The Research On The Method And Theory Of A New Map Projection In GIS

A new map projection 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.In this paper, we adopt two projection modes: Sphenoid projection and the projection according to the normal of ellipsoid surface.Sphenoid projection, a projection has more projective centers which are the crossing points intersected by minor axis of the ellipsoid and the parallel planes. The projection formulas, which can conform to the sphenoid projection transforming from the new form of geodetic coordinate to plane rectangular coordinate, are given; according to it, calculation and verification are worked out.The projection formulas which can be applied to transform geodetic coordinates of any point on the ellipsoid into rectangular coordinates on the plane according to the normal of ellipsoid surface are deduced. And the formulas of the length distortion are also given. The results of the experiments on 1:10000 and 1:50000 map sheets which are in the south and north of China indicate that all kinds of projection distortions are very small in each map.The ellipsoidal surface can be perfectly approximated by a series of continuous secant facets, but they are obviously not on the same plane, and the coordinate axes of different map sheets are not parallel. If we put the secant facets on same plane surface, the fissure between two adjacent map sheets is inevitable. In this paper, we will propose a new idea to reduce the influence of fissures. The results indicate that 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.