Publicação
Utilizing GNNs to predict 3D convex polyhedra from 2D planes
| dc.contributor.advisor | Araújo,Nuno Miguel Azevedo Machado de | |
| dc.contributor.advisor | Pesquita,Cátia Luísa Santana Calisto | |
| dc.contributor.author | Schmitz,Niklas | |
| dc.contributor.institution | Faculty of Sciences | |
| dc.contributor.institution | Department of Informatics | |
| dc.date.accessioned | 2026-04-15T17:30:01Z | |
| dc.date.available | 2026-04-15T17:30:01Z | |
| dc.date.issued | 2026 | |
| dc.description | Tese de mestrado, Ciência de Dados, 2026, Universidade de Lisboa, Faculdade de Ciências | |
| dc.description.abstract | This thesis tackles the folding problem: starting from a 2D template of rigid, hinge-linked faces, pre-dict which face pairs should be adjacent in the final structure, purely topologically, so that the tem-plate closes into a convex 3D polyhedron. The main challenge is the large combinatorial search space, which grows quadratically with face count, making rule-based approaches difficult to scale. This motivates investigating data-driven methods, specifically Graph Neural Networks (GNNs),to assess their suitability for folding. The work constructs a data set pairing polyhedral with their unique 2D unfoldings, spanning 2039 convex polyhedral and about 1.6M unfoldings. Building on this, I present FINE-GNN (Fixed-nodeI Ncremental EdgeGNN), an adapted GNN architecture that per-forms sequential, node-centric edge predictions. At each step, it decides whether and where to add an edge, providing a general architecture for edge prediction on fixed node sets that extends beyond folding. Using this architecture, I inject degree-budget constraints derived from the face’s shape. This simple topological signal cuts false positives, lifts Precision, and enables exact-match recon-structions at lower face counts (predicted adjacency equals ground truth), something prior GNNs fail to achieve. I further study node-ordering policies, which determine the next face to process. While macro metrics (Precision, Recall) differ little, per-graph analyses reveal clear distinctions: Structured policies consistently outperform a random order. The strongest model configuration in this thesis, using constraints with a cyclic order policy, achieves 37.2% Precision overall, with much higher val-ues at lower face counts (78.3% at 6 faces, 61.2% at 7, 47.0% at 8).These results show that GNNs are a promising fit for folding at small to moderate sizes and offer a practical foundation for scaling to larger, more complex polyhedra. To my knowledge, this is the first data-driven study to directly predict face adjacencies for polyhedral folding, establishing a base line for subsequent research. | en |
| dc.format | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/10400.5/118040 | |
| dc.language.iso | eng | |
| dc.subject | GNNs | |
| dc.subject | Sequential prediction | |
| dc.subject | Adjacency Prediction | |
| dc.subject | Polyhedra | |
| dc.subject | 2D-to-3DFolding | |
| dc.title | Utilizing GNNs to predict 3D convex polyhedra from 2D planes | en |
| dc.type | master thesis | |
| dspace.entity.type | Publication | |
| rcaap.rights | openAccess |
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