compromise element quality, even if such large geometry changes may be semantically desired. Shape deformation methods could thus benefit from changing the triangulation; however, this is not done by most generative, text-based, visually-supervised mesh deformation methods. Remeshing is a discrete operation, proven to be especially challenging to couple with the notoriously noisy supervision signal provided by visual losses. We propose a vertex-based deformation optimization quantity capable of large deformations and robustness to such noise; we periodically remesh using an isotropic remesher that interpolates and carries forward the deformation optimization state. This enables continuous, geometry-informed progress in coarse-to-fine addition of resolution. The resulting shapes' triangulations fit their optimized geometry and have neat isotropic elements. Further, our method is localizable, able to grow new features on a base shape with expressive detail, leaving the rest unchanged. We showcase the effectiveness of our method on a variety of shapes and prompts, both local and global deformations, and demonstrate its superior visual quality and triangle efficiency. Our project page is at https://threedle.github.io/radmesh.

This paper introduces GenCorres, a novel unsupervised joint shape matching (JSM) approach. Our key idea is to learn a mesh generator to fit an unorganized deformable shape collection while constraining deformations between adjacent synthetic shapes to preserve geometric structures such as local rigidity and local conformality. GenCorres presents three appealing advantages over existing JSM techniques. First, GenCorres performs JSM among a synthetic shape collection whose size is much bigger than the input shapes and fully leverages the datadriven power of JSM. Second, GenCorres unifies consistent shape matching and pairwise matching (i.e., by enforcing deformation priors between adjacent synthetic shapes). Third, the generator provides a concise encoding of consistent shape correspondences. However, learning a mesh generator from an unorganized shape collection is challenging, requiring a good initialization. GenCorres addresses this issue by learning an implicit generator from the input shapes, which provides intermediate shapes between two arbitrary shapes. We introduce a novel approach for computing correspondences between adjacent implicit surfaces, which we use to regularize the implicit generator. Synthetic shapes of the implicit generator then guide initial fittings (i.e., via template-based deformation) for learning the mesh generator. Experimental results show that GenCorres considerably outperforms state-of-the-art JSM techniques. The synthetic shapes of GenCorres also achieve salient performance gains against state-of-the-art deformable shape generators.

In this work, we present a novel framework built to simplify 3D asset generation for amateur users. To enable interactive generation, our method supports a variety of input modalities that can be easily provided by a human, including images, text, partially observed shapes and combinations of these, further allowing to adjust the strength of each input. At the core of our approach is an encoder-decoder, compressing 3D shapes into a compact latent representation, upon which a diffusion model is learned. To enable a variety of multi-modal inputs, we employ task-specific encoders with dropout followed by a cross-attention mechanism. Due to its flexibility, our model naturally supports a variety of tasks, outperforming prior works on shape completion, image-based 3D reconstruction, and text-to-3D. Most interestingly, our model can combine all these tasks into one swiss-army-knife tool, enabling the user to perform shape generation using incomplete shapes, images, and textual descriptions at the same time, providing the relative weights for each input and facilitating interactivity. Despite our approach being shape-only, we further show an efficient method to texture the generated shape using large-scale text-to-image models.

In this paper, we present a practical approach to improve anatomical shape accuracy in whole-body medical segmentation. Our analysis shows that a shape-focused toolkit can enhance segmentation performance by over 8%, without the need for model re-training or fine-tuning. In comparison, modifications to model architecture typically lead to marginal gains of less than 3%. Motivated by this observation, we introduce ShapeKit, a flexible and easy-to-integrate toolkit designed to refine anatomical shapes. This work highlights the underappreciated value of shape-based tools and calls attention to their potential impact within the medical segmentation community.

Existing text-based 3D generation methods generate attractive results but lack detailed geometry control. Sketches, known for their conciseness and expressiveness, have contributed to intuitive 3D modeling but are confined to producing texture-less mesh models within predefined categories. Integrating sketch and text simultaneously for 3D generation promises enhanced control over geometry and appearance but faces challenges from 2D-to-3D translation ambiguity and multi-modal condition integration. Moreover, further editing of 3D models in arbitrary views will give users more freedom to customize their models. However, it is difficult to achieve high generation quality, preserve unedited regions, and manage proper interactions between shape components. To solve the above issues, we propose a text-driven 3D content generation and editing method, SketchDream, which supports NeRF generation from given hand-drawn sketches and achieves free-view sketch-based local editing. To tackle the 2D-to-3D ambiguity challenge, we introduce a sketch-based multi-view image generation diffusion model, which leverages depth guidance to establish spatial correspondence. A 3D ControlNet with a 3D attention module is utilized to control multi-view images and ensure their 3D consistency. To support local editing, we further propose a coarse-to-fine editing approach: the coarse phase analyzes component interactions and provides 3D masks to label edited regions, while the fine stage generates realistic results with refined details by local enhancement. Extensive experiments validate that our method generates higher-quality results compared with a combination of 2D ControlNet and image-to-3D generation techniques and achieves detailed control compared with existing diffusion-based 3D editing approaches.

Interactive 3D assets used in games and simulation are typically decomposed into specific semantic parts to support animation, physics, and scripted behaviors, yet most generative 3D models produce either monolithic meshes or arbitrary part decompositions that cannot be aligned with application-specific requirements. We present CubePart, a generative framework for open-vocabulary, part-controllable 3D mesh generation that exposes part structure as an explicit inference-time control signal. Given a global text prompt and a user-defined parts schema expressed as an open-ended list of part names, our method generates a set of meshes - one per schema element - that assemble into a coherent object while respecting the specified semantic structure. To enable this capability, we introduce a scalable data pipeline to construct a large open-vocabulary, part-labeled 3D dataset, along with a two-stage generative architecture that separates global shape synthesis from part-level decoding. We demonstrate that the resulting assets can be directly integrated into game engines and driven by animation and behavior scripts without manual post-processing. Project Page: https://cubepart.github.io/

Programmatic representations provide a compelling paradigm for 3D content creation, enabling fine-grained edits, interpretability, and explicit structural control. Yet, agentic workflows that rely on large language models (LLMs) to author 3D programs remain brittle, often failing to translate high-level intent into consistent low-level geometry. We attribute this fragility to a mismatch between existing programmatic interfaces and the reasoning strengths of LLMs, which favor semantic structure and spatial relations over fragile numeric choices. In this paper, we jointly design an Agent-centric Domain-Specific Language (aDSL) and a role-specialized multi-agent system to close this gap. aDSL bridges semantic logic and geometric constraints by emphasizing composability and spatial reasoning; it enables agents to manipulate geometry through relational operators instead of brittle absolute coordinates. Building on aDSL, our training-free multi-agent system follows a Plan-Execute-Critic loop to decompose requests, synthesize code, and iteratively repair errors and constraint violations using execution feedback. Experiments show that this co-design improves robustness, controllability, and faithfulness to user intent. Our method outperforms prior LLM-based baselines on text-to-shape and image-to-shape tasks while preserving explicit structure, editability, and interpretability. It also enables downstream applications such as articulated object creation and structured scene composition. Our code is available at https://github.com/sig-pku/aDSL.

Accurate 3D shape abstraction from a single 2D image is a long-standing problem in computer vision and graphics. By leveraging a set of primitives to represent the target shape, recent methods have achieved promising results. However, these methods either use a relatively large number of primitives or lack geometric flexibility due to the limited expressibility of the primitives. In this paper, we propose a novel bi-channel Transformer architecture, integrated with parameterized deformable models, termed DeFormer, to simultaneously estimate the global and local deformations of primitives. In this way, DeFormer can abstract complex object shapes while using a small number of primitives which offer a broader geometry coverage and finer details. Then, we introduce a force-driven dynamic fitting and a cycle-consistent re-projection loss to optimize the primitive parameters. Extensive experiments on ShapeNet across various settings show that DeFormer achieves better reconstruction accuracy over the state-of-the-art, and visualizes with consistent semantic correspondences for improved interpretability.

Ship-form design combines smooth geometric representation, local shape editing, and constraints on the resulting hull. We present the Natural-Language-to-Hull Framework (NL2Hull Framework), which formulates ship-form editing as a typed discrete decision problem and connects language decisions to numerical geometry. Its Constrained Free-Form Deformation Engine (CFFD Engine) represents hull waterlines with non-uniform rational B-splines (NURBS), applies free-form deformation (FFD) to their control points, reconstructs the hull, and checks geometric constraints. We construct the Ship Design Decision Dataset (SDD Dataset) with 134,558 cleaned records and evaluate compared models on its subset Ship Design Decision Benchmark (SDDBench), containing 5,000 records and 43,496 typed questions. We propose Chip, a constrained ship-design decision model for processing natural-language requests. Chip reaches 95.90\% question accuracy and 99.32\% FFD exact match, with a negative log-likelihood of 0.0951, an expected calibration error of 0.0032, and a Brier score of 0.0551. The NL2Hull Framework provides a reproducible interface for evaluating language-based ship-form decisions while identifying the geometry and continuous-control components that require further development. Our code and dataset is available at https://github.com/wenhuahuo/NL2Hull.

Reassembly tasks play a fundamental role in many fields and multiple approaches exist to solve specific reassembly problems. In this context, we posit that a general unified model can effectively address them all, irrespective of the input data type (images, 3D, etc.). We introduce DiffAssemble, a Graph Neural Network (GNN)-based architecture that learns to solve reassembly tasks using a diffusion model formulation. Our method treats the elements of a set, whether pieces of 2D patch or 3D object fragments, as nodes of a spatial graph. Training is performed by introducing noise into the position and rotation of the elements and iteratively denoising them to reconstruct the coherent initial pose. DiffAssemble achieves state-of-the-art (SOTA) results in most 2D and 3D reassembly tasks and is the first learning-based approach that solves 2D puzzles for both rotation and translation. Furthermore, we highlight its remarkable reduction in run-time, performing 11 times faster than the quickest optimization-based method for puzzle solving. Code available at https://github.com/IIT-PAVIS/DiffAssemble