Mesh Simplification Method Based on Implicit Geometric Constraints

Abstract

To address the lack of continuous geometric constraints in traditional quadric error metrics (QEM)-based mesh simplification under high simplification ratios, this paper proposes a 3D mesh simplification method with implicit geometric constraints. First, TetWeave is used to perform implicit modeling on the original high-resolution mesh, from which a continuous implicit reference field is constructed, together with query modules for implicit deviation and implicit normal evaluation at candidate collapse points. Then, within the classical edge-collapse framework, the implicit geometric deviation is introduced as an additional constraint term in a normalized composite cost, while implicit normal consistency is employed as a legality criterion for collapse execution. Finally, experiments on multiple models are conducted to analyze the influence of different weight settings on simplification error and computational cost. The results show that the constructed implicit query module can reliably reflect the geometry of the original continuous surface, and that the normalized implicit constraint has a significant influence on candidate edge ranking and the final Hausdorff distance. With an appropriate weight setting, the proposed method improves the preservation of the original surface geometry, although it also introduces additional computational overhead. The proposed framework provides a feasible way to incorporate continuous implicit geometric supervision into classical edge-collapse simplification.