Reveal

[Piotr]

In future Geocart, Reveal will be added by Daan Strebe. It will generalize the formulas of the projections and apply them to a higher range. This will not be possible if a projection is infinite (as in gnomonic) or generalizing the formulas will cause rolling back to center (as in orthographic).

[daan]

It will generalize the formulas of the projections and apply them to a higher range.

What do you mean by “generalize” in this context? What is a “higher” “range”?

— daan

[Piotr]

It will generalize the formulas of the projections and apply them to a higher range.

What do you mean by “generalize” in this context? What is a “higher” “range”?

— daan

generalize — reapply the formulas on other points

Higher range — higher range of the projection; a setting in Boundaries. GS50 seems to have a graticule crop.

[Piotr]

That might cause glitches in case of GS50, which you said is non–bijective after some point.

[daan]

That might cause glitches in case of GS50, which you said is non–bijective after some point.

It would.

— daan

[Piotr]

It's quite strange that GS50 is perfectly bijective for a small range, then suddenly departs from it at some point.

[daan]

It's quite strange that GS50 is perfectly bijective for a small range, then suddenly departs from it at some point.

That’s common in arbitrary conformal mappings. GS50 uses a 10th-order complex polynomial to approximate an optimal conformal map. It would be surprising if it remained bijective throughout.

— daan

[Piotr]

It's quite strange that GS50 is perfectly bijective for a small range, then suddenly departs from it at some point.

That’s common in arbitrary conformal mappings. GS50 uses a 10th-order complex polynomial to approximate an optimal conformal map. It would be surprising if it remained bijective throughout.

— daan

So, how does it happen that after some point the inverse formula starts diverging from the forwards formula?

[daan]

So, how does it happen that after some point the inverse formula starts diverging from the forwards formula?

That’s not what happens. What happens is that two or more points from the spheroid project onto the same point on the plane.

It’s true that you have to be careful with inverses of some projections: careful to choose the correct root of an equation; otherwise forward and inverse diverge. That problem can happen even if the projection is bijective, but it is solvable. Sometimes it’s pretty hard, though.

— daan

[Piotr]

So, how does it happen that after some point the inverse formula starts diverging from the forwards formula?

That’s not what happens. What happens is that two or more points from the spheroid project onto the same point on the plane.

It’s true that you have to be careful with inverses of some projections: careful to choose the correct root of an equation; otherwise forward and inverse diverge. That problem can happen even if the projection is bijective, but it is solvable. Sometimes it’s pretty hard, though.

— daan

So you're saying that in random conformal projections including GS50 there is one singular point that many coordinates map to. Reveal could attempt to skip that point, trying to render as much of rest of the world as possible.