I had already linked a map, with an interactive changing scale, in which the countries were the correct size, distance apart etc. It was rejected because it had an interactive scale which changes depending on which country you look at. So I presented a map which did not have an interactive scale in the the countries were more to scale which was not interactive.
The only other link I saw you link was Bing maps, which uses the Mercator projection (at least when you zoom out far). The Mercator projection is certainly distorted: https://en.wikipedia.org/wiki/Mercator_projection#Distortion
My definition of undistorted when referring to a map:
1. The map must have countries the correct size (based on the scale of the map. If the map is interactive then the scale of the map will change depending on where you look and your zoom level).
2. Countries should be the correct distance away from each other (based on the scale of the map. If the map is interactive then the scale of the map will change depending on where you look and your zoom level)
3. Countries should be the correct direction relative to each other
4. The map must be able to be used to accurately navigate every country on earth
Bing maps has all of those listed above but was rejected because it has an interactive scale. I've only really done a lot of extensive traveling in North America, South America, and Europe so I can't corroborate the accuracy of #4 in Africa, Asia, and Australia but, based on my sample data, I will assume that you can.
Let me help you out.
1) The first test I'm going to apply to your "undistorted map" is "Can I measure distances between major cities and verify that they match accepted values?" It's simple enough to look up flight times to verify that the distances are at least in the plausible range. I will not consider this map "undistorted" unless a single, static scale can be used to represent these distances.
2) The next test would be to check whether those flights match up with real-world flights at all. For example, if we were to fly from New York to London, the course should take us Eastward over the Atlantic Ocean. If we end up flying West across Canada and Russia along the way, somebody is going to notice.
3) Next up, I'm going to look for pac-manning. Those are situations where you fly off one edge of the map and appear on the other. Like in your most recent attempt, if I fly out of New York across the Atlantic Ocean, I'll fly off the top of the map and then appear again flying down off the top of the map on the left - near Europe.
4) The Bing map shows this effect quite plainly. Perhaps it's more "Defender" than "Pac-Man," but the problem is the same. You should see that on the left and right edges of the map, flying off one edge makes you appear back on the other edge. You can drag-scroll it left/right to move where that boundary is. Place the US right in the middle. Fly East out of NY to London. Fly West out of LA to Tokyo. How do you get from Tokyo to London? Can we fly West off the edge of the map and appear on the right side again?
If you could solve these issues, you'd have REAL progress. If you somehow made that work, we'd next want to check the location and orientations of things.
5) Is the latitude and longitude of each major city correct? These can be verified by the Sun & Stars.
6) Is the relative direction from one city to the next correct?
In short, I want the equivalent of a God's eye view of the flat Earth. A top-down image that looks as if it were a photograph taken from a great distance above the plane.
These are the reasons that you cannot make an undistorted 2D map of a sphere. It's geometrically impossible. You need to cut it somewhere, and most projections stretch it as well.
Both of the maps you have presented so far are massively distorted. They both exhibit cuts (pac-manning) and stretching. Those are distortions.