Modified perspective cylindrical map projection

Some of the famous cylindrical projections are defined by a geometric process that is based on the perspective. This process can be imagined as a semitransparent sphere wrapped by a tube, secant, or tangent, with the same center; then all features of the sphere surface are projected onto the tube surface by light rays from a source in the equatorial plane. Just by changing the light source’s position and tube’s diameter, different maps can result. In every cylindrical perspective projections, distortions are functions of latitude only, thus, the value of distortion is fixed along a parallel (or a small circle). Therefore, distortion isograms are parallels (or small circles), symmetrical in relation of the equator. Consequently, it is suitable for territories having narrow band shape, extended by the equator (or an oblique equator). The proposed projection in this paper introduces another possible adjustment in cylindrical projections, in which axis of cylinder does not pass through the center of the sphere. This may satisfy case, where territories have a closed curve shape. By comparing the distribution of distortions in other famous perspective cylindrical projections (Lambert, stereographic, and central), with that in the proposed modified perspective cylindrical projection, it was found that distribution of area distortion in the proposed projection can be considered better than others. Therefore, in relation to area representation, the modified perspective cylindrical projection can be considered suitable for mapping regions, having shape close to an ellipse.