[Marble-devel] Projections

[Henry de Valence]

On Thu September 25 2008 8:50:08 am Torsten Rahn wrote:
> If it's intended to be shipped with Marble by default I think that Winkel
> III would be the best choice among its kind.  Wikipedia says about it:
>
> "Goldberg & Gott show that the Winkel-Tripel is arguably the best overall
> whole-earth map projection known, producing very small distance errors,
> small combinations of ellipticity and area errors, and the smallest
> skewness of any map. [2]
> In 1998, the Winkel Tripel projection replaced the Robinson projection as
> the standard projection for world maps made by the National Geographic
> Society. Many educational institutes and textbooks followed National
> Geographic's example in adopting the projection, and most of those still
> use it." Admittedly I personally find it visually most pleasing but of
> course that just comes as a bonus ;-) .

The problem with Winkel Tripel is that (according to Wikipedia)
"Not surprisingly, a closed form inverse mapping does not exist, and computing 
the inverse numerically is somewhat complicated."

I don't know how complicated "somewhat complicated" is, but unfortunately (as 
opposed to Mollweide) I don't have the detailed description of how it works; 
it is not included in the otherwise-excellent book "Map Projections -- A 
Working Manual" and the Wikipedia page doesn't tell me.

The Mollweide, however, needs to use some other math I don't know ("Newton-
Raphson iterations") so i suppose that's about equal.

Henry