Reveal

[daan]

So you're saying that in random conformal projections including GS50 there is one singular point that many coordinates map to.

No, it’s whole regions that overlap.

— daan

[Piotr]

So you're saying that in random conformal projections including GS50 there is one singular point that many coordinates map to.

No, it’s whole regions that overlap.

— daan

You formerly said "What happens is that two or more points from the spheroid project onto the same point on the plane.", as in a singularity.

[daan]

That’s because I was talking about what happens at the level of individual coordinates. Now spread that phenomenon out across regions.

— daan

[Piotr]

That’s because I was talking about what happens at the level of individual coordinates. Now spread that phenomenon out across regions.

— daan

So, you're saying that there are so many non-conformal singularities that the bijectivity gets lost and the projection is no longer reliable beyond an uncomputable range.

[daan]

So, you're saying that there are so many non-conformal singularities that the bijectivity gets lost and the projection is no longer reliable beyond an uncomputable range.

No, they are not singularities. The projection is still conformal. It just overlaps itself, somewhat analogous to orthographic’s back hemisphere, but not nearly so orderly.

— daan

[Piotr]

So, you're saying that there are so many non-conformal singularities that the bijectivity gets lost and the projection is no longer reliable beyond an uncomputable range.

No, they are not singularities. The projection is still conformal. It just overlaps itself, somewhat analogous to orthographic’s back hemisphere, but not nearly so orderly.

— daan

Isn't back hemisphere only in Hammer retroazimuthal projection?

So you're saying GS50 would be conformal for the entire world, as long as it's printed in multiple sections?

[daan]

Isn't back hemisphere only in Hammer retroazimuthal projection?

Hammer retroazimuthal is the only one I have implemented. The back hemisphere differs from the front, so there isn’t any other way to arrive at it. Orthographic back hemisphere is trivial and can be arrived at via Geocart’s UI as a transformation of the front.

— daan

[Piotr]

If the non-bijective errors aren't singularities, GS50 would be conformal for the entire world, as long as it's printed in multiple sections, right?

[daan]

If the non-bijective errors aren't singularities, GS50 would be conformal for the entire world, as long as it's printed in multiple sections, right?

Mostly right, but I’m not sure the entire range is finite. The inflation goes crazy in most places away from the center. Some portions shrink toward nothingness as well.

— daan

[Piotr]

If the non-bijective errors aren't singularities, GS50 would be conformal for the entire world, as long as it's printed in multiple sections, right?

Mostly right, but I’m not sure the entire range is finite. The inflation goes crazy in most places away from the center. Some portions shrink toward nothingness as well.

— daan

Would such a map be in infinitely many pieces?