mesh quality assessment

This work addresses the common failure of geometric approximation during mesh generation from parametric boundary representation (B-Rep) models, which often corrupts the original topological structure and leads to incorrect adjacency relationships. The paper proposes a topology-first meshing approach that, for the first time, enforces B-Rep topology as a hard constraint at the algorithmic level, rigorously preserving topological invariance throughout the discretization process. Geometric deviation is controlled solely through user-defined tolerances, thereby decoupling topological correctness from geometric approximation. The method produces robust, topologically consistent meshes without requiring post-processing and has been validated on thousands of real-world CAD models—including cases where conventional tools fail—demonstrating significantly improved reliability for downstream applications.

This work addresses the challenge of preserving embedding relationships and ensuring topological-geometric consistency during the discrete evolution of multi-dimensional nested geometries (curves, surfaces, and volumetric domains). To this end, we propose a hierarchical multigrid data structure. Methodologically, our approach integrates an extended half-edge representation, homological mapping constraints, hierarchical correspondence encoding, and adaptive remeshing algorithms—enabling, for the first time, automatic, cross-dimensional topological-geometric co-updating and consistency maintenance of embedded geometries. The framework rigorously preserves boundary embedding relations. Its effectiveness is validated on tasks including UV-seam-aware surface simplification and periodic 2D/3D mesh generation. Furthermore, we extend TetWild with our framework, significantly improving the topological correctness and robustness of embedded volumetric structures.

Existing full-reference 3D mesh quality assessment (MQA) methods struggle to model the complex interplay between geometric structure and texture information, leading to significant discrepancies between predicted scores and human perceptual judgments. To address this, we propose the first hybrid MQA framework that synergistically integrates model-driven and projection-driven paradigms. Our key contributions are: (1) a geometry–texture interaction-aware assessment paradigm; (2) a differentiable rendering mechanism with feature alignment, enabling joint representation of 3D geometry and color textures; and (3) a cross-modal cross-attention module coupled with a multi-scale graph neural network for hierarchical feature fusion. Extensive experiments on multiple benchmark datasets demonstrate that our method consistently outperforms state-of-the-art approaches, achieving over 8% improvement in Spearman rank correlation coefficient (SRCC) and linear correlation coefficient (LCC) against subjective ratings. The source code will be made publicly available.

Existing volumetric fraction field methods fail to robustly generate topologically valid meshes from “dirty geometry” models—those corrupted by noise, topological inconsistencies, or minute geometric features—leading to spurious connectivity and pinching artifacts that violate downstream CAE requirements. Method: We propose a topology-controllable volumetric fraction field framework integrating background mesh embedding, persistent-homology-driven topological analysis, generalized volumetric fraction modeling, and monotonic threshold-based topological control. We introduce “topological anti-aliasing” to eliminate pinching and false connectivity induced by mesh resolution and orientation. Contribution/Results: We construct the first counterexample demonstrating the intrinsic topological non-convergence of conventional volumetric fraction fields under mesh refinement. Implemented in our in-house software Tusqh, the method achieves robust, automatic feature suppression on 2D/3D geographic, mechanical, and graphics models, producing meshes with guaranteed geometric and topological fidelity for CAE and other simulation workflows.

Reconstructing high-quality, manifold, and feature-preserving triangular meshes from unstructured point clouds remains challenging. Method: This paper proposes an isotropic reconstruction method based on unit-sphere covering. It systematically models local point cloud geometry using spherical covering theory, rigorously derives parameter bounds to theoretically guarantee manifold output, and jointly optimizes geometric uniformity (edge-length and angle distributions) and topological correctness. The approach integrates geometric approximation analysis, adaptive neighborhood graph construction, and Delaunay-type triangulation optimization, supporting feature detection and multi-patch remeshing. Results: Experiments show that our method reduces edge-length and angle standard deviations by ~35% compared to Poisson surface reconstruction and Ball-Pivoting, while decreasing average runtime by 45% (1.8× speedup). Under reasonable sampling conditions, the resulting mesh is provably manifold.

This work proposes a novel method for constructing high-quality intrinsic triangulations of closed discrete surfaces without altering their original geometry. By performing local operations—such as edge flips, splits, and collapses—directly on the surface and integrating the continuous Dijkstra algorithm with an A* search acceleration strategy, the approach efficiently computes exact geodesic distances, overcoming the traditional reliance on developable triangles. The method introduces an angle quality criterion based on intrinsic distances and employs a feature-length field to control element sizing, enabling adaptive mesh refinement and coarsening, thereby laying the groundwork for high-order mesh generation. Experiments on nearly 5,000 complex models from the Thingi10K dataset demonstrate that the computational cost of geodesic distance calculation is reduced to approximately 3% of that required by conventional methods.

This work addresses the problem of automatically generating low-distortion, orthogonal quadrilateral surface meshes that satisfy user-specified feature alignment and sizing constraints. The authors propose a novel approach based on integrable orthogonal frame fields, where the symmetry of the frames is implicitly modeled using three-dimensional orthogonally decomposable (odeco) tensors. Within a finite element framework, the method jointly optimizes area and stretch distortion while enforcing shear-free orthogonality constraints. A key contribution is the extension of two-dimensional odeco integrability to three dimensions, coupled with an automatic singularity placement strategy that ensures global integrability without manual intervention or greedy heuristics. Experimental results demonstrate that the method consistently outperforms existing techniques on both smooth surfaces and complex CAD models, achieving significantly reduced mesh distortion under strict sizing control.

This work addresses the challenge of watertight remeshing for meshes with complex topology, single-layer structures, or large missing regions, where existing methods often fail to infer globally consistent inside–outside partitions from local geometry, leading to volume-inconsistent pseudo-watertight reconstructions such as double-shell artifacts. We propose the first approach that rigorously formulates watertight remeshing as a voxel labeling problem, building a binary labeling model over a Delaunay tetrahedralization and achieving globally consistent watertight surface reconstruction through graph-cut energy minimization with one-sided constraints. The method inherently guarantees watertightness, effectively suppresses double-shell artifacts, and eliminates unsupported boundaries via a weighted interface penalty term. Extensive evaluations on CelloScan, CelloFill, and ModelNet10 benchmarks demonstrate significant improvements over state-of-the-art methods, particularly yielding compact and volume-consistent solid reconstructions for complex topologies and single-layer geometries.

Recovering editable, parameterized CAD construction sequences from geometric inputs such as meshes remains a fundamental challenge in design and manufacturing. This work proposes an IoU-driven hybrid optimization framework that, for the first time, formulates the reconstruction problem as structured CAD program optimization. By leveraging geometric feedback, the method iteratively fits and validates a rich set of parametric operations—including fillets and chamfers—within the procedural representation. The approach enables end-to-end image-to-CAD reconstruction across multiple modalities and significantly outperforms existing methods on established benchmarks, achieving superior performance in both volumetric IoU and Chamfer distance metrics. Moreover, it substantially reduces redundancy in the reconstructed programs, enabling efficient and high-fidelity recovery of complex CAD models.