Generalized Wagner, Parameters dialog

[Atarimaster]

Hello,

I noticed that there’s a wrong label in the Projection Parameters dialog for the generalized Wagner.
The label for the third parameter says:

0 << m ≤ 1


However, m is allowed to be greater than 1 (in terms of Wagner’s formula) and Geocart rightfully accepts corresponding input values here, e.g.

a = 3.12875, b = 1.45578, m = 1.17645, m₂ = 0.559864, n = 0.333333


For equal-area projections, m ≤ 1 applies, but not if you want to render a compromise projection.

Kind regards,
Tobias

[daan]

Thanks. It’s fixed locally and will come out in the next release.

— daan

[Atarimaster]

You’re welcome.

btw, I’ve tried to determine the real upper limit for m.
It seems to me that it isn’t a fixed value – the max value of m seems to depend on the value of m₂. Is this observation correct?

Kind regards,
Tobias

[daan]

I’ve tried to determine the real upper limit for m. It seems to me that it isn’t a fixed value – the max value of m seems to depend on the value of m₂. Is this observation correct?

Yes. Here’s one constraint:
–1 ≤ m sin (m₂ φ) ≤ 1

with φ being the latitude. But there is another, more complicated constraint on top of that that depends on, well, basically everything.


Best,
— daan

[Atarimaster]

But there is another, more complicated constraint on top of that that depends on, well, basically everything.

Thank you!
I was actually hoping for an answer like this, because…
Well, for some time now, I’m able to convert the "Böhm notation" for Wagner variants (e.g. 65-60-60-20-200 for Wagner VIII) to the numerical values that are used in the formula and by Geocart (a = 2.811481, b = 1.308153, m = 0.921166, m₂ = 0.885502, n = 0.333333 for Wagner VIII), but recently I’ve been working on a way to do this conversion the other way round. In the course of that, I noticed that there are cases that won’t render a map although each individual value of a, b, m, m₂ and n is within the allowed range.

So now I know that this is prefectly normal.

Kind regards,
Tobias