Organizations: State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou, 310058, Zhejiang, People’s Republic of China · School of Media and Design, Hangzhou Dianzi University, Hangzhou, 310001, Zhejiang, People’s Republic of China
Assembly modeling plays an important role in constructing product models, yet it is still mainly performed via interactive operations that are experience-dependent and labor-intensive. Data-driven strategies hold promise for automating this process; however, existing approaches either predict poses that cannot directly generate editable B-Rep assembly constraints or require prescribed part pairs or predefined assembly faces. To reduce the large candidate space of constraint prediction without predefined assembly faces, we propose a data-driven framework based on assembly feature mate prediction. The framework performs automatic assembly modeling from unassembled B-Rep parts, using assembly features to group the geometric entities of local mating interfaces and restrict candidate formation. Given the lack of suitable assembly feature annotations in existing datasets, we construct a large-scale dataset through an automatic annotation pipeline. Using the annotated dataset, we train an attention-based network to predict assembly feature mates, with Engineering Compatibility Fusion (ECF) incorporating explicit engineering compatibility into learned matching scores. To improve the accuracy of automatic assembly modeling, we use assembly feature patterns (AFPs) to guide the matching process. Finally, a post-processing search selects assembly feature mate and AFP mate candidates, whose associated constraints are generated and solved to complete assembly modeling. Experimental results show that the framework achieves assembly constraint accuracies of 74.79% on the six-assembly comparison set and 64.09% on the extended test set of 16 assemblies, which includes the comparison set. With ground-truth face labels supplied as additional input, the corresponding accuracies increase to 81.78% and 80.93%, respectively.
Figures & tables
Figure 1: Illustration of a complementary assembly constraint group and an isolated assembly constraint candidate. The orange and purple highlights distinguish the pair of geometric entities involved in each specific geometric constraint. Constraint 1, a coaxial constraint, and constraint 2, a plane-coincidence constraint, collectively define the feasible assembly result shown at the upper left. In contrast, constraint k is an isolated plane-coincidence constraint and cannot by itself constitute a candidate for the intended assembly relation, which requires a group of complementary constraints. The upper-right view shows the corresponding incorrect result, with red highlighting the geometric interference between the parts. Such complementary grouping, which characterizes the vast majority of assembly constraints, motivates our assembly feature concept.
Figure 2: Illustration of assembly feature and assembly feature mate (highlighted in yellow). The assembly feature mate consists of a shaft feature (left) and a hole feature (right), each comprising a cylindrical face and a planar face. Together, they constitute an assembly feature mate, indicating that the shaft should be inserted into the hole.
Figure 3: Illustration of assembly feature patterns and an AFP mate. Left: the highlighted AFPs on the two parts each consist of six hole features arranged in a circle. The AFP mate relates the two patterns through a layout-consistent feature correspondence. Right: the assembled configuration.
Figure 4: Overall architecture of the proposed approach. The framework consists of a training stage (top gray box) and an assembly modeling stage (bottom flow). The part encoder is first pretrained through part mate prediction and then frozen during assembly feature mate prediction training. During assembly modeling, the encoder provides part embeddings as context for assembly feature mate prediction, which also uses the extracted assembly feature candidates. Coplanar feature groups enter the AFP recognition and mate candidate generation module, which uses parametric matching for canonical AFP hypotheses and metric-consistency search for groups that cannot be assigned a canonical layout type. Both paths output AFP mate candidates. The assembly constraint generator uses the scored assembly feature mate candidates and AFP mate candidates to select assembly relations and instantiate assembly constraints. The geometric constraint solver processes these constraints to obtain the assembly configuration.
Figure 5: Illustration of missing and incorrect assembly constraints in assembly models. The orange and purple highlights indicate the geometric entities referenced by the assembly constraints. (a) Missing assembly constraints: The two parts are assembled using two coaxial assembly constraints and a plane-coincidence assembly constraint. The fasteners of four holes are omitted, leaving coaxially aligned holes in the simplified assembly. Moreover, since the three given assembly constraints have already fully restricted the degrees of freedom, no assembly constraint is annotated on the other two holes (red circle). (b) Incorrect assembly constraint entity: To align the pin, the user selected the external cylindrical surface (highlighted in purple) instead of the mechanically correct inner bore. While this selection shares the same axis and satisfies the geometric constraint solver, it misrepresents the physical semantics of the assembly.
Figure 6: The automatic annotation pipeline.
Figure 7: Part encoder pretraining through part mate prediction.
Figure 8: Framework of assembly feature mate prediction. The attention-based feature mate predictor estimates learned matching scores, and ECF combines them with cross-part eligibility and type-conditioned dimensional compatibility to obtain compatibility-adjusted assembly feature mate candidate scores.
Type
Component
Dim.
Content / Description
All
Part ID ( idp )
1
Hash of the part’s identifier.
Type ID ( idt )
1
Integer for feature type.
Hole/Shaft
Feature Body (Total 19 dims)
Cylinder Params ( fcyl )
8
Concatenation of radius, axis, origin, and sense: (r,vaxis,porg,s) .
Plane Params ( fpl )
6
Concatenation of normal and origin: (vnorm,porg) .
Padding
5
Zero-padding to reach the total length.
Table 1: Composition of the 21-dimensional assembly feature vector ( f ) for hole and shaft features.
Method
ACCc↑
ACCℓ↑
ACCv↑
JoinABLe [ 6 ]
24.00%
0.00%
61.29%
Vergez et al.’s greedy [ 7 ]
16.15%
0.00%
70.99%
Vergez et al.’s Best-First [ 7 ]
72.94%
32.86%
81.81%
Ours w/o pattern
38.93%
7.69%
83.93%
Ours (gt face input)
81.78 %
65.38 %
100 %
Ours
74.79%
34.61%
92.86%
Table 2: Quantitative comparison of automatic assembly approaches.
Figure 9: Qualitative comparison on the assembly comparison set. The top section (colored models) shows the baseline results for JoinABLe [ 6 ] and Vergez et al. [ 7 ] , as reported in [ 7 ] . The bottom section (gray models) shows the results of our method on the six corresponding original assemblies.
Method
ACCc
ACCℓ
ACCv
Ours w/o pattern
31.77%
9.68%
56.74%
Ours (gt face input)
80.93%
65.48%
100%
Ours
64.09%
32.14%
82.27%
Table 3: Quantitative results on the extended test set of 16 assemblies.
Figure 10: Qualitative results on the ten additional assemblies in the extended test set.
Evaluation Setting
Assembly Feature Mate Accuracy ( ACCf )
Drop (points)
Ours (Full Model)
76.27%
-
w/o Engineering Compatibility Fusion (ECF)
55.79%
20.48
Table 4: Assembly feature mate prediction accuracy ( ACCf ) on the extended test set of 16 assemblies. The model without ECF is retrained and evaluated with ECF removed.
Assembly outcome
Ours
Ours (gt face input)
Completely correct
0% (0/16)
56.25% (9/16)
Relations of at most two parts require correction
31.25% (5/16)
68.75% (11/16)
Table 5: Assembly-level results based on manual inspection of the extended test set. Correcting a part means revising its assembly relations. The second row includes completely correct assemblies.
Figure 11: Examples of multi-solution ambiguity. Left: the two colored handles illustrate alternative mounting directions for the same handle, which can be inserted into the through hole from either side. Right: similar hole and shaft interfaces permit different ways of connecting the links in a multi-link assembly. In each example, only one configuration corresponds to the ground-truth assembly: the mounting direction shown by the red handle on the left and the rightmost toy bear configuration on the right.
Figure 12: Examples illustrating limitations of the assembly feature representation. Left: the highlighted cylindrical face and planar face belong to different parts and jointly form a shaft feature after assembly. Right: the highlighted cylindrical faces participate in an isolated coaxial constraint; the double-headed arrow indicates relative motion along the common axis.
Parametric CAD modeling represents 3D designs as editable, constraint-driven construction histories and develops methods to generate, reconstruct, and revise them.
We present Linkify, a framework for learning from interface-augmented assembly graphs to enable context-aware part retrieval in mechanical assemblies. While recent generative AI methods for CAD have focused largely on isolated parts or monolithic assemblies, the rich geometric information at the interfaces between parts, where function is realized, remains underexplored. We address this gap by recomputing high-fidelity interface geometry for the Fusion 360 Gallery Assembly dataset, correcting missing and erroneous contacts, and generating point-cloud representations of local contact regions. Using this data, we construct assembly graphs whose nodes encode part geometry and whose edges encode interface geometry via a pretrained point-cloud encoder. On top of this representation, we train a Graph Attention Network based on GATv2 to solve a masked part prediction task: given an assembly with one part held out, the model predicts the class of the missing component from a large vocabulary of geometrically clustered parts, thereby approximating a realistic part-retrieval scenario. Compared to non-graph baselines such as logistic regression and k-nearest neighbors operating on aggregated node features, Linkify achieves higher Top-K accuracy and F1 scores. Ablation studies on graph connectivity, edge attributes, and attention mechanisms demonstrate that accurate contact computation and dynamic attention over interfaces are critical for performance. Our corrected interface dataset and training pipeline, released publicly, provide a foundation for future interface-aware models for assembly retrieval, validation, and generative design.
Anushrut Jignasu, Daniele Grandi
Iowa State University, USA · Autodesk Research, USA
Most existing 3D assembly methods treat the problem as pure pose estimation, rearranging observed parts via rigid transformations. In contrast, human assembly naturally couples structural reasoning with holistic shape inference. Inspired by this intuition, we reformulate 3D assembly as a joint problem of assembly and generation. We show that these two processes are mutually reinforcing: assembly provides part-level structural priors for generation, while generation injects holistic shape context that resolves ambiguities in assembly. Unlike prior methods that cannot synthesize missing geometry, we propose CRAG, which simultaneously generates plausible complete shapes and predicts poses for input parts. Extensive experiments demonstrate state-of-the-art performance across in-the-wild objects with diverse geometries, varying part counts, and missing pieces. Project Page: https://ai4ce.github.io/CRAG/
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.
Danrui Li, Jiahao Zhang, Bernhard Egger +4
Rutgers, The State University of New Jersey, USA · The Australian National University, Australia · Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany +1