顾及绝对曲率和面积角度的模型简化算法研究  

Research on model simplification algorithm considering absolute curvature and area angle

作　　者：姜展 李梅 孙超 刘俊材 汪普楠 JIANG Zhan;LI Mei;SUN Chao;LIU Juncai;WANG Punan(Institute of Remote Sensing and Geographical Information System,Peking University,Beijing 100871,China;College of Urban and Environmental Sciences,Peking University,Beijing 100871,China;Remote Sensing Co.,Ltd,Beijing 100076,China)

机构地区：[1]北京大学遥感与地理信息系统研究所,北京100871 [2]北京大学城市与环境学院,北京100871 [3]北京市遥感公司,北京100076

出　　处：《测绘科学》2024年第7期89-96,共8页Science of Surveying and Mapping

基　　金：国家重点研发计划项目(2020YFB1314000,2020YFB1314001)。

摘　　要：针对三维模型简化过程中模型细节特征丢失、简化网格过于均匀、拓扑结构未优化等问题,在QEM二次误差度量的边折叠算法基础上,改进了三维模型的几何网格简化算法:①对三维模型进行预处理,按几何重要程度将顶点分为3类,对重要度高的点予以保留,避免模型缺失重要几何特征;②在传统QEM边折叠算法基础上,引入绝对曲率、局部区域面积和法向量角度三个约束因子计算新的顶点二次误差矩阵;③实现了顾及绝对曲率和面积的三维模型网格简化算法,从而平衡了模型的简化效果和时间复杂度。实验结果表明,在相同简化率条件下,与QEM边折叠算法相比,本文提出的顾及绝对曲率和面积角度的QEM边折叠算法耗时增加率小于6%,与其他算法相比,更能完整地保持模型的细节特征,简化时间也优于虚幻引擎LOD自动生成系统。[结论]与QEM算法相比,算法能够在保证模型细节特征前提下有效减少20%以上的数据量,可用于构建复杂场景中的几何网格简化,提高三维场景加载的流畅性和用户体验。In order to solve the problems such as the loss of details,the inappropriate uniform grid,and the unreasonable topology structure during the process of 3D model simplification,an improved geometric mesh simplification algorithm for 3D mode is proposed based on the edge collapse algorithm of quadratic error measure(QEM).Firstly,the 3D model is preprocessed,and the vertices are classified into 3 groups according to geometric importance.Points with high importance are reserved to avoid missing important geometric features of the model.Secondly,three constraint factors including absolute curvature,local region area and normal vector angle are introduced into QEM edge collapse algorithm to simplify the pretreated 3D model.Finally,the simplification algorithm is redesigned to get a better balance between simplification effect and time consume of 3D model.Experimental result shows that,under the same simplification rate(SR),compared with QEM edge collapse algorithm,our improved algorithm's time increase rate is less than 6%,and the more details of the model can be preserved.The time consume of the improved algorithm is also better than that of automatic LOD generation system in Unreal Engine.Compared with QEM algorithms,more than 20%data of the scene model can be effectively reduced whereas the detail feature are completely reserved.This research can be used for geometric mesh simplification in constructing complex 3D scenes,which would improve the fluency of loading 3D scenes,optimize the performance of computer graphics rendering,and further improve the user experience.

关 键 词：三维模型 网格简化 边折叠 二次误差度量 

分 类 号：P208[天文地球—地图制图学与地理信息工程]