Acta Geodaetica et Cartographica Sinica ›› 2016, Vol. 45 ›› Issue (2): 241-249.doi: 10.11947/j.AGCS.2016.20140503

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

JIANG Huiping1 3 4, TAN Shudong2, HU Hai1   

  1. 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)

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

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