The Theory Of Digital Elevation Model In The New Geodetic Coordinate System On The Ellipsoidal Surface

Currently, DEM is based on the projection plane adding elevation information. The DEM through this way does not really describe the 3D information, because the plane coordinate and the elevation are not uniform. On the other hand, the earth is an irregular ellipsoid, the projection must bring distortion from ellipsoid surface to plane. In the small area, the level plane is approximately plane, but the level plane is not regarded as the plane in the large area.In the paper, author introduces a new geodetic coordinate system. The longitude curve and the latitude curve are the coordinate curve in the new geodetic coordinate system with length as coordinate parameter. The DEM in the new geodetic coordinate system on the ellipsoidal surface is different from the DEM in the projection plane. The work of projection from the ellipsoidal surface is not done, which avoids the projection distortion. This coordinate system is adapted to put together the different area maps and construct DEM in large area.Considering the advantages of TIN, TIN can obtain the better precision through the less points, TIN can attain good effect in the complex terrain area, and TIN has the better topology data structure. In the paper, DEM is constructed through the way of constructing Delaunay triangulation on the ellipsoidal surface.There are a lot of differences between the DEM in the new geodetic coordinate system and the DEM on the projection plane. Some new ways are used, for example the determination of geodesic coordinate of center for geodetic circle which passes through three top points of a triangle on the ellipsoidal surface, the arithmetic of the point of intersection of two curves on the ellipsoidal surface, the arithmetic of the triangle area on the ellipsoid. The author deduced the formula about these ways and tested the formula. In the theories, author used the arithmetic of inserting point by point to constructed Delaunay triangulations and used Visual C++ and OpenGL to displayed the 3D digital model.