An analytical expression for the Natural Earth projection has been developed, which adds additional curvature to the meridians. This new version cannot be altered with Flex Projector, but it is included in Flex Projector as a background projection (use Show Second Projection), and should be used instead of this older version.

Equations and code are available on request. Please contact us: jenny@karto.baug.ethz.ch

The article below mentions that the directions of meridians at poles is 60 degrees. This value has been corrected. The new value is 62.277 degrees. This change was necessary due to a bug in early versions of Flex Projector, which has been fixed in a more recent version. The correction to the angle value was required to avoid any change to the graticule of the A4 projection when loading the parameters with newer versions of Flex Projector.

Article:
Jenny, B., Patterson, T. and Hurni L. (2008). Flex Projector—Interactive software for designing world map projections. Cartographic Perspectives, 59, p. 12–27.
Available at http://jenny.cartography.ch/pdf/2008_Jenny_etal_FlexProjector.pdf