椭球面三角形外心的地图代数解法

doi:10.11947/j.AGCS.2016.20140503

测绘学报 ›› 2016, Vol. 45 ›› Issue (2): 241-249.doi: 10.11947/j.AGCS.2016.20140503

椭球面三角形外心的地图代数解法

蒋会平^{1 3 4}, 谭树东², 胡海¹

1. 武汉大学资源与环境科学学院, 湖北武汉 430079;
2. 国家海洋信息中心, 天津 300171;
3. 中国科学院地理科学与资源研究所资源与环境信息系统国家重点实验室, 北京 100101;
4. 中国科学院大学, 北京 100049

收稿日期:2014-10-14 修回日期:2015-08-10 出版日期:2016-02-20 发布日期:2016-02-29
通讯作者: 胡海,E-mail: huhai@whu.edu.cn E-mail:huhai@whu.edu.cn
作者简介:蒋会平(1990-),男,硕士生,主要研究方向为地图代数、椭球空间分析以及全球性地理信息系统。
基金资助:
国家自然科学基金 (41271443;41471328);国家863计划 (2009AA12Z224)

Determination of Circumcenter of Triangle on Ellipsoidal Surface Based on Map Algebra

JIANG Huiping^{1 3 4}, TAN Shudong², HU Hai¹

1. School of Resources and Environment Sciences, Wuhan University, Wuhan 430079, China;
2. National Marine Data and Information Service, Tianjin 300171, China;
3. State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China;
4. University of Chinese Academy of Sciences, Beijing 100049, China

Received:2014-10-14 Revised:2015-08-10 Online:2016-02-20 Published:2016-02-29
Supported by:
The National Natural Science Foundation of China (Nos. 41271443;41471328);The National High-tech Research and Development Program of China (863 Program) (No. 2009AA12Z224)

摘要/Abstract

摘要： 椭球面三角形外心到3个相邻顶点的大地线距离都相等。面向椭球面空间的外心大地坐标的求解对于椭球面Voronoi图的生成和椭球面Delaunay三角网的构造具有重要作用。利用基于地图代数理论的矢栅结合方法,首先基于地图代数测地变换建立高精度椭球面空间距离场,再通过边界跟踪配对确定外心所在的栅格范围,最后通过数值计算内插生成初始等距点并不断逼近外心的精确大地坐标。试验结果表明,采用本文方法求解的椭球面三角形外心大地坐标,在10³～10⁴ km跨度内其定位误差小于0.001 m,且算法非常适用于海量空间数据的高精度快速计算。

关键词: 地图代数, 测地变换, 椭球面, 三角形外心, 矢栅结合

Abstract: The geodesic distances from the circumcenter to 3 vertexes of the triangle on ellipsoidal surface are equal. The ellipsoid-oriented determination of circumcenter of triangle on ellipsoidal surface is applicable when it comes to generation of the Voronoi diagram and construction of the Delaunay triangulation net on the ellipsoidal earth, which can be considered as a solution of significance in computation of geometries and spatial analysis on the ellipsoid. Based on the idea of combining the raster and vector methods and the theory of map algebra, the working process can be described as below: firstly, initiate the geographical distance transformation and create the distance field with a high degree of accuracy; secondly, conduct boundary tracking and matching and then determinate the range of grids where the circumcenter of triangle locates; thirdly, interpolate the initial equidistant point; finally, approximate the circumcenter of triangle on earth ellipsoidal surface by means of numeric calculation. The positioning error of this algorithm is controlled less than 0.001 m within several thousand kilometers range of span. As regards the method proposed in the present paper, its computational efficiency is O(m) where m is the number of pixels in the image, i.e., grid resolution. In conclusion, this algorithm can be considered as both ellipsoid-oriented and not content-related, which is especially appropriate for complex geocomputation globally.

Key words: map algebra, geographical distance transformation, ellipsoidal surface, circumcenter of triangle, raster&vector-based

中图分类号:

P208

蒋会平, 谭树东, 胡海. 椭球面三角形外心的地图代数解法[J]. 测绘学报, 2016, 45(2): 241-249.

JIANG Huiping, TAN Shudong, HU Hai. Determination of Circumcenter of Triangle on Ellipsoidal Surface Based on Map Algebra[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(2): 241-249.

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椭球面三角形外心的地图代数解法

Determination of Circumcenter of Triangle on Ellipsoidal Surface Based on Map Algebra

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