Mesh Simplification Method Based on Fast Retrieval and Region-Preserving Quadric Error Metrics

This article explores an optimization method for lightweight 3D models by implementing mesh simplification through the Enhanced Quadratic Error Metric (QEM) algorithm. In response to the common problems of feature loss and geometric structure anomalies in the QEM algorithm, this study introduces surface density, vertex curvature, vertex distance, and boundary folding cost as simplification factors. These factors precisely control the folding cost of the edges, effectively preserving model features and maintaining the integrity of the geometric structure. In addition, the principle of KD tree is utilized to accelerate the search for effective point pairs, thereby reducing the complexity of the algorithm and improving processing efficiency. Experimental verification shows that the proposed improved QEM algorithm not only maintains high detail features, but also reduces the Hausdorff distance by at least $\mathbf{8 4. 9 5 \%}$ compared to the original QEM algorithm. Therefore, this algorithm provides a more efficient and reliable solution for lightweight 3D models.