Minimum-error world map projections defined by polydimensional meshes

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.

RÉSUMÉ

Afin de transformer la surface courbe de la terre en surface plane d'une carte, des distorsions doivent être introduites. Les projections cartographiques conventionnelles sont définies par des formules mathématiques et sont par conséquent limitées dans leur capacité à contrôler ces distorsions par la complexité de ces formules. Les projections de cartes par morceaux basées sur l'interpolation sur des maillages non structurés n'ont pas de telles contraintes et peuvent donc créer des cartes mieux adaptées à de nombreux cas d'utilisation. Une méthode utilisant l'optimisation multidimensionnelle pour optimiser de telles projections cartographiques est présentée ici et illustrée par la génération de plusieurs nouvelles projections cartographiques. Ces projections cartographiques, appelées projections Danseiji, sont présentées ainsi que leurs applications potentielles.

KEYWORDS:

• Map projections
• world maps
• optimization
• minimum-error
• finite element analysis

Acknowledgments

I thank Maximilian Schommer for early conceptual work that lead to this study, and Daniel Strebe and John Savard for providing technical feedback on this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes on contributor

Justin Kunimune (/ʹdƷʌstɪn kunɪˈmuneɪ/) is a nuclear engineering student at the Massachusetts Institute of Technology who recently graduated from the Olin College of Engineering. He is professionally interested in nuclear fusion energy. He is hobbially interested in map projections, constructed languages, and historical cosmological models.

Data availability statement

The source code for this study is openly available on GitHub at https://github.com/jkunimune15/Rubber-Earth/. The data that support the findings of this study are openly available in Mendeley Data at http://doi.org/10.17632/x3zjcdpt7b.1.