Equal-Area Projection for Construction of Rhombic Triacontahedron Grid Systems

WANG Rui; BEN Jin; LIANG Xiaoyu; LIANG Qishuang; TU Zurui

doi:10.13203/j.whugis20220231

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Equal-Area Projection for Construction of Rhombic Triacontahedron Grid Systems

Cartography and GIS | 更新时间：2026-11-05

- Equal-Area Projection for Construction of Rhombic Triacontahedron Grid Systems
- Geomatics and Information Science of Wuhan University Vol. 50, Issue 3, Pages: 579-586(2025)
- 作者机构：
  
  信息工程大学地理空间信息学院,河南郑州，450001
- 作者简介：
- 基金信息：
- DOI：10.13203/j.whugis20220231
  CLC： P208
- Received：28 October 2023，
  
  Published：05 March 2025
- 稿件说明：
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王蕊,贲进,梁晓宇，等.菱形三十面体格网系统构建的等积投影方法研究[J].武汉大学学报（信息科学版）,2025,50(3):579-586.

WANG Rui,BEN Jin,LIANG Xiaoyu,et al.Equal-Area Projection for Construction of Rhombic Triacontahedron Grid Systems[J].Geomatics and Information Science of Wuhan University,2025,50(3):579-586.
王蕊,贲进,梁晓宇，等.菱形三十面体格网系统构建的等积投影方法研究[J].武汉大学学报（信息科学版）,2025,50(3):579-586. DOI：10.13203/j.whugis20220231

WANG Rui,BEN Jin,LIANG Xiaoyu,et al.Equal-Area Projection for Construction of Rhombic Triacontahedron Grid Systems[J].Geomatics and Information Science of Wuhan University,2025,50(3):579-586. DOI：10.13203/j.whugis20220231

摘要

全球离散格网系统（discrete global grid systems，DGGS）是一类新兴的数字地球参考框架，在大尺度多源地理空间数据集的组织、集成与分析方面具有天然优势。现有全球离散格网系统构建方法中，基于多面体投影方法生成的格网系统具有更加优异的几何性质，因而被广泛研究。基础多面体及投影方法是格网系统设计选项中影响格网单元几何性质的主要因素。为构建更加均匀、高效的格网系统，选择菱形三十面体作为基础多面体，推导菱形三十面体与地球球体等积投影的正反算解析公式，并将其应用于3种不同单元形状等积全球离散格网的生成。对比实验结果表明，与二十面体Snyder等积投影相比，所提方法的角度变形减小约51%，且克服了Snyder逆投影迭代求解导致格网生成效率较低的不足，为全球离散格网系统的相关应用提供了优选解决方案。

Abstract

Objectives

Discrete global grid systems (DGGS) are new reference frameworks for digital earth，and are suitable for organization

integration and analysis of multi-source big geospatial datasets. Among the existing construction methods of DGGS

polyhedron projection to sphere can generate DGGS with superior geometric properties and has been widely used. Basic polyhedrons and projection methods are main factors of DGGS design choices with respect to grid cell geometrics. Most existing DGGS schemes choose the platonic solids to approximate the Earth

but the icosahedron achieves the smallest distortion due to the most faces and still has difference with spherical surface.

Methods

This paper chooses rhombic triacontahedron as a new basic polyhedron

and researches its equal-area projection methods. The slice-and-dice approach provides the equal-area mapping between spherical triangles and planar triangles for polyhedral projections

which has different implementations according to the partitioning strategies. The vertex-oriented great circle projection is chosen to realize the equal-area mapping between the surface of rhombic triacontahedron and the sphere because of more uniform angular distortion compared with the Snyder equal-area polyhedral projection. Each diamond face of rhombic triacontahedron is divided into two triangles along the short diagonal as the basic planar triangles for projection. First

according to the equal surface area of rhombic triacontahedron and the sphere

we calculate the edge and angle parameters of rhombic triacontahedron and its corresponding spherical polyhedron. Then

the forward and inverse projection formulas are derived based on the equal-area conditions of the vertex-oriented great circle projection. All procedures are closed form without iterations like the inverse Snyder equal-area polyhedral projection.

Results

Compared with the icosahedron using Snyder equal-area polyhedral projection

the angular distortion caused by the proposed method is reduced by 51%. The mean of angular distortion declines from 0.166 radians to 0.082 radians

and the standard deviation declines from 0.055 to 0.023. The proposed scheme is used to generate three types of global grids with different cell shapes

including triangles

quadrilaterals and the hexagons

which verifies the validity of the proposed scheme. The efficiency of grid generation by the proposed inverse projection of rhombic triacontahedron is about four times that of the icosahedron grids based on the inverse Snyder equal-area projection

which needs iterations.

Conclusions

A new DGGS scheme is proposed by introducing rhombic triacontahedron

which provides a new idea for the development and application of DGGS. The proposed scheme has more angular distortion

which helps to generate more uniform grids and improve the accuracy of subsequent data processing and representation

and can be applied to different cell shapes.

关键词

Keywords

references

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