Efficient 3D Model Simplification Algorithms Based on OpenMP

Han Chang (), Sanhe Wan (), Jingyu Ni, Yidan Fan, Xiangxue Zhang and Yuxuan Xiong
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Han Chang: School of Human Settlement and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Sanhe Wan: Wales College, Lanzhou University, Lanzhou 730000, China
Jingyu Ni: Wales College, Lanzhou University, Lanzhou 730000, China
Yidan Fan: Wales College, Lanzhou University, Lanzhou 730000, China
Xiangxue Zhang: Wales College, Lanzhou University, Lanzhou 730000, China
Yuxuan Xiong: Wales College, Lanzhou University, Lanzhou 730000, China

Mathematics, 2025, vol. 13, issue 19, 1-18

Abstract: Efficient simplification of 3D models is essential for mobile and other resource-constrained application scenarios. Industrial 3D assemblies, typically composed of numerous components and dense triangular meshes, often pose significant challenges in rendering and transmission due to their large scale and high complexity. The Quadric Error Metrics (QEM) algorithm offers a practical balance between simplification accuracy and computational efficiency. However, its application to large-scale industrial models remain limited by performance bottlenecks, especially when combined with curvature-based optimization techniques that improve fidelity at the cost of increased computation. Therefore, this paper presents a parallel implementation of the QEM algorithm and its curvature-optimized variant using the OpenMP framework. By identifying key bottlenecks in the serial workflow, this research parallelizes critical processes such as curvature estimation, error metric computation, and data structure manipulation. Experiments on large industrial assembly models at a simplification ratio of 0.3, 0.5, and 0.7 demonstrate that the proposed parallel algorithms achieve significant speedups, with a maximum observed speedup of 5.5×, while maintaining geometric quality and topological consistency. The proposed approach significantly improves model processing efficiency, particularly for medium- to large-scale industrial models, and provides a scalable and practical solution for real-time loading and interaction in engineering applications.

Keywords: 3D model simplification algorithm; Quadric Error Metrics (QEM); parallel calculation (OpenMP); industrial assembly simplification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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