In recent years, encoding explicit mesh surfaces into compact neural representations has emerged as a prominent research direction. Compression ratio and representation accuracy present a fundamental trade-off for evaluating such algorithms. Traditional approaches typically decompose the input mesh into two components: a simplified base mesh and a neural displacement field. However, this paradigm faces inherent limitations. First, employing triangles or quadrilaterals as geometric primitives necessitates the explicit storage of vertex connectivity, incurring substantial memory overhead. Second, existing approaches typically treat base mesh generation as a decoupled preprocessing step, failing to fully leverage automatic differentiation frameworks to optimize the distribution of the base mesh. To address these issues, we propose RTF2Mesh, a method that achieves compact representation using only unstructured point clouds with feature vectors and network parameters. At its core, our approach leverages a meshless vertex-normal representation derived from the Restricted Tangent Face (RTF). Furthermore, we employ the Kolmogorov-Arnold Network (KAN) to encode both the displacement information and the normals of the vertex-normal representation. The KAN is chosen for its superior parameter efficiency compared to traditional Multi-Layer Perceptrons (MLPs). These two improvements enable RTF2Mesh to achieve a more compact neural representation while eliminating the need for explicit storage of vertex connectivity. During decoding, surface normals are reconstructed from the input point cloud using the KAN's learned weights to generate a base surface. The KAN-based network then predicts the displacements of the subdivided base surface, producing a high-resolution triangle mesh. Compared to current state-of-the-art (SOTA) methods, RTF2Mesh achieves highly competitive performance at equivalent compression rates.

The rapid evolution of digital orthodontics has highlighted a critical need for automated treatment planning systems that balance computational efficiency with clinical reliability. However, existing methods still suffer from several limitations, including excessive clinician involvement (accounting for over 35% of treatment planning time), reliance on empirically defined key frames, and limited biomechanical plausibility, particularly in cases of severe dental crowding. This paper proposes a novel collision-free optimization framework to address these issues simultaneously. Our method defines a total movement energy function evaluated over each tooth’s pose at intermediate time frames. This energy is minimized iteratively using a steepest descent strategy. A rollback mechanism is employed: if inter-tooth penetration is detected during an update, the step size is halved repeatedly until collisions are eliminated. The framework allows flexible control over the number of intermediate frames to enforce a strict constraint on per-tooth displacement, limiting it to 0.2 mm translation or 2 ° rotation every 10 to 14 days. Clinical evaluations show that the proposed algorithm can generate desirable and clinically valid tooth movement plans, even in complex cases, while significantly reducing the need for manual intervention.

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach [Garland and Heckbert 1997] prioritizes accuracy and can preserve strong feature lines/points as well, but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) [Du et al. 1999] energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset [Koch et al. 2019], along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding. Please refer to the teaser figure for illustration.