Point2Quad: Generating Quad Meshes from Point Clouds via Face Prediction (2504.19545v1)

Abstract: Quad meshes are essential in geometric modeling and computational mechanics. Although learning-based methods for triangle mesh demonstrate considerable advancements, quad mesh generation remains less explored due to the challenge of ensuring coplanarity, convexity, and quad-only meshes. In this paper, we present Point2Quad, the first learning-based method for quad-only mesh generation from point clouds. The key idea is learning to identify quad mesh with fused pointwise and facewise features. Specifically, Point2Quad begins with a k-NN-based candidate generation considering the coplanarity and squareness. Then, two encoders are followed to extract geometric and topological features that address the challenge of quad-related constraints, especially by combining in-depth quadrilaterals-specific characteristics. Subsequently, the extracted features are fused to train the classifier with a designed compound loss. The final results are derived after the refinement by a quad-specific post-processing. Extensive experiments on both clear and noise data demonstrate the effectiveness and superiority of Point2Quad, compared to baseline methods under comprehensive metrics.

• The paper introduces Point2Quad, the first learning-based approach for generating quad-only meshes directly from point clouds, addressing limitations of prior methods.
• Point2Quad models quad meshing as face prediction, using dual neural encoders to leverage geometric and topological features for accurate quadrilateral element generation.
• Experiments demonstrate Point2Quad surpasses existing methods in surface accuracy, mesh quality, and noise robustness with competitive efficiency.

Overview of "Point2Quad: Generating Quad Meshes from Point Clouds via Face Prediction"

The paper introduces Point2Quad, the first learning-based approach specifically focused on generating quad-only meshes directly from point clouds. Unlike prior methods primarily concerned with triangle mesh reconstruction, this approach addresses the challenge of quadrilateral mesh generation through a deep learning framework, leveraging both pointwise and facewise features to ensure coplanarity, convexity, and exclusivity of quadrilateral elements.

Problem Formulation and Methodology

Quad meshes are highly relevant in several computational fields due to their advantages in reducing approximation errors and element counts. Despite significant advancements in triangle mesh generation, quad mesh methods remain less explored. This gap is attributed to the additional constraints quadratic elements impose, including maintaining both convex and coplanar states, which are not inherently ensured, unlike their triangular counterparts.

Point2Quad innovatively models quad meshing as a face prediction task. It begins by constructing a k-nearest neighbor (k-NN) graph for each point, generating candidate faces based on coplanarity and geometric symmetry. In tackling the combinatorial problem intrinsic to mesh generation, the system utilizes dual neural encoders to encode geometric and topological features from the point cloud and candidate faces, subsequently filtered by a face classifier.

The model's architecture is strategically designed to capture and integrate multiple features. The geometric encoder captures pointwise spatial features, while the face encoder identifies facewise relational and topological attributes. These extracted features form the input for the classifier, trained with a compound loss function combining classification and face-quality objectives. This loss function aids in managing data imbalances and potential mesh inconsistencies prevalent in quad mesh generation.

Experimentation and Results

The authors conducted extensive experiments to validate Point2Quad's performance, benchmarking against existing methods like Instant-Meshes and IER. The results show that Point2Quad outperforms its peers, offering superior surface fitting accuracy and mesh quality, robustly maintaining high-scale Jacobian values, and minimal edge deviation. The method's efficiency is also highlighted by its competitive execution time despite the complex nature of quad-only mesh generation.

Noise robustness tests further demonstrate Point2Quad's resilience, where it shows minimal performance degradation compared to notable drops by previous methods when noise is introduced. This robustness can potentially benefit applications in real-world environments where point cloud data often involves noise.

Implications and Future Directions

The practical implications of Point2Quad are significant for fields requiring accurate and efficient surface representation, including computational mechanics, geometric modeling, and CAD/CAM applications. Its capabilities in noise handling, high topological accuracy, and surface fitting provide a robust foundation for more advanced and large-scale modeling tasks.

Theoretically, Point2Quad's framework can be a stepping stone for further advances in neural network applications for more complex mesh generations, including adaptive and hierarchical meshing. As the research community continues exploring AI-driven solutions, the integration of Point2Quad's methodologies can facilitate new algorithms addressing more varied and topologically challenging datasets.

Future work may include enhancements focusing on even tighter integration of geometric learning, exploring adaptive neural architectures, refining loss functions for better convergence in highly noisy environments, or extending the framework to mixed-element meshes that combine quads and triangles for versatile modeling applications.