Zone to zone transformation on the transverse mercator projection

Abstract

. A simple method is presented for transforming the coordinates of a pomt ~e~~ a Transverse M~rcator Zone boundary into its coordinates in the ad.;omzng zone. The poznt is assumed to be within the zone overlap for the.particular grid considered. Worked examples in the Australian Map Grzd (AMG) and the New South Wales Integrated Survey Grid (ISG) are included, togetlzer with a short table to facilitate the use of the method on the latter grid. The Problem When working in a Transverse Mercator projection, it is sometimes necessary to compute the grid coordinates in a particular zone for a point whose coordinates in an adjoining zone are known. There are a number of methods of achieving this. The most obvious one involves conversion of the known coordinates into latitude and longitude, and then converting back to grid coordinates in the adjacent zone. This involves the evaluation of four series expressions, each of several terms, requiring entry into tables of meridian distances and footpoint latitudes. Where the geographical coordinates are not themselves required, a number of direct methods have been proposed. Among these are the use of formulae in Jordan-Eggert 1 and the adaptation of these formulae published by the National Mapping Council of Australia. 2 Both of these methods involve reference to a point which lies exactly on the boundary between the two zones involved. The method presented in this paper is similar in this respect.