Two-Round Optimization Algorithm Based on Quadric Error Metrics

Abstract

Triangular mesh models are widely used for 3D model displays, but large models can cause slow loading and transmission, especially on mobile or web platforms. The quadric error metrics (QEM) algorithm is known for its efficient simplification and effectiveness. Nevertheless, it lacks clear prioritization for folding flat areas within the model, leaving room for improvement. This paper reproduces the work of Zhang Yun et al., finding that while their method reduces simplification errors, it increases the folding time of flat areas. The study improves the QEM algorithm by combining the angle and area of the first-order neighboring triangles of the edge, resulting in faster simplification but higher errors, making it less versatile. To address these issues, a two-round simplification method is proposed. The first round simplifies planar areas, and the second focuses on the entire model. Compared to the recursive algorithm, the two-round method showcases shorter simplification times, particularly evident when the wall.obj exhibits a lower simplification ratio. For simplification rates below 40%, it reduces the average simplification time by 22.77% and yields better model accuracy than the QEM algorithm. On bunny_norm.obj, the simplification error is smaller than with the QEM algorithm, showcasing an average error reduction of 21.82%. Visually, the two-round proposed algorithm retains more detailed features and has better visual effects. However, because of the lower computational efficiency of the two-round simplification, future research directions may involve parallel computing and GPU utilization for acceleration.

Keywords

• Quadric error metrics
• two-round proposed algorithm
• first-order neighborhood triangle area
• approximate curvature