🤖 AI Summary
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.
📝 Abstract
This work develops a framework to create meshes with user-specified homology from potentially dirty geometry by coupling background grids, persistent homology, and a generalization of volume fractions. For a mesh with fixed grid size, the topology of the output mesh changes predictably and monotonically as its volume-fraction threshold decreases. Topological anti-aliasing methods are introduced to resolve pinch points and disconnected regions that are artifacts of user choice of grid size and orientation, making the output meshes suitable for downstream processes including analysis. The methodology is demonstrated on geographical, mechanical, and graphics models in 2D and 3D using a custom-made software called Tusqh. The work demonstrates that the proposed framework is viable for generating meshes on topologically invalid geometries and for automatic defeaturing of small geometric artifacts. Finally, the work shows that although subdividing the background grid frequently improves the topological and geometrical fidelity of the output mesh, there are simple 2D examples for which the topology does not converge under refinement for volume-fraction codes.