Graphical design of world map projections

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. The design of new map projections has up until now required mathematical and carto-graphic expertise that has limited this activity to a small group of specialists. This article introduces the background mathematics for a software-based method that enables cartographers to easily design new small-scale world map projections. The software is usable even by those without mathematical expertise. A new projection is designed interactively in an iterative process that allows the designer to graphically and numerically assess the graticule, the representation of the continents, and the distortion properties of the new projection. The method has been implemented in Flex Projector, a free and open-source application enabling users to quickly create new map projections and modify existing projections. We also introduce new tools that help evaluate the distortion properties of projections, namely a configurable acceptance index to assess areal and angular distortion , a derived acceptance visualization, and interactive profiles through the distortion space of a projection. To illustrate the proposed method, a new projection, the Cropped Ginzburg VIII projection, is presented. 1. Introduction The design of new map projections has hitherto required mathematical and cartographic expertise and has therefore been reserved to a small group of specialists. The method proposed in this article is based on a user-friendly software application called Flex Projector that strives to simplify and to democratize the making of world map projections so that more cartographers will be able to design such projections. Flex Projector lets the author of a projection visually design the graticule and provides specialized tools for distortion analysis, resulting in a new graphical approach to the design of world map projections. World map projections are typically intermediate projections that are neither conformal nor equal-area. While the equal-area property …