A new method for coordinate transformation between conformal map projections

Geospatial Information System (GIS) has emerged as a very powerful tool for capturing, storing, analyzing, managing, and presenting data that is linked to location. The location information, which is usually obtained from existing maps or the Global Positioning Systems (GPS), refers to different coordinate and map projection systems. Therefore, unification of the coordinate and mapping systems of the spatial information is absolutely necessary before any data processing in a GIS system.
In the classical approach, coordinate transformation among different map projection systems is performed via the reference geodetic ellipsoids. The transformation is possible if the reference ellipsoids and their corresponding datum definition parameters are known. In many cases, implementation of the classical approach is impossible due to lack of information.
Herein, we introduce an innovative approach for coordinate transformation which is completely datum-independent. It is based on the mathematical relationship between the coordinate systems. From mathematical point of view, two functions mathematically define the relationship between the horizontal coordinates in two systems. For simplicity, two polynomial functions are employed. The optimal degree of the polynomials and the unknown coefficients can be determined using the common points in two systems.
In this paper, the proposed method is theoretically developed for conformal map projections. The Cauchy-Riemann differential equations as a necessary and sufficient conformity condition are used to derive the mapping polynomials. Moreover, the validity of the new method is numerically checked on a real data set. Both the classical and the new method are employed on the data set. The achieved results show very good agreement between the classical and the new approach.