Questions regarding blending

[Atarimaster]

Hello,

I know that blending maps will not always work and might produce unexpected results.
So I don’t regard what I’m going to report as a »bug«, I merely wonder what is happening here.

I blended Behrmann equal-area + sinusoidal projection with P = 0.5, and the result looked like this:

blending-result.jpg (103.03 KiB) Viewed 1856 times

Somehow, a boundary line gets drawn right across the map, although the usual boundary lines are there, too.
Can this be explained?

But what puzzled me even more:
From Geocart’s menu, I selected the cylindrical equal-area with standard parallel set to 30°N – which of course is the Behrmann projection – and I blended this one with the sinusoidal (again, with P = 0.5). The result doesn’t have a »clean« boundary line, but there’s no curve across the map.
How is it possible that the results differ when basically the selected projections are the same?

In case that’s helpful, I’ve uploaded an example Geocart file containing the input projections and the results:
blending-example.geo3.zip (1.4 MB approx.)

Kind regards,
and best wishes for 2017,
Tobias

[daan]

Happy New Year, Tobias!

Yes, you have found one of the many problems with the current blending algorithm. It’s really complex. I have put a lot of work into improvements, but I still am not ready to release those yet.

One seemingly simple way for me to improve the algorithm is to recognize when the topology of the two projections is similar, such as blending two pseudocylindric projections. However, because you can customize projections so many ways before even starting the blending, the detection algorithm would have to be congizant of each of those kinds of customizations and methodically confirm none have been applied. Hence, rather than spending a lot of time working on special cases like that, I just want to improve the blending algorithm to always work when it is workable.

Does that makes sense? Sorry for the troubles…

Best for 2017,
— daan

[Piotr]

It's even stranger with Hammer and Briesemeister: The top and bottom are concave and there is an overlap!

[daan]

It's even stranger with Hammer and Briesemeister: The top and bottom are concave and there is an overlap!

That is correct behavior, given the coordinate rotation effects of Briesemeister. However, you can see the effect of a bug in the computation of the boundary.

— daan