Weird curves at map boundaries near pole lines when blending

[justlikeoldtimes]

geocart issue.jpg (306.86 KiB) Viewed 15780 times

(I circled the weird points in red.)

As I mentioned in other recent threads on this forum, I'm working on making animated gif transitions between map projections (a weird pet project of mine I had as an idea for years that I finally could pursue now that I finally purchased Geocart), and I've been encountering this quirk occasionally. Usually, I find a workaround.

In the attached image, one is the 17/32 blend between plate carrée and sinosoidal. The other is the 1/16 blend between Eckert V and and sinosoidal. I've seen this issue emerge in other blends with different projections at well, even at basic points like at .5 .

At other points between the those projections, sometimes it pops up and sometimes it doesn't. It's a bit inconsistent. I believe it supposed to look like an obtuse angle corner, without being rounded. I tried to change the blend value from .0625 to .062500001 to see if that could work around the problem, but it didn't help.

Sometimes it seems like it's an issue with the added boundary line itself, other times it looks like a rendering issue that happens before that. I'm willing to try other workarounds as well if you have any ideas, as long as I end with the desired image.

(I'd attach the original .geo3 file itself if I could. It's a relatively small file.)

[Atarimaster]

Yeah, well… regrettably, that is an old bug and as far as I know, there’s no workaround.

[justlikeoldtimes]

Should I keep mentioning quirks I'm encountering with blending? I don't want to be annoying, but I figure it could be worth cataloging.

I blended the orthographic perspective from the North Pole with both the the azimuthal equidistant and equal-area projections just fine (with the southern hemisphere simply being deleted, as I hoped), but when I blended it with the conformal stereographic projection, a hole emerges in the Pacific Ocean.

If I set the center to 0/0, the hole is not visible, but if set the center to the 180th longitude, the hole emerges in the dead center.

[Atarimaster]

My guess is that this is no bug.
The stereographic projection cannot show the entire earth at once, so if you blend it with another projection, there HAS to be an area that is undefined.

[mapnerd2022]

Just like how Arden-Close's arithmetic mean of the Mercator with the cylindrical equal-area still doesn't show the poles just like what happens with the Mercator itself?

[justlikeoldtimes]

But the undefined area should be on the opposite side of the pole. Not just 90 degrees or 0 degrees away, like in the examples I gave, I believe.

[daan]

Sorry about the rough implementation. Because of topological differences between projections as well as the hard problem of the boundary, I don’t really intend for the feature to be used to blend completely arbitrary projection with arbitrary aspects. Geocart allows too much customization, and has too complicated a description grammar for projections to permit that. I’m not convinced I should have released the feature at all, given its warts. Mostly I found it useful for experimentation to design new projections with, and if I liked the results, then I could specifically create the new projection. Obviously that’s not an option for users who are not me.

In summary, the feature is sort of an embarrassment, and I apologize.

— daan

[justlikeoldtimes]

It's fine. I knew I was pushing the limit of the intentions of the software. And I'm still having fun.