Addressing the issues of mismatched data volume and mapping precision in the current Mercator projection plane ge-odesic line plotting methods,as well as the excessive arch height errors in equator-crossing geodesic line plotting,this paper,based on the analysis of the geometric characteristics of geodesic line projection curve on the Mercator projection plane,drawing on the idea of binary search,establishes a model for precise calculation of the equatorial division points of geodesic lines,achie-ving the resolution of these points under any given scale for equator-crossing geodesic lines.By analyzing the changing relation-ship between the tangent azimuth angles of interpolation points and the arch apex,the study constructs a set of search rules for the apex,guided by precise geodetic azimuth angles,thus facilitating rapid calculation of arch height errors for any segment of the projection curve on the Mercator projection plane.Drawing analogy with the Douglas-Peucker algorithm concept,the study adopts permissible cartographic error as threshold for curve simplification,ultimately enabling rapid and precise plotting of geo-desic lines at any given scale.Experimental results demonstrate that this algorithm significantly improves computational effi-ciency and reduces interpolation redundancy.In typical application scenarios,under the strict control of limiting arch height er-ror to not exceed permissible cartographic error,the maximum reduction in the number of interpolation points obtained by this algorithm can reach approximately one-thousandth of existing algorithms,and the computation time can be reduced to approxi-mately one-hundredth.
geodesic line plottingMercator projectionbinary searchDouglas-Peucker algorithmgeodesic theme calculation
万方数据
维普
