The Data-Optimized Oblique Mercator Projection

Map projections transform the Earth's curved surface into a plane and are thus crucial for mapping and geospatial analysis. However, projections inevitably introduce distortion and the conventional approach is to select a suitable,  predefined map projection for the mapped region. Unfortunately, the available projections are limited in variety and can be difficult to evaluate effectively. We propose an alternative approach: rather than selecting from a predefined set of projections, we introduce an algorithm that optimizes a single projection for a given data set: Data-Optimized Oblique Mercator (DOOM). At its core is the Hotine oblique Mercator projection, featuring a flexible set of adjustable parameters and a universal implementation in GIS platforms and related software. DOOM utilizes the well-established optimization algorithms Levenberg-Marquardt, Adamax, and BFGS, to optimize the projection parameters, minimizing distortion in the mapping of geospatial data. The algorithm supports various objective functions (e.g., L 1 - and L 2 -norms, minmax) and can be extended to incorporate data weighting. The methodology is validated through several case studies, highlighting its adaptability across diverse applications.  Additionally, we introduce a GIS plugin to streamline the use of optimized projection parameters, enhancing accessibility for the geospatial community.