Mercator map - but with a new pole through an equator

[jessy]

I was looking at a Mercator projection today, and tossing up all the usual questions thrown up (as in the famous episode of The West Wing) around proportionality etc.

Has anyone ever seen a Mercator projection drawn where we imagine that the equator goes through the South pole, which is centred (let's assume say, that the equator was therefore the top and bottom of the map, and that the prime meridian was the left and right of the map).

I'm just wondering what this would look like. I'd create it if I had the right mapping software! I'm an Aussie and it would be nice to see stretched locations near the traditional Equator, rather than near the poles.

[Redrobes]

Yes I see what your saying and it would look pretty cool and odd at the same time.

There is an almost equivalent variant where you turn the equator on it side so it goes up and down and this is called a Transverse Mercator Projection and the super popular version of this is the Universal Transverse Mercator or UTM. As you have realized where you have a great equator and terrible poles in a standard Mercator projection, when you then turn it sideways to make it transverse, you have a great vertical line and then left and right of it become terrible. So in the UTM you break the world up into 60 slices of longitude and have a different transverse Mercator for each slice. So then all of your world is projected with high accuracy all over it.

UTM is the preferred projection for the military and high accuracy mapping such as for autonomous vehicles that need to keep on track to a few centimetres instead of the terrible accuracy afforded by a normal Mercator projection.

The massive downside for UTM is that when you transition from one of the 60 zones into the next one its discontinuous. So one place has different coordinates per zone. So the zone is super important for the coordinate. There are other downsides to the UTM zone notation which is barking mad but that's less important.

But what your suggesting is that the poles and one line would have great accuracy and then perhaps somewhere around the USA would be terrible if you chose Aus as being the bit of the world that was on the accurate line. So if you picked one of the UTM zones (such as say 54) that passed through AUS then you would have exactly what you are suggesting. But it would be a Transverse Mercator of a sort.

[Rwhyte]

This site here can give a mini-map view of your question, and all kinds of scenarios, if not a full-fledged map.

(I’d call it) Choose your own Mercator: https://www.jasondavies.com/maps/transition/

It allows you to, choose a map projection and then rotate where it is centered, to view those alternative map distortions and ask what if...? Or, why not this?

And the Pause button can stop the world from spinning out of control, at least, you know, on the website.