基于正多面体的球面三角剖分与分析

计算机工程与应用 ›› 2008, Vol. 44 ›› Issue (9): 16-19.

基于正多面体的球面三角剖分与分析

张胜茂,吴健平,周科松

华东师范大学地理信息科学教育部重点实验室，上海 200062

收稿日期:2007-11-14 修回日期:2007-12-21 出版日期:2008-03-21 发布日期:2008-03-21
通讯作者: 张胜茂

Spherical triangle subdivision and analysis based on polyhedron

ZHANG Sheng-mao,WU Jian-ping,Zhou Ke-song

Key Laboratory of Geo-information Science of the Ministry of Education，East China Normal University，Shanghai 200062，China

Received:2007-11-14 Revised:2007-12-21 Online:2008-03-21 Published:2008-03-21
Contact: ZHANG Sheng-mao

摘要/Abstract

摘要： 球面离散格网模型单元的面积、形状是否相似关系到模型的精度，因此定量分析单元的几何变形、分布规律等是格网模型建模的重要组成部分。文章通过对基于正八面体和正二十面体球面剖分获得的球面三角单元进行分析，分析结果表明随着剖分层次的增加单元面积和形状变化趋于稳定，基于正二十面体的球面剖分与基于正八面体相比有更好的相似性；单元的变形程度与其到正多面体顶点的距离成负相关，而周长和面积变化成正相关；单元各属性比值所占的百分比与剖分层次无关，其较大峰值都分布在正多面体的顶点附近。

关键词: 球面三角剖分, 球面离散格网, 正八面体, 正二十面体

Abstract: Whether the area and the shape of the discrete global grids model units are similar to each other affects the precision of the model.Therefore the quantitative analysis of the unit geometry distorts，distribution rule and so on is one of the important parts in model creating.The paper analyzes the spherical triangle units getting from spherical triangle subdivision based on octahedron and icosahedron.There are some results getting from the analysis.Along with the increasing of the subdivision level，the area and the shape changes of the units tend to stability.The units are more similar getting from spherical triangle subdivision based on octahedron than on icosahedron.The distortion degree of the units is negative correlation to the distance from the unit to the vertex of the polyhedron，but the changes of the perimeter and the area are positive correlation to the distance.The percentage of the unit attribute ratios has nothing to do with the subdivision level.The peak values of the percentage distribute nearby the vertex of the polyhedron.

Key words: spherical triangle subdivision, discrete global grids, octahedron, icosahedron

张胜茂,吴健平,周科松. 基于正多面体的球面三角剖分与分析[J]. 计算机工程与应用, 2008, 44(9): 16-19.

ZHANG Sheng-mao,WU Jian-ping,Zhou Ke-song. Spherical triangle subdivision and analysis based on polyhedron[J]. Computer Engineering and Applications, 2008, 44(9): 16-19.