Function matching for Soviet-era table-based modified polyconic projections

Some map projections are defined by table values rather than mathematical equations. The most popular and famous one in this category is the Robinson Projection. The Ginzburg projections, which were developed and used in the former Soviet Union, are among the other table-based world projections. A computational method is required in order to efficiently use these kinds of projections in Geographic Information Systems (GIS) and similar environments. Function matching for projections based on table values can be realized for a numerical forward transformation. Matched functions also allow the calculation of distortions in the projection easily. In this study, polynomials and radial basis functions, such as multiquadric and thin-plate spline functions, are applied to derive an analytical expression from an array of tabular coordinates. The tests are realized on three table-based polyconic projections, the Ginzburg IV, V and VI. The distortion characteristics of table-based projections are sought by using partial derivatives obtained through numerical approximation. The distortion analysis shows that the Ginzburg V has very reasonable distortions. A solution for the inverse transformation of these projections is also provided. With the awareness of such projections, more alternatives in seeking a suitable map projection in world-scale GIS applications can be proposed.