Reveal

[daan]

Would such a map be in infinitely many pieces?

My guess is finite, and not a huge number of sections, but I really don’t know. I do know that some of the sections would be huge.

— daan

[Piotr]

I do know that some of the sections would be huge.

— daan

Do you know that because you have tested it? What is the source code?

[Piotr]

What would a complete world map in GS50, with all sides of overlapping sections, look like? I suppose this is what Reveal would do to reveal GS50.

[daan]

Do you know that because you have tested it? What is the source code?

I know because I experimented with it a long time ago and have experimented with many conformal projections constructed via complex polynomials.

Snyder shows what happens if you render even a little ways outside of the useful boundaries. Notice the lower right corner, and notice the abrupt bend in the lower parallel toward the west edge that results in a large expansion of that region.

GS50, slightly expanded perimeter

IMG_0275.jpg (62.7 KiB) Viewed 17870 times

He writes,

It should be stressed that most transformations resulting from the use of [these equations] can only be used within a limited range, depending on the number and value of coefficients. As the distance from the projection center increases, meridians, parallels, and shorelines begin to exhibit loops, overlapping, and other undesirable curves. A world map using the GS50 projection is nearly illegible, with the meridians and parallels intertwined like wild vines.

— daan

[Piotr]

He writes,

It should be stressed that most transformations resulting from the use of [these equations] can only be used within a limited range, depending on the number and value of coefficients. As the distance from the projection center increases, meridians, parallels, and shorelines begin to exhibit loops, overlapping, and other undesirable curves. A world map using the GS50 projection is nearly illegible, with the meridians and parallels intertwined like wild vines.

— daan

What if you instead took the overlapping sections and separated them (for example, in Orthographic, the world would be in 2 pieces), so the map is in multiple pieces? What would that look like?

What if you instead used an interruption scheme to render the world?

What is the exact boundary of bijectivity?

Also, someone came up with this map: https://www.dreamstime.com/world-map-mo ... e168674780