基于法向量与三角形正则度约束的三维网格简化算法  

3D Mesh Simplification Algorithm Based on Normal Vector and Triangle Regularity Constraints

作　　者：王赛 丁建伟 李汉光 张超 唐建宏 韩军 WANG Sai;DING Jianwei;LI Hanguang;ZHANG Chao;TANG Jianhong;HAN Jun(Institute of Advanced Studies,China University of Geosciences(Wuhan),Wuhan 430074,China;The Second Surveying and Mapping Institute of Hebei Province,Shijiazhuang 050000,China;School of Computer Science,China University of Geosciences(Wuhan),Wuhan 430074,China)

机构地区：[1]中国地质大学(武汉)高等研究院,湖北武汉430074 [2]河北省第二测绘院,河北石家庄050000 [3]中国地质大学(武汉)计算机学院,湖北武汉430074

出　　处：《软件导刊》2024年第12期181-188,共8页Software Guide

基　　金：河北省自然资源科技基金项目(13000024P006CA4104056)。

摘　　要：三维网格简化是计算机图形学中的一项重要技术,广泛应用于虚拟现实、游戏开发和计算机动画等领域。传统的QEM算法虽然在简化过程中能有效降低模型的复杂性,但是在保留重要细节特征方面存在一定的局限性。为解决这一问题,在QEM算法的基础上引入折叠前后三角面法向量夹角的判断,以及三角形正则度作为边折叠的约束条件。这一改进策略旨在确保简化过程中模型的视觉效果保持连续性,并尽量减少狭长三角形的生成。在多个三维模型上进行实验,结果显示,改进后的算法在相同简化率条件下相较传统QEM算法和顶点聚类算法更能有效保留特征点,确保简化前后的视觉效果相近,且改进算法处理后的模型网格与原始模型网格的豪斯多夫距离最小。3D mesh simplification is an important technology in computer graphics,widely used in fields such as virtual reality,game development,and computer animation.Although traditional QEM algorithms can effectively reduce the complexity of models during simplification,they have certain limitations in preserving important details and features.To solve this problem,the QEM algorithm introduces the determination of the angle between the normal vectors of the triangle before and after folding,as well as the regularity of the triangle as a constraint condition for edge folding.This improvement strategy aims to ensure the continuity of the visual effects of the model during the simplification process and minimize the generation of narrow triangles.Experiments were conducted on multiple 3D models,and the results showed that the improved algorithm is more effective in preserving feature points compared to traditional QEM algorithms and vertex clustering algorithms under the same simplification rate conditions,ensuring similar visual effects before and after simplification.Additionally,the improved algorithm minimizes the Hausdorff distance between the processed model mesh and the original model mesh.

关 键 词：网格简化 二次误差度量 法线向量 三角形正则度 边折叠 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]