A new algorithm for map projection reverse transformation

There are two common methods for map projection reverse transformation, namely, polynomial fitting method and analytical method of map projection equation. The polynomial fitting method is carried out by least squares fitting based on control points, it is universal but has lower reverse resolutions. The analytical method of map projection equation is carried out by solving map projection equations, it has highprecision in inverse computaion but is verycomplex. The paper provides a new algorithm for map projection reverse transformation, namely, bi-directional iteration reverse algorithm (BDIRA), which integrates the advantages of two methods above, and meets the needs for most types of common map projections. The iteration of this algorithm for most map projections is convergent, so it is universal in some way. Another advantage of BDIRA isthat its reverse errors can be controlled and simple to code in GIS Software developing.