The method of the map projection according to the normal of the ellipsoidal surface and the sheet join

Abstract

A new map projection according to the normal of ellipsoidal surface is proposed in this paper. In this projection mode, the ellipsoidal surface can be approximated mathematically by a series of continuous secant facets which are all isosceles trapezoids. Every projection plane is just a secant facet projected by two geodetic parallels and two meridians in each coordinate grid, latitude and longitude intervals of which can be determined by the map scale. The projection formulas which can be applied to transform geodetic coordinates of any point on the ellipsoid into rectangular coordinates on the plane are deduced, and the method and formulas of joining four map sheets are also given. The results of the experiment on 1:50000 map sheets indicate that all kinds of projection distortions are very small in each map; the slits between two map sheets are so small that they can be ignored; and coordinates of different map sheets after joining can be used as the spatial measurement.