Minimum-error world map projections defined by polydimensional meshes

Abstract

ABSTRACT In order to transform the curved surface of the earth onto the planar surface of a map, some distortion must be introduced. Conventional map projections are defined by mathematical formulas, and are thereby limited in their ability to control that distortion by the complexity of those formulas. Piecewise map projections based on interpolation onto unstructured meshes have no such constraints, and can therefore create maps that are better suited to many use cases. A method using multi-dimensional optimization to optimize such map projections is presented here, and demonstrated by the generation of several new map projections. These map projections are presented as the Danseiji projections, along with their potential applications.