Abstract
<title>Abstract</title> <p>Learning on triangular meshes shows strong promise for 3D shape classification and segmentation, yet many mesh neural networks rely on edge- or vertex-centric features without an explicit, sign-aware notion of face orientation. This can cause ambiguity between convex and concave structures and can weaken generalization under structural perturbations such as cutting and open boundaries. We propose an orientation-aware mesh learning representation that encodes local face orientation as a single signed scalar. Specifically, we define a signed half-dihedral scalar at the edge--face level that captures both the direction and magnitude of local orientation while remaining invariant to translation, rotation, and scale. The scalar is integrated into a MeshCNN-style pipeline as an additional edge--face orientation feature, enabling existing edge-centric architectures to access sign-aware face information. On the SHREC benchmark, the proposed method achieves 99.5\% classification accuracy, showing competitive performance on closed meshes compared with recent mesh-based learning methods. More importantly, under cutting, rotation, and positional variation, it retains 93.33\% accuracy, indicating improved robustness under structural perturbations where conventional unsigned or edge-centric representations degrade. Ablation experiments further show that the proposed orientation scalar is complementary to shape descriptors. These results suggest that the main benefit of the proposed representation lies in its ability to preserve explicit local orientation cues under incomplete or perturbed mesh conditions. Overall, the proposed signed scalar provides a compact and interpretable representation-level extension for robust mesh learning.</p>